Post on 24-Feb-2016
description
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Tamara BergMachine Learning
790-133Recognizing People, Objects, & Actions
Announcements
• Topic presentation groups posted. Anyone not have a group yet?
• Last day of background material
• For Monday - Object recognition papers will be posted online. Please read!
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What is machine learning?
• Computer programs that can learn from data
• Two key components– Representation: how should we represent the
data?– Generalization: the system should generalize from
its past experience (observed data items) to perform well on unseen data items.
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Types of ML algorithms
• Unsupervised– Algorithms operate on unlabeled examples
• Supervised– Algorithms operate on labeled examples
• Semi/Partially-supervised– Algorithms combine both labeled and unlabeled examples
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Unsupervised Learning
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K-means clustering• Want to minimize sum of squared Euclidean
distances between points xi and their nearest cluster centers mk
Algorithm:• Randomly initialize K cluster centers• Iterate until convergence:
• Assign each data point to the nearest center• Recompute each cluster center as the mean of all points assigned
to it
k
ki
ki mxMXDcluster
clusterinpoint
2)(),(
source: Svetlana Lazebnik Slide 7 of 113
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Different clustering strategies• Agglomerative clustering
• Start with each point in a separate cluster• At each iteration, merge two of the “closest” clusters
• Divisive clustering• Start with all points grouped into a single cluster• At each iteration, split the “largest” cluster
• K-means clustering• Iterate: assign points to clusters, compute means
• K-medoids• Same as k-means, only cluster center cannot be computed by
averaging• The “medoid” of each cluster is the most centrally located point in
that cluster (i.e., point with lowest average distance to the other points)
source: Svetlana Lazebnik Slide 19 of 113
Supervised Learning
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Example: Image classification
apple
pear
tomato
cow
dog
horse
input desired output
Slide credit: Svetlana LazebnikSlide 25 of 113
Slide from Dan Kleinhttp://yann.lecun.com/exdb/mnist/index.html Slide 26 of 113
Example: Seismic data
Body wave magnitude
Surfa
ce w
ave
mag
nitu
de
Nuclear explosions
Earthquakes
Slide credit: Svetlana LazebnikSlide 27 of 113
Slide from Dan KleinSlide 28 of 113
The basic classification framework
y = f(x)
• Learning: given a training set of labeled examples {(x1,y1), …, (xN,yN)}, estimate the parameters of the prediction function f
• Inference: apply f to a never before seen test example x and output the predicted value y = f(x)
output classification function
input
Slide credit: Svetlana LazebnikSlide 29 of 113
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Some ML classification methods
106 examples
Nearest neighbor
Shakhnarovich, Viola, Darrell 2003Berg, Berg, Malik 2005…
Neural networks
LeCun, Bottou, Bengio, Haffner 1998Rowley, Baluja, Kanade 1998…
Support Vector Machines and Kernels Conditional Random Fields
McCallum, Freitag, Pereira 2000Kumar, Hebert 2003…
Guyon, VapnikHeisele, Serre, Poggio, 2001…
Slide credit: Antonio Torralba
Example: Training and testing
• Key challenge: generalization to unseen examples
Training set (labels known) Test set (labels unknown)
Slide credit: Svetlana LazebnikSlide 31 of 113
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Slide from Min-Yen Kan
Classification by Nearest Neighbor
Word vector document classification – here the vector space is illustrated as having 2 dimensions. How many dimensions would the data actually live in?
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Slide from Min-Yen Kan
Classification by Nearest Neighbor
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Classification by Nearest Neighbor
Classify the test document as the class of the document “nearest” to the query document (use vector similarity to find most similar doc)
Slide from Min-Yen Kan
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Classification by kNN
Classify the test document as the majority class of the k documents “nearest” to the query document. Slide from Min-Yen Kan
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What are the features? What’s the training data? Testing data? Parameters?
Classification by kNN
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What are the features? What’s the training data? Testing data? Parameters?
