Choice of activation gate - Carnegie Mellon School of ...lwehbe/10701_S19/files/Lecture_10.pdf ·...

10
10-701 Introduction to Machine Learning (PhD) Lecture 10: SVMs Leila Wehbe Carnegie Mellon University Machine Learning Department Slides based on on Tom Mitchell’s 10-701 Spring 2016 material and Andrew Ng’s lecture notes at: http://cs229.stanford.edu/notes/cs229-notes3.pdf Neural Networks Choice of activation gate Linear Can be used to predict continuous values at output. What happens when you stay linear layers? Choice of activation gate Sigmoid Outputs between 0 and 1, can be used for probability Can saturate when very low or very high weights Contributes to vanishing gradient

Transcript of Choice of activation gate - Carnegie Mellon School of ...lwehbe/10701_S19/files/Lecture_10.pdf ·...

Page 1: Choice of activation gate - Carnegie Mellon School of ...lwehbe/10701_S19/files/Lecture_10.pdf · 10-701 Introduction to Machine Learning (PhD) Lecture 10: SVMs Leila Wehbe Carnegie

10-701 Introduction to Machine Learning (PhD) Lecture 10: SVMs

Leila Wehbe Carnegie Mellon University

Machine Learning Department

Slides based on on Tom Mitchell’s 10-701 Spring 2016 material

and Andrew Ng’s lecture notes at: http://cs229.stanford.edu/notes/cs229-notes3.pdf

Neural Networks

Choice of activation gate

Linear

Can be used to predict continuous values at output. What happens when you stay linear layers?

Choice of activation gate

Sigmoid

Outputs between 0 and 1, can be used for probability Can saturate when very low or very high weights Contributes to vanishing gradient

Page 2: Choice of activation gate - Carnegie Mellon School of ...lwehbe/10701_S19/files/Lecture_10.pdf · 10-701 Introduction to Machine Learning (PhD) Lecture 10: SVMs Leila Wehbe Carnegie

Choice of activation gate

Sigmoid

Outputs between 0 and 1, can be used for probability Can saturate Contributes to vanishing gradient

f’(x)

Choice of activation gate

tanh

Range -1 to 1

Choice of activation gate

Rectified Linear Unit (ReLu)

Solve the vanishing gradient problem, but have a problem that nodes might die when negative value and never update. Can fix with leaky ReLu

Choice of activation gate

Softmax

Page 3: Choice of activation gate - Carnegie Mellon School of ...lwehbe/10701_S19/files/Lecture_10.pdf · 10-701 Introduction to Machine Learning (PhD) Lecture 10: SVMs Leila Wehbe Carnegie

Choice of activation gate

Maxpool

Choice of loss function

MSE

L2

Choice of loss function

Binary cross-entropy

Multiclass:

Choice of loss function

Binary cross-entropy

Doesn’t have saturation problem

Page 4: Choice of activation gate - Carnegie Mellon School of ...lwehbe/10701_S19/files/Lecture_10.pdf · 10-701 Introduction to Machine Learning (PhD) Lecture 10: SVMs Leila Wehbe Carnegie

Deep Networks

Deep networks: informal term for more recent generation of neural nets, with features such as: • more hidden layers • built from more heterogenous units

– sigmoid, rectilinear, max pooling, LSTM, … • shared weights across units (convolutional) • with application-specific network architecture

– time series, computer vision, speech recognition, ... – recurrent networks, max-pooled convolutional layers with

local receptive fields... • bi-directional units • pretrained on unlabelled data (auto-encoders) • ...

Impact of Deep Learning

• Speech Recognition

• Computer Vision

• Language Understanding

• Recommender Systems

• Drug Discovery and Medical Image Analysis

[Courtesy of R. Salakhutdinov]

Training Networks on Time Series• Suppose we want to predict next state of world

– and it depends on history of unknown length – e.g., robot with forward-facing sensors trying to predict next

sensor reading as it moves and turns – e.g., anticipate the next word in the sentence

Recurrent Networks: Time Series• Suppose we want to predict next state of world

– and it depends on history of unknown length – e.g., robot with forward-facing sensors trying to predict next

sensor reading as it moves and turns

• Idea: use hidden layer in network to capture/remember state history

context/history

Page 5: Choice of activation gate - Carnegie Mellon School of ...lwehbe/10701_S19/files/Lecture_10.pdf · 10-701 Introduction to Machine Learning (PhD) Lecture 10: SVMs Leila Wehbe Carnegie

Recurrent Networks on Time Series Long-Short Term Memory (LSTM) Units• Threshold unit/subnetwork with memory

– still trainable with gradient descent

LSTM-g unit from [Monner & Regia, 2013]

Convolutional Neural Nets for Image Recognition

• specialized architecture: mix different types of units, not completely connected, motivated by primate visual cortex

• many shared parameters, stochastic gradient training • very successful! now many specialized architectures for

vision, speech, translation, …

[Le Cun, 1992]Simple box blur

By Utkarsh Sinha from: http://aishack.in/tutorials/image-convolution-examples/

Gaussian blur

Horizontal lines

Page 6: Choice of activation gate - Carnegie Mellon School of ...lwehbe/10701_S19/files/Lecture_10.pdf · 10-701 Introduction to Machine Learning (PhD) Lecture 10: SVMs Leila Wehbe Carnegie

By Utkarsh Sinha from: http://aishack.in/tutorials/image-convolution-examples/

Edge detection

Filters learned from data [Le Cun, 1992]

See http://cs231n.github.io/understanding-cnn/ And this article on distill.pub: https://distill.pub/2018/building-blocks/

Feature Representations: Traditionally

Image vision features Recognition

Object detection

Audio classification

Audio audio featuresSpeaker

identification

Data Feature extraction

Learning algorithm

[Courtesy of R. Salakhutdinov]

Computer Vision Features

SIFT

HoG RIFT

Textons

GIST

[Courtesy, R. Salakhutdinov]

Page 7: Choice of activation gate - Carnegie Mellon School of ...lwehbe/10701_S19/files/Lecture_10.pdf · 10-701 Introduction to Machine Learning (PhD) Lecture 10: SVMs Leila Wehbe Carnegie

ZCR

Spectrogram MFCC

RolloffFlux

Audio Features

[Courtesy, R. Salakhutdinov]ZCR

Spectrogram MFCC

RolloffFlux

Representation Learning: Can we automatically learn these representations?

Audio Features

[Courtesy, R. Salakhutdinov]

SVMs

Find a linear separator with the largest margin

+ ++ +

+

--

-

-

-

Page 8: Choice of activation gate - Carnegie Mellon School of ...lwehbe/10701_S19/files/Lecture_10.pdf · 10-701 Introduction to Machine Learning (PhD) Lecture 10: SVMs Leila Wehbe Carnegie

Find a linear separator with the largest margin

+ ++ +

+

--

-

-

-hxi,wi+ b = 0

<latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit><latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit><latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit><latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit>

Find a linear separator with the largest margin

+ ++ +

+

--

-

-

-hxi,wi+ b = 0

<latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit><latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit><latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit><latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit>

hxi,wi+ b > 0<latexit sha1_base64="HkOAn7XedBZPyCApEl40X4Qhjow=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYlBTcuK9gLNCFMppN26GQSZiZqCX0HN76KGxeKuHXjzrdxmnahrQcGPv7/HM6cP0g4U9q2v62FxaXlldXCWnF9Y3Nru7Sz21RxKgltkJjHsh1gRTkTtKGZ5rSdSIqjgNNWMLga+607KhWLxa0eJtSLcE+wkBGsjeSXjl2ORY9TlLlBiB5GPjvN6X6EXDlx0AkK0CWy/VLZrth5oXlwplCGadX90pfbjUkaUaEJx0p1HDvRXoalZoTTUdFNFU0wGeAe7RgUOKLKy/KbRujQKF0UxtI8oVGu/p7IcKTUMApMZ4R1X816Y/E/r5PqsOplTCSppoJMFoUpRzpG44BQl0lKNB8awEQy81dE+lhiok2MRROCM3vyPDTPKo5dcW7Oy7XqNI4C7MMBHIEDF1CDa6hDAwg8wjO8wpv1ZL1Y79bHpHXBms7swZ+yPn8AzzScHw==</latexit><latexit sha1_base64="HkOAn7XedBZPyCApEl40X4Qhjow=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYlBTcuK9gLNCFMppN26GQSZiZqCX0HN76KGxeKuHXjzrdxmnahrQcGPv7/HM6cP0g4U9q2v62FxaXlldXCWnF9Y3Nru7Sz21RxKgltkJjHsh1gRTkTtKGZ5rSdSIqjgNNWMLga+607KhWLxa0eJtSLcE+wkBGsjeSXjl2ORY9TlLlBiB5GPjvN6X6EXDlx0AkK0CWy/VLZrth5oXlwplCGadX90pfbjUkaUaEJx0p1HDvRXoalZoTTUdFNFU0wGeAe7RgUOKLKy/KbRujQKF0UxtI8oVGu/p7IcKTUMApMZ4R1X816Y/E/r5PqsOplTCSppoJMFoUpRzpG44BQl0lKNB8awEQy81dE+lhiok2MRROCM3vyPDTPKo5dcW7Oy7XqNI4C7MMBHIEDF1CDa6hDAwg8wjO8wpv1ZL1Y79bHpHXBms7swZ+yPn8AzzScHw==</latexit><latexit sha1_base64="HkOAn7XedBZPyCApEl40X4Qhjow=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYlBTcuK9gLNCFMppN26GQSZiZqCX0HN76KGxeKuHXjzrdxmnahrQcGPv7/HM6cP0g4U9q2v62FxaXlldXCWnF9Y3Nru7Sz21RxKgltkJjHsh1gRTkTtKGZ5rSdSIqjgNNWMLga+607KhWLxa0eJtSLcE+wkBGsjeSXjl2ORY9TlLlBiB5GPjvN6X6EXDlx0AkK0CWy/VLZrth5oXlwplCGadX90pfbjUkaUaEJx0p1HDvRXoalZoTTUdFNFU0wGeAe7RgUOKLKy/KbRujQKF0UxtI8oVGu/p7IcKTUMApMZ4R1X816Y/E/r5PqsOplTCSppoJMFoUpRzpG44BQl0lKNB8awEQy81dE+lhiok2MRROCM3vyPDTPKo5dcW7Oy7XqNI4C7MMBHIEDF1CDa6hDAwg8wjO8wpv1ZL1Y79bHpHXBms7swZ+yPn8AzzScHw==</latexit><latexit sha1_base64="HkOAn7XedBZPyCApEl40X4Qhjow=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYlBTcuK9gLNCFMppN26GQSZiZqCX0HN76KGxeKuHXjzrdxmnahrQcGPv7/HM6cP0g4U9q2v62FxaXlldXCWnF9Y3Nru7Sz21RxKgltkJjHsh1gRTkTtKGZ5rSdSIqjgNNWMLga+607KhWLxa0eJtSLcE+wkBGsjeSXjl2ORY9TlLlBiB5GPjvN6X6EXDlx0AkK0CWy/VLZrth5oXlwplCGadX90pfbjUkaUaEJx0p1HDvRXoalZoTTUdFNFU0wGeAe7RgUOKLKy/KbRujQKF0UxtI8oVGu/p7IcKTUMApMZ4R1X816Y/E/r5PqsOplTCSppoJMFoUpRzpG44BQl0lKNB8awEQy81dE+lhiok2MRROCM3vyPDTPKo5dcW7Oy7XqNI4C7MMBHIEDF1CDa6hDAwg8wjO8wpv1ZL1Y79bHpHXBms7swZ+yPn8AzzScHw==</latexit>

hxi,wi+ b < 0<latexit sha1_base64="QfQKruCMAKVHheOIkgKeSiYcX58=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHbhouDGZQV7gSaEyXTSDp1MwsxELaHv4MZXceNCEbdu3Pk2TtMutPXAwMf/n8OZ8wcJZ0rb9re1sLi0vLJaWCuub2xubZd2dpsqTiWhDRLzWLYDrChngjY005y2E0lxFHDaCgZXY791R6VisbjVw4R6Ee4JFjKCtZH80rHLsehxijI3CNHDyGenOd2PkCsnDjpBAbpEtl8q2xU7LzQPzhTKMK26X/pyuzFJIyo04VipjmMn2suw1IxwOiq6qaIJJgPcox2DAkdUeVl+0wgdGqWLwliaJzTK1d8TGY6UGkaB6Yyw7qtZbyz+53VSHVa9jIkk1VSQyaIw5UjHaBwQ6jJJieZDA5hIZv6KSB9LTLSJsWhCcGZPnofmWcWxK87NeblWncZRgH04gCNw4AJqcA11aACBR3iGV3iznqwX6936mLQuWNOZPfhT1ucPzCicHQ==</latexit><latexit sha1_base64="QfQKruCMAKVHheOIkgKeSiYcX58=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHbhouDGZQV7gSaEyXTSDp1MwsxELaHv4MZXceNCEbdu3Pk2TtMutPXAwMf/n8OZ8wcJZ0rb9re1sLi0vLJaWCuub2xubZd2dpsqTiWhDRLzWLYDrChngjY005y2E0lxFHDaCgZXY791R6VisbjVw4R6Ee4JFjKCtZH80rHLsehxijI3CNHDyGenOd2PkCsnDjpBAbpEtl8q2xU7LzQPzhTKMK26X/pyuzFJIyo04VipjmMn2suw1IxwOiq6qaIJJgPcox2DAkdUeVl+0wgdGqWLwliaJzTK1d8TGY6UGkaB6Yyw7qtZbyz+53VSHVa9jIkk1VSQyaIw5UjHaBwQ6jJJieZDA5hIZv6KSB9LTLSJsWhCcGZPnofmWcWxK87NeblWncZRgH04gCNw4AJqcA11aACBR3iGV3iznqwX6936mLQuWNOZPfhT1ucPzCicHQ==</latexit><latexit sha1_base64="QfQKruCMAKVHheOIkgKeSiYcX58=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHbhouDGZQV7gSaEyXTSDp1MwsxELaHv4MZXceNCEbdu3Pk2TtMutPXAwMf/n8OZ8wcJZ0rb9re1sLi0vLJaWCuub2xubZd2dpsqTiWhDRLzWLYDrChngjY005y2E0lxFHDaCgZXY791R6VisbjVw4R6Ee4JFjKCtZH80rHLsehxijI3CNHDyGenOd2PkCsnDjpBAbpEtl8q2xU7LzQPzhTKMK26X/pyuzFJIyo04VipjmMn2suw1IxwOiq6qaIJJgPcox2DAkdUeVl+0wgdGqWLwliaJzTK1d8TGY6UGkaB6Yyw7qtZbyz+53VSHVa9jIkk1VSQyaIw5UjHaBwQ6jJJieZDA5hIZv6KSB9LTLSJsWhCcGZPnofmWcWxK87NeblWncZRgH04gCNw4AJqcA11aACBR3iGV3iznqwX6936mLQuWNOZPfhT1ucPzCicHQ==</latexit><latexit sha1_base64="QfQKruCMAKVHheOIkgKeSiYcX58=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHbhouDGZQV7gSaEyXTSDp1MwsxELaHv4MZXceNCEbdu3Pk2TtMutPXAwMf/n8OZ8wcJZ0rb9re1sLi0vLJaWCuub2xubZd2dpsqTiWhDRLzWLYDrChngjY005y2E0lxFHDaCgZXY791R6VisbjVw4R6Ee4JFjKCtZH80rHLsehxijI3CNHDyGenOd2PkCsnDjpBAbpEtl8q2xU7LzQPzhTKMK26X/pyuzFJIyo04VipjmMn2suw1IxwOiq6qaIJJgPcox2DAkdUeVl+0wgdGqWLwliaJzTK1d8TGY6UGkaB6Yyw7qtZbyz+53VSHVa9jIkk1VSQyaIw5UjHaBwQ6jJJieZDA5hIZv6KSB9LTLSJsWhCcGZPnofmWcWxK87NeblWncZRgH04gCNw4AJqcA11aACBR3iGV3iznqwX6936mLQuWNOZPfhT1ucPzCicHQ==</latexit>

Find a linear separator with the largest margin

+ ++ +

+

--

-

-

-hxi,wi+ b = 0

<latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit><latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit><latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit><latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit>

Linearly separable

hx+,wi+ b = C<latexit sha1_base64="4TM6X2tQ9iKQjLs+o0wdejzaPy8=">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</latexit><latexit sha1_base64="4TM6X2tQ9iKQjLs+o0wdejzaPy8=">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</latexit><latexit sha1_base64="4TM6X2tQ9iKQjLs+o0wdejzaPy8=">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</latexit><latexit sha1_base64="4TM6X2tQ9iKQjLs+o0wdejzaPy8=">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</latexit>

hx�,wi+ b = �C<latexit sha1_base64="OfY396hsxup1hLvEaR7w4xm+Ya8=">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</latexit><latexit sha1_base64="OfY396hsxup1hLvEaR7w4xm+Ya8=">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</latexit><latexit sha1_base64="OfY396hsxup1hLvEaR7w4xm+Ya8=">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</latexit><latexit sha1_base64="OfY396hsxup1hLvEaR7w4xm+Ya8=">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</latexit> hxi,wi+ b < �C

<latexit sha1_base64="IVRVnKaQ3chPiKcTSUamvHSwr7w=">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</latexit><latexit sha1_base64="IVRVnKaQ3chPiKcTSUamvHSwr7w=">AAACFXicdZDNSgMxFIUz/tb6V3Xp5mIRBLUkRbSCi4IblwpWhU4pmTRTg5nMkGTUMvQl3Pgqblwo4lZw59uYaSuo6IXAxzn3cnNPkEhhLMYf3tj4xOTUdGGmODs3v7BYWlo+M3GqGW+wWMb6IqCGS6F4wwor+UWiOY0Cyc+Dq8PcP7/m2ohYndpewlsR7SoRCkatk9qlLV9S1ZUcMj8I4bbfFlsDuumDr4cObEIAB7ANh+1SGVcwxoQQyIHs7WIH+/u1KqkByS1XZTSq43bp3e/ELI24skxSY5oEJ7aVUW0Fk7xf9FPDE8quaJc3HSoacdPKBlf1Yd0pHQhj7Z6yMFC/T2Q0MqYXBa4zovbS/PZy8S+vmdqw1sqESlLLFRsuClMJNoY8IugIzZmVPQeUaeH+CuySasqsC7LoQvi6FP6Hs2qF4Ao52SnXa6M4CmgVraENRNAeqqMjdIwaiKE79ICe0LN37z16L97rsHXMG82soB/lvX0CETKcxw==</latexit><latexit sha1_base64="IVRVnKaQ3chPiKcTSUamvHSwr7w=">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</latexit><latexit sha1_base64="IVRVnKaQ3chPiKcTSUamvHSwr7w=">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</latexit>

hxi,wi+ b > C<latexit sha1_base64="UL7NI8AeIiyGz4ZNUGU2CE2pXNE=">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</latexit><latexit sha1_base64="UL7NI8AeIiyGz4ZNUGU2CE2pXNE=">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</latexit><latexit sha1_base64="UL7NI8AeIiyGz4ZNUGU2CE2pXNE=">AAACE3icdVBNS8NAEN34WetX1aOXwSKISklqaetFCr14rGCr0JSy2W7q0s0m7G7UEvofvPhXvHhQxKsXb/4bN20FFX0w8Hhvhpl5XsSZ0rb9Yc3Mzs0vLGaWsssrq2vruY3NlgpjSWiThDyUlx5WlDNBm5ppTi8jSXHgcXrhDeqpf3FNpWKhONfDiHYC3BfMZwRrI3Vz+y7Hos8pJK7nw+2oyw7H7GYErpw4cAAenEC9m8vbheNquVgqg12w7YpTdFJSrJSOSuAYJUUeTdHo5t7dXkjigApNOFaq7diR7iRYakY4HWXdWNEIkwHu07ahAgdUdZLxTyPYNUoP/FCaEhrG6veJBAdKDQPPdAZYX6nfXir+5bVj7Vc7CRNRrKkgk0V+zEGHkAYEPSYp0XxoCCaSmVuBXGGJiTYxZk0IX5/C/6RVLDh2wTkr5WvVaRwZtI120B5yUAXV0ClqoCYi6A49oCf0bN1bj9aL9TppnbGmM1voB6y3T0wenHQ=</latexit><latexit sha1_base64="UL7NI8AeIiyGz4ZNUGU2CE2pXNE=">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</latexit>