Classification by kNN
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NN for vision
Fast Pose Estimation with Parameter Sensitive HashingShakhnarovich, Viola, Darrell
J. Hays and A. Efros, Scene Completion using Millions of Photographs, SIGGRAPH 2007
NN for vision
J. Hays and A. Efros, IM2GPS: estimating geographic information from a single image, CVPR 2008
NN for vision
Decision tree classifierExample problem: decide whether to wait for a table at a
restaurant, based on the following attributes:1. Alternate: is there an alternative restaurant nearby?2. Bar: is there a comfortable bar area to wait in?3. Fri/Sat: is today Friday or Saturday?4. Hungry: are we hungry?5. Patrons: number of people in the restaurant (None, Some, Full)6. Price: price range ($, $$, $$$)7. Raining: is it raining outside?8. Reservation: have we made a reservation?9. Type: kind of restaurant (French, Italian, Thai, Burger)10. WaitEstimate: estimated waiting time (0-10, 10-30, 30-60, >60)
Slide credit: Svetlana LazebnikSlide 47 of 113
Decision tree classifier
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Decision tree classifier
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Linear classifier
• Find a linear function to separate the classes
f(x) = sgn(w1x1 + w2x2 + … + wDxD) = sgn(w x)
Slide credit: Svetlana LazebnikSlide 50 of 113
Discriminant Function• It can be arbitrary functions of x, such as:
Nearest Neighbor
Decision Tree
LinearFunctions
( ) Tg b x w x
Slide credit: Jinwei GuSlide 51 of 113
Linear Discriminant Function• g(x) is a linear function:
( ) Tg b x w x
x1
x2
wT x + b = 0
wT x + b < 0
wT x + b > 0
A hyper-plane in the feature space
Slide credit: Jinwei Gu
denotes +1denotes -1
x1
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• How would you classify these points using a linear discriminant function in order to minimize the error rate?
Linear Discriminant Function
denotes +1denotes -1
x1
x2
Infinite number of answers!
Slide credit: Jinwei GuSlide 53 of 113
• How would you classify these points using a linear discriminant function in order to minimize the error rate?
Linear Discriminant Function
x1
x2
Infinite number of answers!
denotes +1denotes -1
Slide credit: Jinwei GuSlide 54 of 113
• How would you classify these points using a linear discriminant function in order to minimize the error rate?
Linear Discriminant Function
x1
x2
Infinite number of answers!
denotes +1denotes -1
Slide credit: Jinwei GuSlide 55 of 113
x1
x2• How would you classify these points using a linear discriminant function in order to minimize the error rate?
Linear Discriminant Function
Infinite number of answers!
Which one is the best?
denotes +1denotes -1
Slide credit: Jinwei GuSlide 56 of 113
Large Margin Linear Classifier
“safe zone”• The linear discriminant
function (classifier) with the maximum margin is the best
Margin is defined as the width that the boundary could be increased by before hitting a data point
Why it is the best? strong generalization ability
Margin
x1
x2
Linear SVMSlide credit: Jinwei Gu
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Large Margin Linear Classifier
x1
x2 Margin
wT x + b = 0
wT x + b = -1w
T x + b = 1
x+
x+
x-
Support Vectors
Slide credit: Jinwei GuSlide 58 of 113
Large Margin Linear Classifier • Formulation:
x1
x2 Margin
wT x + b = 0
wT x + b = -1w
T x + b = 1
x+
x+
x-n
21minimize 2
w
such that
For 1, 1
For 1, 1
Ti i
Ti i
y b
y b
w x
w x
Slide credit: Jinwei GuSlide 61 of 113
Large Margin Linear Classifier • Formulation:
x1
x2 Margin
wT x + b = 0
wT x + b = -1w
T x + b = 1
x+
x+
x-n( ) 1T
i iy b w x
21minimize 2
w
such that
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Solving the Optimization Problem
( ) 1Ti iy b w x
21minimize 2
w
s.t.