Find a linear separator with the largest margin

+ ++ +

+

--

-

-

-hxi,wi+ b = 0

<latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit><latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit><latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit><latexit sha1_base64="H0OuGTbahqPB3MNNyZy2RUfQvCg=">AAACE3icbZDLSsNAFIZPvNZ6q7p0M1gEUSmJCHYjFNy4rGAv0IQwmU7aoZNJmJmoJfQd3Pgqblwo4taNO9/GadqFth4Y+Pj/czhz/iDhTGnb/rYWFpeWV1YLa8X1jc2t7dLOblPFqSS0QWIey3aAFeVM0IZmmtN2IimOAk5bweBq7LfuqFQsFrd6mFAvwj3BQkawNpJfOnY5Fj1OUeYGIXoY+ew0p/sRcuXEQScoQJfI9ktlu2LnhebBmUIZplX3S19uNyZpRIUmHCvVcexEexmWmhFOR0U3VTTBZIB7tGNQ4IgqL8tvGqFDo3RRGEvzhEa5+nsiw5FSwygwnRHWfTXrjcX/vE6qw6qXMZGkmgoyWRSmHOkYjQNCXSYp0XxoABPJzF8R6WOJiTYxFk0IzuzJ89A8qzh2xbk5L9eq0zgKsA8HcAQOXEANrqEODSDwCM/wCm/Wk/VivVsfk9YFazqzB3/K+vwBza6cHg==</latexit>

Linearly separable

hxi,wi+ b < �1<latexit sha1_base64="IJYjPS8aaRyR+w9VP1UYrl+Ir2k=">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</latexit><latexit sha1_base64="IJYjPS8aaRyR+w9VP1UYrl+Ir2k=">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</latexit><latexit sha1_base64="IJYjPS8aaRyR+w9VP1UYrl+Ir2k=">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</latexit><latexit sha1_base64="IJYjPS8aaRyR+w9VP1UYrl+Ir2k=">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</latexit>

hx�,wi+ b = �1<latexit sha1_base64="Pi17ndKVV6eOuXJdpm26+xo3nuM=">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</latexit><latexit sha1_base64="Pi17ndKVV6eOuXJdpm26+xo3nuM=">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</latexit><latexit sha1_base64="Pi17ndKVV6eOuXJdpm26+xo3nuM=">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</latexit><latexit sha1_base64="Pi17ndKVV6eOuXJdpm26+xo3nuM=">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</latexit>

hx+,wi+ b = 1<latexit sha1_base64="IJfAXZHY7lo+2z6igom8IyV2OIs=">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</latexit><latexit sha1_base64="IJfAXZHY7lo+2z6igom8IyV2OIs=">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</latexit><latexit sha1_base64="IJfAXZHY7lo+2z6igom8IyV2OIs=">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</latexit><latexit sha1_base64="IJfAXZHY7lo+2z6igom8IyV2OIs=">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</latexit>

hxi,wi+ b > 1<latexit sha1_base64="DaHeCJ++ddp1GaQVkmyxFjdZJMU=">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</latexit><latexit sha1_base64="DaHeCJ++ddp1GaQVkmyxFjdZJMU=">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</latexit><latexit sha1_base64="DaHeCJ++ddp1GaQVkmyxFjdZJMU=">AAACE3icdVBNS8NAEN3U7/pV9ehlsAiiUpJYbL1IwYvHClaFppTNdtMu3WzC7kYtof/Bi3/FiwdFvHrx5r9x01ZQ0QcDj/dmmJnnx5wpbdsfVm5qemZ2bn4hv7i0vLJaWFu/UFEiCW2QiEfyyseKciZoQzPN6VUsKQ59Ti/9/knmX15TqVgkzvUgpq0QdwULGMHaSO3Crsex6HIKqecHcDtss/0RuxmCJ8cO7IEPx+C0C0W7dFQ9dMuHYJdsu+K4TkbcSvmgDI5RMhTRBPV24d3rRCQJqdCEY6Wajh3rVoqlZoTTYd5LFI0x6eMubRoqcEhVKx39NIRto3QgiKQpoWGkfp9IcajUIPRNZ4h1T/32MvEvr5nooNpKmYgTTQUZLwoSDjqCLCDoMEmJ5gNDMJHM3AqkhyUm2sSYNyF8fQr/kwu35Ngl56xcrFUnccyjTbSFdpCDKqiGTlEdNRBBd+gBPaFn6956tF6s13FrzprMbKAfsN4+ATDWnGI=</latexit><latexit sha1_base64="DaHeCJ++ddp1GaQVkmyxFjdZJMU=">AAACE3icdVBNS8NAEN3U7/pV9ehlsAiiUpJYbL1IwYvHClaFppTNdtMu3WzC7kYtof/Bi3/FiwdFvHrx5r9x01ZQ0QcDj/dmmJnnx5wpbdsfVm5qemZ2bn4hv7i0vLJaWFu/UFEiCW2QiEfyyseKciZoQzPN6VUsKQ59Ti/9/knmX15TqVgkzvUgpq0QdwULGMHaSO3Crsex6HIKqecHcDtss/0RuxmCJ8cO7IEPx+C0C0W7dFQ9dMuHYJdsu+K4TkbcSvmgDI5RMhTRBPV24d3rRCQJqdCEY6Wajh3rVoqlZoTTYd5LFI0x6eMubRoqcEhVKx39NIRto3QgiKQpoWGkfp9IcajUIPRNZ4h1T/32MvEvr5nooNpKmYgTTQUZLwoSDjqCLCDoMEmJ5gNDMJHM3AqkhyUm2sSYNyF8fQr/kwu35Ngl56xcrFUnccyjTbSFdpCDKqiGTlEdNRBBd+gBPaFn6956tF6s13FrzprMbKAfsN4+ATDWnGI=</latexit>

Set C = 1

Page 9: Choice of activation gate - Carnegie Mellon School of ...lwehbe/10701_S19/files/Lecture_10.pdf · 10-701 Introduction to Machine Learning (PhD) Lecture 10: SVMs Leila Wehbe Carnegie

Find a linear separator with the largest margin

+ ++ +

+

--

-

-

-

x+<latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit>

x�<latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit>

x+ �

x�

<latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="NuMUO5v0VZj/xgCFfus/4L7Zo5U=">AAAB83icbZBLSwMxFIXv1FetVavgyk2wCIK0zLjRpeDGZQX7gHYYMumdNjSTGZKMWIaCf8WNC0X8L+78N6YPQVsPBD7OSbg3J0wF18Z1v5zC2vrG5lZxu7RT3t3brxyUWzrJFMMmS0SiOiHVKLjEpuFGYCdVSONQYDsc3Uzz9gMqzRN5b8Yp+jEdSB5xRo21gspR3gsj8jgJzkmN/HAtqFTdujsTWQVvAVVYqBFUPnv9hGUxSsME1brruanxc6oMZwInpV6mMaVsRAfYtShpjNrPZ+tPyKl1+iRKlD3SkJn7+0VOY63HcWhvxtQM9XI2Nf/LupmJrvycyzQzKNl8UJQJYhIy7YL0uUJmxNgCZYrbXQkbUkWZsY2VbAne8pdXoXVR99y6d+dCEY7hBM7Ag0u4hltoQBMY5PAMr/DmPDkvzvu8roKz6O0Q/sj5+AbtpZL/</latexit><latexit sha1_base64="XB/8q2hCBb2avCAAV+9zrpVA09Y=">AAAB83icdZBLSwMxFIXv1FetVUfBlZtgEQRpyYjWdie4cVnBPqAdSibNtKGZB0lGLEPBv+LGhSL+F3f+GzN9gIoeCBy+k3BvjhcLrjTGn1ZuZXVtfSO/Wdgqbu/s2nvFlooSSVmTRiKSHY8oJnjImpprwTqxZCTwBGt74+ssb98zqXgU3ulJzNyADEPuc0q0QX37IO15PnqY9k9RGS19uW+XcOUCO/VqFeEKxs55zTGmXq8ZiBxDMpVgoUbf/ugNIpoELNRUEKW6Do61mxKpORVsWuglisWEjsmQdY0NScCUm87Wn6JjQwbIj6Q5oUYz+v1FSgKlJoFnbgZEj9TvLIN/Zd1E+zU35WGcaBbS+SA/EUhHKOsCDbhkVIuJMYRKbnZFdEQkodo0VjAlLH+K/jets4qDK84thjwcwhGcgAOXcAU30IAmUEjhCV7g1Xq0nq23eV05a9HbPvyQ9f4FVA6TSA==</latexit><latexit sha1_base64="fTYAa0kN5nHKGBV6qLL1Y97RL8M=">AAAB/nicdZDLSgMxFIYz9VbrbVRcuQkWQZAOGdE63RXcuKxgL9AOQybNtKGZC0lGLEPBV3HjQhG3Poc738ZML6CiPwR+vnMO5+T3E86kQujTKCwtr6yuFddLG5tb2zvm7l5LxqkgtEliHouOjyXlLKJNxRSnnURQHPqctv3RVV5v31EhWRzdqnFC3RAPIhYwgpVGnnmQ9fwA3k+8U1iBC1/xzDKyLpBdq1YhshCyzx1bm1rN0RDamuQqg7kanvnR68ckDWmkCMdSdm2UKDfDQjHC6aTUSyVNMBnhAe1qG+GQSjebnj+Bx5r0YRAL/SIFp/T7RIZDKcehrztDrIbydy2Hf9W6qQocN2NRkioakdmiIOVQxTDPAvaZoETxsTaYCKZvhWSIBSZKJ1bSISx+Cv83rTPLRpZ9g8p1Zx5HERyCI3ACbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrQVjPrMPfsh4/wK1RZSj</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit>

}w

<latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit>

�<latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit>

2� =hx+ � x�,wi

||w||

� =1

2

hx+ � x�,wi||w||

<latexit sha1_base64="+FKYqVI3ZmdwbgNFYbZqrCXw1h0=">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</latexit><latexit sha1_base64="+FKYqVI3ZmdwbgNFYbZqrCXw1h0=">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</latexit><latexit sha1_base64="+FKYqVI3ZmdwbgNFYbZqrCXw1h0=">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</latexit><latexit sha1_base64="+FKYqVI3ZmdwbgNFYbZqrCXw1h0=">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</latexit>

Find a linear separator with the largest margin

+ ++ +

+

--

-

-

-

x+<latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit>

x�<latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit>

x+ �

x�

<latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="NuMUO5v0VZj/xgCFfus/4L7Zo5U=">AAAB83icbZBLSwMxFIXv1FetVavgyk2wCIK0zLjRpeDGZQX7gHYYMumdNjSTGZKMWIaCf8WNC0X8L+78N6YPQVsPBD7OSbg3J0wF18Z1v5zC2vrG5lZxu7RT3t3brxyUWzrJFMMmS0SiOiHVKLjEpuFGYCdVSONQYDsc3Uzz9gMqzRN5b8Yp+jEdSB5xRo21gspR3gsj8jgJzkmN/HAtqFTdujsTWQVvAVVYqBFUPnv9hGUxSsME1brruanxc6oMZwInpV6mMaVsRAfYtShpjNrPZ+tPyKl1+iRKlD3SkJn7+0VOY63HcWhvxtQM9XI2Nf/LupmJrvycyzQzKNl8UJQJYhIy7YL0uUJmxNgCZYrbXQkbUkWZsY2VbAne8pdXoXVR99y6d+dCEY7hBM7Ag0u4hltoQBMY5PAMr/DmPDkvzvu8roKz6O0Q/sj5+AbtpZL/</latexit><latexit sha1_base64="XB/8q2hCBb2avCAAV+9zrpVA09Y=">AAAB83icdZBLSwMxFIXv1FetVUfBlZtgEQRpyYjWdie4cVnBPqAdSibNtKGZB0lGLEPBv+LGhSL+F3f+GzN9gIoeCBy+k3BvjhcLrjTGn1ZuZXVtfSO/Wdgqbu/s2nvFlooSSVmTRiKSHY8oJnjImpprwTqxZCTwBGt74+ssb98zqXgU3ulJzNyADEPuc0q0QX37IO15PnqY9k9RGS19uW+XcOUCO/VqFeEKxs55zTGmXq8ZiBxDMpVgoUbf/ugNIpoELNRUEKW6Do61mxKpORVsWuglisWEjsmQdY0NScCUm87Wn6JjQwbIj6Q5oUYz+v1FSgKlJoFnbgZEj9TvLIN/Zd1E+zU35WGcaBbS+SA/EUhHKOsCDbhkVIuJMYRKbnZFdEQkodo0VjAlLH+K/jets4qDK84thjwcwhGcgAOXcAU30IAmUEjhCV7g1Xq0nq23eV05a9HbPvyQ9f4FVA6TSA==</latexit><latexit sha1_base64="fTYAa0kN5nHKGBV6qLL1Y97RL8M=">AAAB/nicdZDLSgMxFIYz9VbrbVRcuQkWQZAOGdE63RXcuKxgL9AOQybNtKGZC0lGLEPBV3HjQhG3Poc738ZML6CiPwR+vnMO5+T3E86kQujTKCwtr6yuFddLG5tb2zvm7l5LxqkgtEliHouOjyXlLKJNxRSnnURQHPqctv3RVV5v31EhWRzdqnFC3RAPIhYwgpVGnnmQ9fwA3k+8U1iBC1/xzDKyLpBdq1YhshCyzx1bm1rN0RDamuQqg7kanvnR68ckDWmkCMdSdm2UKDfDQjHC6aTUSyVNMBnhAe1qG+GQSjebnj+Bx5r0YRAL/SIFp/T7RIZDKcehrztDrIbydy2Hf9W6qQocN2NRkioakdmiIOVQxTDPAvaZoETxsTaYCKZvhWSIBSZKJ1bSISx+Cv83rTPLRpZ9g8p1Zx5HERyCI3ACbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrQVjPrMPfsh4/wK1RZSj</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit>

}w

<latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit>

�<latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit>

argmaxw,b

� = argmaxw,b

1

2

hx+ � x�,wi||w||

= argmaxw,b

1

2

hx+,wi � hx�,wi||w||

<latexit sha1_base64="yjBgc/SE80wJQeQrpdQVxdzSWx0=">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</latexit><latexit sha1_base64="yjBgc/SE80wJQeQrpdQVxdzSWx0=">AAAC7nicpVJNaxQxGM6M1db1a2uPXoJLRbC7zBTBXoSCF48V3LawWYZ3splp2CQzJJnaJZsf4cWDIr36e7z5b8zuDkV3ixdfCDw8z/Pm/UjyWnBjk+RXFN/Zuntve+d+58HDR4+fdHefnpqq0ZQNaSUqfZ6DYYIrNrTcCnZeawYyF+wsn75b6GeXTBteqY92VrOxhFLxglOwgcp2oy0CuiQSrjLnSF7gT/4g96QEKQG/eItvUzEpNFCXenfoVxATAaoUDC9NVz57hfs3uH/QpmKiVy7v5vOWm889IZ3/KLRxef/G848O1lrIur1kkCwDb4K0BT3UxknW/UkmFW0kU5YKMGaUJrUdO9CWU8F8hzSG1UCnULJRgAokM2O3fC6P9wMzwUWlw1EWL9k/MxxIY2YyzL8vwV6YdW1B3qaNGlscjR1XdWOZoqtCRSOwrfDi7fGEa0atmAUAVPPQK6YXEPZqww/phCWk6yNvgtPDQZoM0g+ve8dH7Tp20DP0HL1EKXqDjtF7dIKGiEbT6HP0NfoW1/GX+Ht8vbLGUZuzh/6K+MdvsUnrXw==</latexit><latexit sha1_base64="yjBgc/SE80wJQeQrpdQVxdzSWx0=">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</latexit><latexit sha1_base64="yjBgc/SE80wJQeQrpdQVxdzSWx0=">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</latexit>

Find a linear separator with the largest margin

+ ++ +

+

--

-

-

-

x+<latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit>

x�<latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit>

x+ �

x�

<latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="NuMUO5v0VZj/xgCFfus/4L7Zo5U=">AAAB83icbZBLSwMxFIXv1FetVavgyk2wCIK0zLjRpeDGZQX7gHYYMumdNjSTGZKMWIaCf8WNC0X8L+78N6YPQVsPBD7OSbg3J0wF18Z1v5zC2vrG5lZxu7RT3t3brxyUWzrJFMMmS0SiOiHVKLjEpuFGYCdVSONQYDsc3Uzz9gMqzRN5b8Yp+jEdSB5xRo21gspR3gsj8jgJzkmN/HAtqFTdujsTWQVvAVVYqBFUPnv9hGUxSsME1brruanxc6oMZwInpV6mMaVsRAfYtShpjNrPZ+tPyKl1+iRKlD3SkJn7+0VOY63HcWhvxtQM9XI2Nf/LupmJrvycyzQzKNl8UJQJYhIy7YL0uUJmxNgCZYrbXQkbUkWZsY2VbAne8pdXoXVR99y6d+dCEY7hBM7Ag0u4hltoQBMY5PAMr/DmPDkvzvu8roKz6O0Q/sj5+AbtpZL/</latexit><latexit sha1_base64="XB/8q2hCBb2avCAAV+9zrpVA09Y=">AAAB83icdZBLSwMxFIXv1FetVUfBlZtgEQRpyYjWdie4cVnBPqAdSibNtKGZB0lGLEPBv+LGhSL+F3f+GzN9gIoeCBy+k3BvjhcLrjTGn1ZuZXVtfSO/Wdgqbu/s2nvFlooSSVmTRiKSHY8oJnjImpprwTqxZCTwBGt74+ssb98zqXgU3ulJzNyADEPuc0q0QX37IO15PnqY9k9RGS19uW+XcOUCO/VqFeEKxs55zTGmXq8ZiBxDMpVgoUbf/ugNIpoELNRUEKW6Do61mxKpORVsWuglisWEjsmQdY0NScCUm87Wn6JjQwbIj6Q5oUYz+v1FSgKlJoFnbgZEj9TvLIN/Zd1E+zU35WGcaBbS+SA/EUhHKOsCDbhkVIuJMYRKbnZFdEQkodo0VjAlLH+K/jets4qDK84thjwcwhGcgAOXcAU30IAmUEjhCV7g1Xq0nq23eV05a9HbPvyQ9f4FVA6TSA==</latexit><latexit sha1_base64="fTYAa0kN5nHKGBV6qLL1Y97RL8M=">AAAB/nicdZDLSgMxFIYz9VbrbVRcuQkWQZAOGdE63RXcuKxgL9AOQybNtKGZC0lGLEPBV3HjQhG3Poc738ZML6CiPwR+vnMO5+T3E86kQujTKCwtr6yuFddLG5tb2zvm7l5LxqkgtEliHouOjyXlLKJNxRSnnURQHPqctv3RVV5v31EhWRzdqnFC3RAPIhYwgpVGnnmQ9fwA3k+8U1iBC1/xzDKyLpBdq1YhshCyzx1bm1rN0RDamuQqg7kanvnR68ckDWmkCMdSdm2UKDfDQjHC6aTUSyVNMBnhAe1qG+GQSjebnj+Bx5r0YRAL/SIFp/T7RIZDKcehrztDrIbydy2Hf9W6qQocN2NRkioakdmiIOVQxTDPAvaZoETxsTaYCKZvhWSIBSZKJ1bSISx+Cv83rTPLRpZ9g8p1Zx5HERyCI3ACbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrQVjPrMPfsh4/wK1RZSj</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit>