Quadratic programming
with linear constraints
Slide credit: Jinwei GuSlide 63 of 113
Solving the Optimization Problem The linear discriminant function is:
Notice it relies on a dot product between the test point x and the support vectors xi
Slide credit: Jinwei GuSlide 66 of 113
Linear separability
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Non-linear SVMs: Feature Space General idea: the original input space can be mapped to
some higher-dimensional feature space where the training set is separable:
Φ: x → φ(x)
Slide courtesy of www.iro.umontreal.ca/~pift6080/documents/papers/svm_tutorial.ppt
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Nonlinear SVMs: The Kernel Trick With this mapping, our discriminant function becomes:
SV
( ) ( ) ( ) ( )T Ti i
i
g b b
x w x x x
No need to know this mapping explicitly, because we only use the dot product of feature vectors in both the training and test.
A kernel function is defined as a function that corresponds to a dot product of two feature vectors in some expanded feature space:
( , ) ( ) ( )Ti j i jK x x x x
Slide credit: Jinwei Gu
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Nonlinear SVMs: The Kernel Trick
Linear kernel:
2
2( , ) exp( )2i j
i jK
x xx x
( , ) Ti j i jK x x x x
( , ) (1 )T pi j i jK x x x x
0 1( , ) tanh( )Ti j i jK x x x x
Examples of commonly-used kernel functions:
Polynomial kernel:
Gaussian (Radial-Basis Function (RBF) ) kernel:
Sigmoid:
Slide credit: Jinwei Gu
Support Vector Machine: Algorithm
1. Choose a kernel function
2. Choose a value for C and any other parameters (e.g. σ)
3. Solve the quadratic programming problem (many software packages available)
4. Classify held out validation instances using the learned model
5. Select the best learned model based on validation accuracy 6. Classify test instances using the final selected model
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Some Issues• Choice of kernel - Gaussian or polynomial kernel is default - if ineffective, more elaborate kernels are needed - domain experts can give assistance in formulating appropriate similarity
measures
• Choice of kernel parameters - e.g. σ in Gaussian kernel - In the absence of reliable criteria, applications rely on the use of a
validation set or cross-validation to set such parameters.
This slide is courtesy of www.iro.umontreal.ca/~pift6080/documents/papers/svm_tutorial.ppt Slide 73 of 113
Summary: Support Vector Machine
• 1. Large Margin Classifier – Better generalization ability & less over-fitting
• 2. The Kernel Trick– Map data points to higher dimensional space in
order to make them linearly separable.– Since only dot product is used, we do not need to
represent the mapping explicitly.
Slide credit: Jinwei GuSlide 74 of 113
• A simple algorithm for learning robust classifiers– Freund & Shapire, 1995– Friedman, Hastie, Tibshhirani, 1998
• Provides efficient algorithm for sparse visual feature selection– Tieu & Viola, 2000– Viola & Jones, 2003
• Easy to implement, doesn’t require external optimization tools.
Boosting
Slide credit: Antonio TorralbaSlide 75 of 113
• Defines a classifier using an additive model:
Boosting
Strong classifier
Weak classifier
WeightFeaturesvector
Slide credit: Antonio TorralbaSlide 76 of 113
• Defines a classifier using an additive model:
• We need to define a family of weak classifiers
Boosting
Strong classifier
Weak classifier
WeightFeaturesvector
from a family of weak classifiers
Slide credit: Antonio TorralbaSlide 77 of 113
Adaboost
Slide credit: Antonio TorralbaSlide 78 of 113
Each data point has
a class label:
wt =1and a weight:
+1 ( )
-1 ( )yt =
Boosting• It is a sequential procedure:
xt=1
xt=2
xt
Slide credit: Antonio TorralbaSlide 79 of 113
Toy exampleWeak learners from the family of lines
h => p(error) = 0.5 it is at chance
Each data point has
a class label:
wt =1and a weight:
+1 ( )
-1 ( )yt =
Slide credit: Antonio TorralbaSlide 80 of 113
Toy example
This one seems to be the best
Each data point has
a class label:
wt =1and a weight:
+1 ( )
-1 ( )yt =
This is a ‘weak classifier’: It performs slightly better than chance.Slide credit: Antonio Torralba
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Toy example
Each data point has
a class label:
wt wt exp{-yt Ht}
We update the weights:
+1 ( )
-1 ( )yt =
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Toy example
Each data point has
a class label:
wt wt exp{-yt Ht}
We update the weights:
+1 ( )
-1 ( )yt =
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Toy example
Each data point has
a class label:
wt wt exp{-yt Ht}
We update the weights:
+1 ( )
-1 ( )yt =
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Toy example
Each data point has
a class label:
wt wt exp{-yt Ht}
We update the weights:
+1 ( )
-1 ( )yt =
Slide credit: Antonio TorralbaSlide 85 of 113
Toy example
The strong (non- linear) classifier is built as the combination of all the weak (linear) classifiers.
f1 f2
f3
f4
Slide credit: Antonio TorralbaSlide 86 of 113
Adaboost
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Semi-Supervised Learning
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Supervised learning has many successes• recognize speech,• steer a car,• classify documents• classify proteins• recognizing faces, objects in images• ...
Slide Credit: Avrim Blum Slide 89 of 113
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However, for many problems, labeled data can be rare or expensive.
Unlabeled data is much cheaper.Need to pay someone to do it, requires special testing,…
Slide Credit: Avrim Blum
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However, for many problems, labeled data can be rare or expensive.
Unlabeled data is much cheaper.
Speech
Images
Medical outcomes
Customer modeling
Protein sequences
Web pages
Need to pay someone to do it, requires special testing,…
Slide Credit: Avrim Blum
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However, for many problems, labeled data can be rare or expensive.
Unlabeled data is much cheaper.
[From Jerry Zhu]
Need to pay someone to do it, requires special testing,…
Slide Credit: Avrim Blum
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Need to pay someone to do it, requires special testing,…
However, for many problems, labeled data can be rare or expensive.
Unlabeled data is much cheaper.
Can we make use of cheap unlabeled data?
Slide Credit: Avrim Blum
Semi-Supervised LearningCan we use unlabeled data to augment a small
labeled sample to improve learning?
But unlabeled data is missing the most important info!!But maybe still has
useful regularities that we can use.
But…But…But…Slide Credit: Avrim Blum Slide 94 of 113
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Method 1:
EM
How to use unlabeled data • One way is to use the EM algorithm
– EM: Expectation Maximization• The EM algorithm is a popular iterative algorithm for
maximum likelihood estimation in problems with missing data.
• The EM algorithm consists of two steps, – Expectation step, i.e., filling in the missing data – Maximization step – calculate a new maximum a posteriori
estimate for the parameters.
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Algorithm Outline
1. Train a classifier with only the labeled documents.
2. Use it to probabilistically classify the unlabeled documents.
3. Use ALL the documents to train a new classifier.4. Iterate steps 2 and 3 to convergence.
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Method 2:
Co-Training
Co-training[Blum&Mitchell’98] Many problems have two different sources of info
(“features/views”) you can use to determine label.E.g., classifying faculty webpages: can use words on page or words on links pointing to the page.
My AdvisorProf. Avrim Blum My AdvisorProf. Avrim Blum
x2- Text infox1- Link infox - Link info & Text info
Slide Credit: Avrim BlumSlide 99 of 113
Co-trainingIdea: Use small labeled sample to learn initial rules.
– E.g., “my advisor” pointing to a page is a good indicator it is a faculty home page.
– E.g., “I am teaching” on a page is a good indicator it is a faculty home page.
my advisor
Slide Credit: Avrim BlumSlide 100 of 113
Co-trainingIdea: Use small labeled sample to learn initial rules.