}w

<latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit>

�<latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit>

hx+,wi+ b = 1<latexit sha1_base64="IJfAXZHY7lo+2z6igom8IyV2OIs=">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</latexit><latexit sha1_base64="IJfAXZHY7lo+2z6igom8IyV2OIs=">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</latexit><latexit sha1_base64="IJfAXZHY7lo+2z6igom8IyV2OIs=">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</latexit><latexit sha1_base64="IJfAXZHY7lo+2z6igom8IyV2OIs=">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</latexit>

hx�,wi+ b = �1<latexit sha1_base64="Pi17ndKVV6eOuXJdpm26+xo3nuM=">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</latexit><latexit sha1_base64="Pi17ndKVV6eOuXJdpm26+xo3nuM=">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</latexit><latexit sha1_base64="Pi17ndKVV6eOuXJdpm26+xo3nuM=">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</latexit><latexit sha1_base64="Pi17ndKVV6eOuXJdpm26+xo3nuM=">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</latexit>

argmaxw,b

� = argmaxw,b

1

2

hx+ � x�,wi||w||

= argmaxw,b

1

2

hx+,wi � hx�,wi||w||

<latexit sha1_base64="yjBgc/SE80wJQeQrpdQVxdzSWx0=">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</latexit><latexit sha1_base64="yjBgc/SE80wJQeQrpdQVxdzSWx0=">AAAC7nicpVJNaxQxGM6M1db1a2uPXoJLRbC7zBTBXoSCF48V3LawWYZ3splp2CQzJJnaJZsf4cWDIr36e7z5b8zuDkV3ixdfCDw8z/Pm/UjyWnBjk+RXFN/Zuntve+d+58HDR4+fdHefnpqq0ZQNaSUqfZ6DYYIrNrTcCnZeawYyF+wsn75b6GeXTBteqY92VrOxhFLxglOwgcp2oy0CuiQSrjLnSF7gT/4g96QEKQG/eItvUzEpNFCXenfoVxATAaoUDC9NVz57hfs3uH/QpmKiVy7v5vOWm889IZ3/KLRxef/G848O1lrIur1kkCwDb4K0BT3UxknW/UkmFW0kU5YKMGaUJrUdO9CWU8F8hzSG1UCnULJRgAokM2O3fC6P9wMzwUWlw1EWL9k/MxxIY2YyzL8vwV6YdW1B3qaNGlscjR1XdWOZoqtCRSOwrfDi7fGEa0atmAUAVPPQK6YXEPZqww/phCWk6yNvgtPDQZoM0g+ve8dH7Tp20DP0HL1EKXqDjtF7dIKGiEbT6HP0NfoW1/GX+Ht8vbLGUZuzh/6K+MdvsUnrXw==</latexit><latexit sha1_base64="yjBgc/SE80wJQeQrpdQVxdzSWx0=">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</latexit><latexit sha1_base64="yjBgc/SE80wJQeQrpdQVxdzSWx0=">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</latexit>

Find a linear separator with the largest margin

+ ++ +

+

--

-

-

-

x+<latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit>

x�<latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit>

x+ �

x�

<latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="NuMUO5v0VZj/xgCFfus/4L7Zo5U=">AAAB83icbZBLSwMxFIXv1FetVavgyk2wCIK0zLjRpeDGZQX7gHYYMumdNjSTGZKMWIaCf8WNC0X8L+78N6YPQVsPBD7OSbg3J0wF18Z1v5zC2vrG5lZxu7RT3t3brxyUWzrJFMMmS0SiOiHVKLjEpuFGYCdVSONQYDsc3Uzz9gMqzRN5b8Yp+jEdSB5xRo21gspR3gsj8jgJzkmN/HAtqFTdujsTWQVvAVVYqBFUPnv9hGUxSsME1brruanxc6oMZwInpV6mMaVsRAfYtShpjNrPZ+tPyKl1+iRKlD3SkJn7+0VOY63HcWhvxtQM9XI2Nf/LupmJrvycyzQzKNl8UJQJYhIy7YL0uUJmxNgCZYrbXQkbUkWZsY2VbAne8pdXoXVR99y6d+dCEY7hBM7Ag0u4hltoQBMY5PAMr/DmPDkvzvu8roKz6O0Q/sj5+AbtpZL/</latexit><latexit sha1_base64="XB/8q2hCBb2avCAAV+9zrpVA09Y=">AAAB83icdZBLSwMxFIXv1FetVUfBlZtgEQRpyYjWdie4cVnBPqAdSibNtKGZB0lGLEPBv+LGhSL+F3f+GzN9gIoeCBy+k3BvjhcLrjTGn1ZuZXVtfSO/Wdgqbu/s2nvFlooSSVmTRiKSHY8oJnjImpprwTqxZCTwBGt74+ssb98zqXgU3ulJzNyADEPuc0q0QX37IO15PnqY9k9RGS19uW+XcOUCO/VqFeEKxs55zTGmXq8ZiBxDMpVgoUbf/ugNIpoELNRUEKW6Do61mxKpORVsWuglisWEjsmQdY0NScCUm87Wn6JjQwbIj6Q5oUYz+v1FSgKlJoFnbgZEj9TvLIN/Zd1E+zU35WGcaBbS+SA/EUhHKOsCDbhkVIuJMYRKbnZFdEQkodo0VjAlLH+K/jets4qDK84thjwcwhGcgAOXcAU30IAmUEjhCV7g1Xq0nq23eV05a9HbPvyQ9f4FVA6TSA==</latexit><latexit sha1_base64="fTYAa0kN5nHKGBV6qLL1Y97RL8M=">AAAB/nicdZDLSgMxFIYz9VbrbVRcuQkWQZAOGdE63RXcuKxgL9AOQybNtKGZC0lGLEPBV3HjQhG3Poc738ZML6CiPwR+vnMO5+T3E86kQujTKCwtr6yuFddLG5tb2zvm7l5LxqkgtEliHouOjyXlLKJNxRSnnURQHPqctv3RVV5v31EhWRzdqnFC3RAPIhYwgpVGnnmQ9fwA3k+8U1iBC1/xzDKyLpBdq1YhshCyzx1bm1rN0RDamuQqg7kanvnR68ckDWmkCMdSdm2UKDfDQjHC6aTUSyVNMBnhAe1qG+GQSjebnj+Bx5r0YRAL/SIFp/T7RIZDKcehrztDrIbydy2Hf9W6qQocN2NRkioakdmiIOVQxTDPAvaZoETxsTaYCKZvhWSIBSZKJ1bSISx+Cv83rTPLRpZ9g8p1Zx5HERyCI3ACbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrQVjPrMPfsh4/wK1RZSj</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit>

}w

<latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit>

�<latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit>

argmaxw,b

� = argmaxw,b

1

2

1� b� (�1� b)

||w||

= argmaxw,b

1

2

2

||w|| = argmaxw,b

1

||w||= argmin

w,b||w||

= argminw,b

1

2||w||2

<latexit sha1_base64="MUjx+Bztq1pL2fa+l4W0xit2IvE=">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</latexit><latexit sha1_base64="MUjx+Bztq1pL2fa+l4W0xit2IvE=">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</latexit><latexit sha1_base64="MUjx+Bztq1pL2fa+l4W0xit2IvE=">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</latexit><latexit sha1_base64="MUjx+Bztq1pL2fa+l4W0xit2IvE=">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</latexit>

Page 10: Choice of activation gate - Carnegie Mellon School of ...lwehbe/10701_S19/files/Lecture_10.pdf · 10-701 Introduction to Machine Learning (PhD) Lecture 10: SVMs Leila Wehbe Carnegie

The (primal) optimization problem is:

+ ++ +

+

--

-

-

-

x+<latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit>

x�<latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit>

x+ �

x�

<latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="NuMUO5v0VZj/xgCFfus/4L7Zo5U=">AAAB83icbZBLSwMxFIXv1FetVavgyk2wCIK0zLjRpeDGZQX7gHYYMumdNjSTGZKMWIaCf8WNC0X8L+78N6YPQVsPBD7OSbg3J0wF18Z1v5zC2vrG5lZxu7RT3t3brxyUWzrJFMMmS0SiOiHVKLjEpuFGYCdVSONQYDsc3Uzz9gMqzRN5b8Yp+jEdSB5xRo21gspR3gsj8jgJzkmN/HAtqFTdujsTWQVvAVVYqBFUPnv9hGUxSsME1brruanxc6oMZwInpV6mMaVsRAfYtShpjNrPZ+tPyKl1+iRKlD3SkJn7+0VOY63HcWhvxtQM9XI2Nf/LupmJrvycyzQzKNl8UJQJYhIy7YL0uUJmxNgCZYrbXQkbUkWZsY2VbAne8pdXoXVR99y6d+dCEY7hBM7Ag0u4hltoQBMY5PAMr/DmPDkvzvu8roKz6O0Q/sj5+AbtpZL/</latexit><latexit sha1_base64="XB/8q2hCBb2avCAAV+9zrpVA09Y=">AAAB83icdZBLSwMxFIXv1FetVUfBlZtgEQRpyYjWdie4cVnBPqAdSibNtKGZB0lGLEPBv+LGhSL+F3f+GzN9gIoeCBy+k3BvjhcLrjTGn1ZuZXVtfSO/Wdgqbu/s2nvFlooSSVmTRiKSHY8oJnjImpprwTqxZCTwBGt74+ssb98zqXgU3ulJzNyADEPuc0q0QX37IO15PnqY9k9RGS19uW+XcOUCO/VqFeEKxs55zTGmXq8ZiBxDMpVgoUbf/ugNIpoELNRUEKW6Do61mxKpORVsWuglisWEjsmQdY0NScCUm87Wn6JjQwbIj6Q5oUYz+v1FSgKlJoFnbgZEj9TvLIN/Zd1E+zU35WGcaBbS+SA/EUhHKOsCDbhkVIuJMYRKbnZFdEQkodo0VjAlLH+K/jets4qDK84thjwcwhGcgAOXcAU30IAmUEjhCV7g1Xq0nq23eV05a9HbPvyQ9f4FVA6TSA==</latexit><latexit sha1_base64="fTYAa0kN5nHKGBV6qLL1Y97RL8M=">AAAB/nicdZDLSgMxFIYz9VbrbVRcuQkWQZAOGdE63RXcuKxgL9AOQybNtKGZC0lGLEPBV3HjQhG3Poc738ZML6CiPwR+vnMO5+T3E86kQujTKCwtr6yuFddLG5tb2zvm7l5LxqkgtEliHouOjyXlLKJNxRSnnURQHPqctv3RVV5v31EhWRzdqnFC3RAPIhYwgpVGnnmQ9fwA3k+8U1iBC1/xzDKyLpBdq1YhshCyzx1bm1rN0RDamuQqg7kanvnR68ckDWmkCMdSdm2UKDfDQjHC6aTUSyVNMBnhAe1qG+GQSjebnj+Bx5r0YRAL/SIFp/T7RIZDKcehrztDrIbydy2Hf9W6qQocN2NRkioakdmiIOVQxTDPAvaZoETxsTaYCKZvhWSIBSZKJ1bSISx+Cv83rTPLRpZ9g8p1Zx5HERyCI3ACbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrQVjPrMPfsh4/wK1RZSj</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit>

}w

<latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit>

�<latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit>

s.t. yi(hxi,wi+ b) � 1, i = 1, ...,m<latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="C45UEKAMJY7TmPrYPKyLxspdgC8=">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</latexit><latexit sha1_base64="C45UEKAMJY7TmPrYPKyLxspdgC8=">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</latexit><latexit sha1_base64="WR71pp6UDdrL1mPMJ9FU3Vq8RME=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit>

<latexit sha1_base64="8rIvQ9SPme+uVDEAhSaQisOjcPs=">AAACFXicbVDLSsNAFJ34rPUVdelmsBRclJIUwS4LblxWsA9oaphMJ+3QySTMTJQyzU+48VfcuFDEreDOv3HaZqGtBy4czrmXe+8JEkalcpxva219Y3Nru7BT3N3bPzi0j47bMk4FJi0cs1h0AyQJo5y0FFWMdBNBUBQw0gnGVzO/c0+EpDG/VZOE9CM05DSkGCkj+XbFiyj3tfaCED5klSCDXigQ1m6maxnU02nuTKd3tcy3S07VmQOuEjcnJZCj6dtf3iDGaUS4wgxJ2XOdRPU1EopiRrKil0qSIDxGQ9IzlKOIyL6ef5XBslEGMIyFKa7gXP09oVEk5SQyJ5cjpEZy2ZuJ/3m9VIX1vqY8SRXheLEoTBlUMZxFBAdUEKzYxBCEBTW3QjxCJhVlgiyaENzll1dJu1Z1nap7c1Fq1PM4CuAUnIFz4IJL0ADXoAlaAINH8AxewZv1ZL1Y79bHonXNymdOwB9Ynz/2k59H</latexit>

The (primal) optimization problem is:

+ ++ +

+

--

-

-

-

x+<latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit><latexit sha1_base64="UQqqs9K1gCViQmyjr2Jv8MRXwXc=">AAAB8HicdVDLSsNAFJ3UV62vqks3g0UQhDCJoa27ghuXFexD2lAm00k7dCYJMxOxhH6FGxeKuPVz3Pk3TtoKKnrgwuGce7n3niDhTGmEPqzCyura+kZxs7S1vbO7V94/aKs4lYS2SMxj2Q2wopxFtKWZ5rSbSIpFwGknmFzmfueOSsXi6EZPE+oLPIpYyAjWRrrN+kEI72eDs0G5guyLetX1qhDZCNUc18mJW/POPegYJUcFLNEclN/7w5ikgkaacKxUz0GJ9jMsNSOczkr9VNEEkwke0Z6hERZU+dn84Bk8McoQhrE0FWk4V79PZFgoNRWB6RRYj9VvLxf/8nqpDut+xqIk1TQii0VhyqGOYf49HDJJieZTQzCRzNwKyRhLTLTJqGRC+PoU/k/aru0g27n2Ko36Mo4iOALH4BQ4oAYa4Ao0QQsQIMADeALPlrQerRfrddFasJYzh+AHrLdPrPeQSg==</latexit>

x�<latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit><latexit sha1_base64="/wkA1XPoFnH14jiweLz5h62BF2g=">AAAB8HicdVDLSgMxFM3UV62vqks3wSK4sSRF7HRXcOOygn1IW0omzbShSWZIMmIZ+hVuXCji1s9x59+YaSuo6IELh3Pu5d57glhwYxH68HIrq2vrG/nNwtb2zu5ecf+gZaJEU9akkYh0JyCGCa5Y03IrWCfWjMhAsHYwucz89h3Thkfqxk5j1pdkpHjIKbFOuk17QQjvZ4OzQbGEygghjDHMCK5eIEdqNb+CfYgzy6EElmgMiu+9YUQTyZSlghjTxSi2/ZRoy6lgs0IvMSwmdEJGrOuoIpKZfjo/eAZPnDKEYaRdKQvn6veJlEhjpjJwnZLYsfntZeJfXjexod9PuYoTyxRdLAoTAW0Es+/hkGtGrZg6Qqjm7lZIx0QTal1GBRfC16fwf9KqlDEq4+vzUt1fxpEHR+AYnAIMqqAOrkADNAEFEjyAJ/Dsae/Re/FeF605bzlzCH7Ae/sEnOaQQA==</latexit>

x+ �

x�

<latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="NuMUO5v0VZj/xgCFfus/4L7Zo5U=">AAAB83icbZBLSwMxFIXv1FetVavgyk2wCIK0zLjRpeDGZQX7gHYYMumdNjSTGZKMWIaCf8WNC0X8L+78N6YPQVsPBD7OSbg3J0wF18Z1v5zC2vrG5lZxu7RT3t3brxyUWzrJFMMmS0SiOiHVKLjEpuFGYCdVSONQYDsc3Uzz9gMqzRN5b8Yp+jEdSB5xRo21gspR3gsj8jgJzkmN/HAtqFTdujsTWQVvAVVYqBFUPnv9hGUxSsME1brruanxc6oMZwInpV6mMaVsRAfYtShpjNrPZ+tPyKl1+iRKlD3SkJn7+0VOY63HcWhvxtQM9XI2Nf/LupmJrvycyzQzKNl8UJQJYhIy7YL0uUJmxNgCZYrbXQkbUkWZsY2VbAne8pdXoXVR99y6d+dCEY7hBM7Ag0u4hltoQBMY5PAMr/DmPDkvzvu8roKz6O0Q/sj5+AbtpZL/</latexit><latexit sha1_base64="XB/8q2hCBb2avCAAV+9zrpVA09Y=">AAAB83icdZBLSwMxFIXv1FetVUfBlZtgEQRpyYjWdie4cVnBPqAdSibNtKGZB0lGLEPBv+LGhSL+F3f+GzN9gIoeCBy+k3BvjhcLrjTGn1ZuZXVtfSO/Wdgqbu/s2nvFlooSSVmTRiKSHY8oJnjImpprwTqxZCTwBGt74+ssb98zqXgU3ulJzNyADEPuc0q0QX37IO15PnqY9k9RGS19uW+XcOUCO/VqFeEKxs55zTGmXq8ZiBxDMpVgoUbf/ugNIpoELNRUEKW6Do61mxKpORVsWuglisWEjsmQdY0NScCUm87Wn6JjQwbIj6Q5oUYz+v1FSgKlJoFnbgZEj9TvLIN/Zd1E+zU35WGcaBbS+SA/EUhHKOsCDbhkVIuJMYRKbnZFdEQkodo0VjAlLH+K/jets4qDK84thjwcwhGcgAOXcAU30IAmUEjhCV7g1Xq0nq23eV05a9HbPvyQ9f4FVA6TSA==</latexit><latexit sha1_base64="fTYAa0kN5nHKGBV6qLL1Y97RL8M=">AAAB/nicdZDLSgMxFIYz9VbrbVRcuQkWQZAOGdE63RXcuKxgL9AOQybNtKGZC0lGLEPBV3HjQhG3Poc738ZML6CiPwR+vnMO5+T3E86kQujTKCwtr6yuFddLG5tb2zvm7l5LxqkgtEliHouOjyXlLKJNxRSnnURQHPqctv3RVV5v31EhWRzdqnFC3RAPIhYwgpVGnnmQ9fwA3k+8U1iBC1/xzDKyLpBdq1YhshCyzx1bm1rN0RDamuQqg7kanvnR68ckDWmkCMdSdm2UKDfDQjHC6aTUSyVNMBnhAe1qG+GQSjebnj+Bx5r0YRAL/SIFp/T7RIZDKcehrztDrIbydy2Hf9W6qQocN2NRkioakdmiIOVQxTDPAvaZoETxsTaYCKZvhWSIBSZKJ1bSISx+Cv83rTPLRpZ9g8p1Zx5HERyCI3ACbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrQVjPrMPfsh4/wK1RZSj</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit><latexit sha1_base64="ar/zlrwBR6hWYBTRqDCdW44rNJY=">AAAB/nicdZDLSgMxFIYzXmu9jYorN8EiCNIhI7VOdwU3LivYC7TDkEkzbWjmQpIRy1DwVdy4UMStz+HOtzHTC6joD4Gf75zDOfn9hDOpEPo0lpZXVtfWCxvFza3tnV1zb78l41QQ2iQxj0XHx5JyFtGmYorTTiIoDn1O2/7oKq+376iQLI5u1TihbogHEQsYwUojzzzMen4A7yfeGSzDhS97ZglZF8iuVasQWQjZFcfWplZzNIS2JrlKYK6GZ370+jFJQxopwrGUXRslys2wUIxwOin2UkkTTEZ4QLvaRjik0s2m50/giSZ9GMRCv0jBKf0+keFQynHo684Qq6H8XcvhX7VuqgLHzViUpIpGZLYoSDlUMcyzgH0mKFF8rA0mgulbIRligYnSiRV1CIufwv9N69yykWXfVEp1Zx5HARyBY3AKbHAJ6uAaNEATEJCBR/AMXowH48l4Nd5mrUvGfOYA/JDx/gW2hZSn</latexit>