– E.g., “my advisor” pointing to a page is a good indicator it is a faculty home page.
– E.g., “I am teaching” on a page is a good indicator it is a faculty home page.
Then look for unlabeled examples where one view is confident and the other is not. Have it label the example for the other.
Training 2 classifiers, one on each type of info. Using each to help train the other.
hx1,x2ihx1,x2ihx1,x2i
hx1,x2ihx1,x2ihx1,x2i
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Co-training Algorithm [Blum and Mitchell, 1998]
Given: labeled data L,
unlabeled data U
Loop:
Train h1 (e.g., hyperlink classifier) using L
Train h2 (e.g., page classifier) using L
Allow h1 to label p positive, n negative examples from U
Allow h2 to label p positive, n negative examples from U
Add these most confident self-labeled examples to L
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Watch, Listen & Learn: Co-training on Captioned Images and Videos
Sonal Gupta, Joohyun Kim, Kristen Grauman, Raymond MooneyThe University of Texas at Austin, U.S.A.
Goals• Classify images and videos with the help
of visual information and associated text captions
• Use unlabeled image and video examples
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Image Examples
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Cultivating farming at Nabataean Ruins of the Ancient Avdat
Bedouin Leads His Donkey That Carries Load Of Straw
Ibex Eating In The Nature Entrance To Mikveh Israel Agricultural School
Desert
Trees
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Approach• Combining two views of images and videos using Co-
training (Blum and Mitchell ‘98) learning algorithm
• Views: Text and Visual
• Text View – Caption of image or video– Readily available
• Visual View– Color, texture, temporal information in image/video
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Co-training
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++-+
Initially Labeled Instances
Visual Classifier
Text Classifier
Text View Visual View
Text View Visual View
Text View Visual View
Text View Visual View
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Co-training
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Initially Labeled Instances
Visual Classifier
Text Classifier
Supervised Learning
Text ViewText ViewText ViewText View
Visual ViewVisual ViewVisual ViewVisual View
++-+
++-+
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Co-training
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Unlabeled Instances
Visual Classifier
Text Classifier
Text ViewText ViewText ViewText View
Visual ViewVisual ViewVisual ViewVisual View
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Co-training
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ClassifierLabeled
Instances
Classify most confident instances
Text Classifier
Visual Classifier
Text ViewText ViewText ViewText View
Visual ViewVisual ViewVisual ViewVisual View
++--
++--
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Co-training
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Retrain Classifiers
Text Classifier
Visual Classifier
Text ViewText ViewText ViewText View
Visual ViewVisual ViewVisual ViewVisual View
++--
++--
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Video FeaturesDetect Interest Points
Harris-Forstener Corner Detector for both spatial and temporal space
Describe Interest PointsHistogram of Oriented Gradients (HoG)
Create Spatio-Temporal VocabularyQuantize interest points to create 200
visual words dictionary
Represent each video as histogram of visual words
[Laptev, IJCV ‘05]
…
N 72
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Textual Features
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• That was a very nice forward camel.• Well I remember her performance last time.• He has some delicate hand movement.• She gave a small jump while gliding• He runs in to chip the ball with his right foot.• He runs in to take the instep drive and executes it well.• The small kid pushes the ball ahead with his tiny kicks.
Standard Bag-of-Words Representation
Raw Text Commentary
Porter Stemmer Remove Stop Words
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Conclusion• Combining textual and visual features
can help improve accuracy• Co-training can be useful to combine
textual and visual features to classify images and videos
• Co-training helps in reducing labeling of images and videos
[More information on http://www.cs.utexas.edu/users/ml/co-training]
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Co-training vs. EM
• Co-training splits features, EM does not.
• Co-training incrementally uses the unlabeled data.
• EM probabilistically labels all the data at each round; EM iteratively uses the unlabeled data.
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