}w

<latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit><latexit sha1_base64="8RUWt0qd8mh9eWDhaOJQq7UJDnc=">AAAB7nicdVDJSgNBEK2JW4xb1KOXxiB4GrpDRucY8OIxglkgCaGn05M06Vno7lHCkI/w4kERr36PN//GziKo6IOCx3tVVNULUim0wfjDKaytb2xuFbdLO7t7+wflw6OWTjLFeJMlMlGdgGouRcybRhjJO6niNAokbweTq7nfvuNKiyS+NdOU9yM6ikUoGDVWaue9IET3s0G5gl184dWIj7DrYeITz5KqRzCuIuLiBSqwQmNQfu8NE5ZFPDZMUq27BKemn1NlBJN8VuplmqeUTeiIdy2NacR1P1+cO0NnVhmiMFG2YoMW6veJnEZaT6PAdkbUjPVvby7+5XUzE/r9XMRpZnjMlovCTCKToPnvaCgUZ0ZOLaFMCXsrYmOqKDM2oZIN4etT9D9pVV2CXXJTq9T9VRxFOIFTOAcCl1CHa2hAExhM4AGe4NlJnUfnxXldthac1cwx/IDz9gl5H4+f</latexit>

�<latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit><latexit sha1_base64="V2j68dtu4Mv+rN4UyQDlkJm3NGU=">AAAB7XicbVDLSgNBEOyNrxhfUY9eBoPgKeyKYI4BLx4jmAckS+idzCZjZmaXmVkhhPyDFw+KePV/vPk3TpI9aGJBQ1HVTXdXlApurO9/e4WNza3tneJuaW//4PCofHzSMkmmKWvSRCS6E6FhgivWtNwK1kk1QxkJ1o7Gt3O//cS04Yl6sJOUhRKHiseconVSqzdEKbFfrvhVfwGyToKcVCBHo1/+6g0SmkmmLBVoTDfwUxtOUVtOBZuVeplhKdIxDlnXUYWSmXC6uHZGLpwyIHGiXSlLFurviSlKYyYycp0S7cisenPxP6+b2bgWTrlKM8sUXS6KM0FsQuavkwHXjFoxcQSp5u5WQkeokVoXUMmFEKy+vE5aV9XArwb315V6LY+jCGdwDpcQwA3U4Q4a0AQKj/AMr/DmJd6L9+59LFsLXj5zCn/gff4Ag+mPCw==</latexit>

s.t. yi(hxi,wi+ b) � 1, i = 1, ...,m<latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">AAACP3icbVBBSxtBGJ3VWmPUGu2xl6GhEDEsu1LQiyB48RihiUI2LLOTb5PB2dll5ttqWPafefEvePPqpYcW6bU3J5s9tEnfMPB473vMfC/KpDDoec/O2vq7jfebja3m9s7uh73W/sHApLnm0OepTPVNxAxIoaCPAiXcZBpYEkm4jm4v5v71d9BGpOobzjIYJWyiRCw4QyuFrUGAcI+FcdEtaVAdi1koOjSQTE0k0CKIYnpfhqK7oHdloBfOUXRIgwlQv1sFBT2z1HXdbhK22p7rVaCrxK9Jm9Toha2nYJzyPAGFXDJjhr6X4ahgGgWXUDaD3EDG+C2bwNBSxRIwo6Lav6RfrDKmcartVUgr9e9EwRJjZklkJxOGU7PszcX/ecMc49NRIVSWIyi+eCjOJcWUzsukY6GBo5xZwrgW9q+UT5lmHG3lTVuCv7zyKhkcu77n+ldf2+endR0N8ol8Jh3ikxNyTi5Jj/QJJw/khfwkv5xH54fz6vxejK45deYj+QfOnzdiRqou</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="C45UEKAMJY7TmPrYPKyLxspdgC8=">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</latexit><latexit sha1_base64="C45UEKAMJY7TmPrYPKyLxspdgC8=">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</latexit><latexit sha1_base64="WR71pp6UDdrL1mPMJ9FU3Vq8RME=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit>

This can be written as:

Where and are both convex functions of our parameters w and b

minw,b

f(w, b)

s.t. g(w, b) 0, i = 1, ...,m<latexit sha1_base64="+y4GgVTO0AnrLv48gyRmNJf0TnU=">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</latexit><latexit sha1_base64="+y4GgVTO0AnrLv48gyRmNJf0TnU=">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</latexit><latexit sha1_base64="+y4GgVTO0AnrLv48gyRmNJf0TnU=">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</latexit><latexit sha1_base64="+y4GgVTO0AnrLv48gyRmNJf0TnU=">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</latexit>

f(w, b) = ||w||2<latexit sha1_base64="Mdn1Qya+mYuFxxq4K5vtgwQSJOQ=">AAACBXicbVC7SgNBFL0bXzG+Vi21GAxCBAm7QTCNELCxjGAekKxhdjKbDJl9MDOrhN00Nv6KjYUitv6DnX/jJNlCowcunDnnXube40acSWVZX0ZuaXlldS2/XtjY3NreMXf3mjKMBaENEvJQtF0sKWcBbSimOG1HgmLf5bTlji6nfuuOCsnC4EaNI+r4eBAwjxGstNQzD71S0nU9dD85dU/QBUrT7Jmmt5WeWbTK1gzoL7EzUoQM9Z752e2HJPZpoAjHUnZsK1JOgoVihNNJoRtLGmEywgPa0TTAPpVOMrtigo610kdeKHQFCs3UnxMJ9qUc+67u9LEaykVvKv7ndWLlVZ2EBVGsaEDmH3kxRypE00hQnwlKFB9rgolgeldEhlhgonRwBR2CvXjyX9KslG2rbF+fFWvVLI48HMARlMCGc6jBFdShAQQe4Ale4NV4NJ6NN+N93pozspl9+AXj4xuvOZdh</latexit><latexit sha1_base64="Mdn1Qya+mYuFxxq4K5vtgwQSJOQ=">AAACBXicbVC7SgNBFL0bXzG+Vi21GAxCBAm7QTCNELCxjGAekKxhdjKbDJl9MDOrhN00Nv6KjYUitv6DnX/jJNlCowcunDnnXube40acSWVZX0ZuaXlldS2/XtjY3NreMXf3mjKMBaENEvJQtF0sKWcBbSimOG1HgmLf5bTlji6nfuuOCsnC4EaNI+r4eBAwjxGstNQzD71S0nU9dD85dU/QBUrT7Jmmt5WeWbTK1gzoL7EzUoQM9Z752e2HJPZpoAjHUnZsK1JOgoVihNNJoRtLGmEywgPa0TTAPpVOMrtigo610kdeKHQFCs3UnxMJ9qUc+67u9LEaykVvKv7ndWLlVZ2EBVGsaEDmH3kxRypE00hQnwlKFB9rgolgeldEhlhgonRwBR2CvXjyX9KslG2rbF+fFWvVLI48HMARlMCGc6jBFdShAQQe4Ale4NV4NJ6NN+N93pozspl9+AXj4xuvOZdh</latexit><latexit sha1_base64="Mdn1Qya+mYuFxxq4K5vtgwQSJOQ=">AAACBXicbVC7SgNBFL0bXzG+Vi21GAxCBAm7QTCNELCxjGAekKxhdjKbDJl9MDOrhN00Nv6KjYUitv6DnX/jJNlCowcunDnnXube40acSWVZX0ZuaXlldS2/XtjY3NreMXf3mjKMBaENEvJQtF0sKWcBbSimOG1HgmLf5bTlji6nfuuOCsnC4EaNI+r4eBAwjxGstNQzD71S0nU9dD85dU/QBUrT7Jmmt5WeWbTK1gzoL7EzUoQM9Z752e2HJPZpoAjHUnZsK1JOgoVihNNJoRtLGmEywgPa0TTAPpVOMrtigo610kdeKHQFCs3UnxMJ9qUc+67u9LEaykVvKv7ndWLlVZ2EBVGsaEDmH3kxRypE00hQnwlKFB9rgolgeldEhlhgonRwBR2CvXjyX9KslG2rbF+fFWvVLI48HMARlMCGc6jBFdShAQQe4Ale4NV4NJ6NN+N93pozspl9+AXj4xuvOZdh</latexit><latexit sha1_base64="Mdn1Qya+mYuFxxq4K5vtgwQSJOQ=">AAACBXicbVC7SgNBFL0bXzG+Vi21GAxCBAm7QTCNELCxjGAekKxhdjKbDJl9MDOrhN00Nv6KjYUitv6DnX/jJNlCowcunDnnXube40acSWVZX0ZuaXlldS2/XtjY3NreMXf3mjKMBaENEvJQtF0sKWcBbSimOG1HgmLf5bTlji6nfuuOCsnC4EaNI+r4eBAwjxGstNQzD71S0nU9dD85dU/QBUrT7Jmmt5WeWbTK1gzoL7EzUoQM9Z752e2HJPZpoAjHUnZsK1JOgoVihNNJoRtLGmEywgPa0TTAPpVOMrtigo610kdeKHQFCs3UnxMJ9qUc+67u9LEaykVvKv7ndWLlVZ2EBVGsaEDmH3kxRypE00hQnwlKFB9rgolgeldEhlhgonRwBR2CvXjyX9KslG2rbF+fFWvVLI48HMARlMCGc6jBFdShAQQe4Ale4NV4NJ6NN+N93pozspl9+AXj4xuvOZdh</latexit>

g(w, b) = 1� yi(hxi,wi+ b)<latexit sha1_base64="uNvjPBEb/Gb+Dx37Q2kOuJ4kvuQ=">AAACJXicbVDLSsNAFJ3UV62vqks3g0VosZZEBLtQKLhxWcE+oAlhMp20QyeTMDNRS+jPuPFX3LiwiODKX3GaZqGtBwYO55zLnXu8iFGpTPPLyK2srq1v5DcLW9s7u3vF/YO2DGOBSQuHLBRdD0nCKCctRRUj3UgQFHiMdLzRzczvPBAhacjv1TgiToAGnPoUI6Ult3g1KCe258PHSdWrwGtoncGxS8vQZogPGIGp+TRxaRVmOVvMnVOv4hZLZs1MAZeJlZESyNB0i1O7H+I4IFxhhqTsWWaknAQJRTEjk4IdSxIhPEID0tOUo4BIJ0mvnMATrfShHwr9uIKp+nsiQYGU48DTyQCpoVz0ZuJ/Xi9Wft1JKI9iRTieL/JjBlUIZ5XBPhUEKzbWBGFB9V8hHiKBsNLFFnQJ1uLJy6R9XrPMmnV3UWrUszry4AgcgzKwwCVogFvQBC2AwTN4Be9garwYb8aH8TmP5oxs5hD8gfH9AxYfoos=</latexit><latexit sha1_base64="uNvjPBEb/Gb+Dx37Q2kOuJ4kvuQ=">AAACJXicbVDLSsNAFJ3UV62vqks3g0VosZZEBLtQKLhxWcE+oAlhMp20QyeTMDNRS+jPuPFX3LiwiODKX3GaZqGtBwYO55zLnXu8iFGpTPPLyK2srq1v5DcLW9s7u3vF/YO2DGOBSQuHLBRdD0nCKCctRRUj3UgQFHiMdLzRzczvPBAhacjv1TgiToAGnPoUI6Ult3g1KCe258PHSdWrwGtoncGxS8vQZogPGIGp+TRxaRVmOVvMnVOv4hZLZs1MAZeJlZESyNB0i1O7H+I4IFxhhqTsWWaknAQJRTEjk4IdSxIhPEID0tOUo4BIJ0mvnMATrfShHwr9uIKp+nsiQYGU48DTyQCpoVz0ZuJ/Xi9Wft1JKI9iRTieL/JjBlUIZ5XBPhUEKzbWBGFB9V8hHiKBsNLFFnQJ1uLJy6R9XrPMmnV3UWrUszry4AgcgzKwwCVogFvQBC2AwTN4Be9garwYb8aH8TmP5oxs5hD8gfH9AxYfoos=</latexit><latexit sha1_base64="uNvjPBEb/Gb+Dx37Q2kOuJ4kvuQ=">AAACJXicbVDLSsNAFJ3UV62vqks3g0VosZZEBLtQKLhxWcE+oAlhMp20QyeTMDNRS+jPuPFX3LiwiODKX3GaZqGtBwYO55zLnXu8iFGpTPPLyK2srq1v5DcLW9s7u3vF/YO2DGOBSQuHLBRdD0nCKCctRRUj3UgQFHiMdLzRzczvPBAhacjv1TgiToAGnPoUI6Ult3g1KCe258PHSdWrwGtoncGxS8vQZogPGIGp+TRxaRVmOVvMnVOv4hZLZs1MAZeJlZESyNB0i1O7H+I4IFxhhqTsWWaknAQJRTEjk4IdSxIhPEID0tOUo4BIJ0mvnMATrfShHwr9uIKp+nsiQYGU48DTyQCpoVz0ZuJ/Xi9Wft1JKI9iRTieL/JjBlUIZ5XBPhUEKzbWBGFB9V8hHiKBsNLFFnQJ1uLJy6R9XrPMmnV3UWrUszry4AgcgzKwwCVogFvQBC2AwTN4Be9garwYb8aH8TmP5oxs5hD8gfH9AxYfoos=</latexit><latexit sha1_base64="uNvjPBEb/Gb+Dx37Q2kOuJ4kvuQ=">AAACJXicbVDLSsNAFJ3UV62vqks3g0VosZZEBLtQKLhxWcE+oAlhMp20QyeTMDNRS+jPuPFX3LiwiODKX3GaZqGtBwYO55zLnXu8iFGpTPPLyK2srq1v5DcLW9s7u3vF/YO2DGOBSQuHLBRdD0nCKCctRRUj3UgQFHiMdLzRzczvPBAhacjv1TgiToAGnPoUI6Ult3g1KCe258PHSdWrwGtoncGxS8vQZogPGIGp+TRxaRVmOVvMnVOv4hZLZs1MAZeJlZESyNB0i1O7H+I4IFxhhqTsWWaknAQJRTEjk4IdSxIhPEID0tOUo4BIJ0mvnMATrfShHwr9uIKp+nsiQYGU48DTyQCpoVz0ZuJ/Xi9Wft1JKI9iRTieL/JjBlUIZ5XBPhUEKzbWBGFB9V8hHiKBsNLFFnQJ1uLJy6R9XrPMmnV3UWrUszry4AgcgzKwwCVogFvQBC2AwTN4Be9garwYb8aH8TmP5oxs5hD8gfH9AxYfoos=</latexit>

<latexit sha1_base64="8rIvQ9SPme+uVDEAhSaQisOjcPs=">AAACFXicbVDLSsNAFJ34rPUVdelmsBRclJIUwS4LblxWsA9oaphMJ+3QySTMTJQyzU+48VfcuFDEreDOv3HaZqGtBy4czrmXe+8JEkalcpxva219Y3Nru7BT3N3bPzi0j47bMk4FJi0cs1h0AyQJo5y0FFWMdBNBUBQw0gnGVzO/c0+EpDG/VZOE9CM05DSkGCkj+XbFiyj3tfaCED5klSCDXigQ1m6maxnU02nuTKd3tcy3S07VmQOuEjcnJZCj6dtf3iDGaUS4wgxJ2XOdRPU1EopiRrKil0qSIDxGQ9IzlKOIyL6ef5XBslEGMIyFKa7gXP09oVEk5SQyJ5cjpEZy2ZuJ/3m9VIX1vqY8SRXheLEoTBlUMZxFBAdUEKzYxBCEBTW3QjxCJhVlgiyaENzll1dJu1Z1nap7c1Fq1PM4CuAUnIFz4IJL0ADXoAlaAINH8AxewZv1ZL1Y79bHonXNymdOwB9Ynz/2k59H</latexit>

LagrangianWe can write the Lagrangian of:

as:

s.t. yi(hxi,wi+ b) � 1, i = 1, ...,m<latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="hP+6LrUf2d3tZaldqaQQvEKMXyw=">AAAB2XicbZDNSgMxFIXv1L86Vq1rN8EiuCozbnQpuHFZwbZCO5RM5k4bmskMyR2hDH0BF25EfC93vo3pz0JbDwQ+zknIvSculLQUBN9ebWd3b/+gfugfNfzjk9Nmo2fz0gjsilzl5jnmFpXU2CVJCp8LgzyLFfbj6f0i77+gsTLXTzQrMMr4WMtUCk7O6oyaraAdLMW2IVxDC9YaNb+GSS7KDDUJxa0dhEFBUcUNSaFw7g9LiwUXUz7GgUPNM7RRtRxzzi6dk7A0N+5oYkv394uKZ9bOstjdzDhN7Ga2MP/LBiWlt1EldVESarH6KC0Vo5wtdmaJNChIzRxwYaSblYkJN1yQa8Z3HYSbG29D77odBu3wMYA6nMMFXEEIN3AHD9CBLghI4BXevYn35n2suqp569LO4I+8zx84xIo4</latexit><latexit sha1_base64="C45UEKAMJY7TmPrYPKyLxspdgC8=">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</latexit><latexit sha1_base64="C45UEKAMJY7TmPrYPKyLxspdgC8=">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</latexit><latexit sha1_base64="WR71pp6UDdrL1mPMJ9FU3Vq8RME=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit><latexit sha1_base64="CyCWW6+/x7C32vlpSOmmsUPVS4A=">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</latexit>

<latexit sha1_base64="8rIvQ9SPme+uVDEAhSaQisOjcPs=">AAACFXicbVDLSsNAFJ34rPUVdelmsBRclJIUwS4LblxWsA9oaphMJ+3QySTMTJQyzU+48VfcuFDEreDOv3HaZqGtBy4czrmXe+8JEkalcpxva219Y3Nru7BT3N3bPzi0j47bMk4FJi0cs1h0AyQJo5y0FFWMdBNBUBQw0gnGVzO/c0+EpDG/VZOE9CM05DSkGCkj+XbFiyj3tfaCED5klSCDXigQ1m6maxnU02nuTKd3tcy3S07VmQOuEjcnJZCj6dtf3iDGaUS4wgxJ2XOdRPU1EopiRrKil0qSIDxGQ9IzlKOIyL6ef5XBslEGMIyFKa7gXP09oVEk5SQyJ5cjpEZy2ZuJ/3m9VIX1vqY8SRXheLEoTBlUMZxFBAdUEKzYxBCEBTW3QjxCJhVlgiyaENzll1dJu1Z1nap7c1Fq1PM4CuAUnIFz4IJL0ADXoAlaAINH8AxewZv1ZL1Y79bHonXNymdOwB9Ynz/2k59H</latexit>

<latexit sha1_base64="A5KXnjnAbHIs94WlO3wNAWcCggA=">AAACJ3icbVDLSsNAFJ3UV62vqks3g0VosZZEBLtRCm5cVrAPaEKYTCft0MkkzEzUEvo3bvwVN4KK6NI/cZpmoa0HBg7nnMude7yIUalM88vILS2vrK7l1wsbm1vbO8XdvbYMY4FJC4csFF0PScIoJy1FFSPdSBAUeIx0vNHV1O/cESFpyG/VOCJOgAac+hQjpSW3eDlwaTmxPR/eT6peBV5A6wSOtQZthviAEZiaDxOXVmGWs8XMOfYqbrFk1swUcJFYGSmBDE23+Gr3QxwHhCvMkJQ9y4yUkyChKGZkUrBjSSKER2hAeppyFBDpJOmdE3iklT70Q6EfVzBVf08kKJByHHg6GSA1lPPeVPzP68XKrzsJ5VGsCMezRX7MoArhtDTYp4JgxcaaICyo/ivEQyQQVrragi7Bmj95kbRPa5ZZs27OSo16VkceHIBDUAYWOAcNcA2aoAUweATP4A28G0/Gi/FhfM6iOSOb2Qd/YHz/AL+Ho2c=</latexit>

<latexit sha1_base64="b5GxGD9Bg2YwY4MUyXvtyTbevxI=">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</latexit>