Event classification & prediction using support vector machine
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By
Ruta Ashok Kambli
(122071013)
Event Classification & Prediction Using
Support Vector Machine
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Scope of Presentation Introduction
Support Vector Machine(SVM)Hard-margin SVM
Soft -margin SVM
Kernels
Multiclass classification
SVM Model Selection
Case Studies & Results
Conclusion
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Introduction
Classification & Prediction
Machine Learning
Support Vector Machine
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Machine learning
Unsupervised learning
Clustering
K-mean
Herarchial
Neural network
Supervised learning
Classification
SVM
Neural Network
Decision tree
Regression
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Support Vector
Machines
• Supervised machine learning model.
• Analyse data and recognize patterns.
• Used for classification and regression
analysis.
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Binary Classification
Consider training data set (𝑥𝑖, 𝑦𝑖) for (i = 1, . . . , M),
with 𝑥𝑖 ∈ ℝ𝑑 and 𝑦𝑖 ∈ {−1, 1}, learn a classifier
D(x) such that,
𝐷(𝑥𝑖) ≥ 1, 𝑓𝑜𝑟 𝑦𝑖 = 1
≤ −1, 𝑓𝑜𝑟 𝑦𝑖 = −1……(1)
ie. 𝑦𝑖𝐷 𝑥𝑖 ≥ 1 for a correct classification.
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Binary Classification
x1
x2 denotes +1
denotes -1
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How would you classify these
points using a linear
discriminant function in order
to minimize the error rate?
Binary Classificationdenotes +1
denotes -1
x1
x2
Infinite number of answers!
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How would you classify these
points using a linear
discriminant function in order
to minimize the error rate?
Binary Classificationdenotes +1
denotes -1
x1
x2
Infinite number of answers!
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How would you classify these
points using a linear
discriminant function in order
to minimize the error rate?
Binary Classificationdenotes +1
denotes -1
x1
x2
Infinite number of answers!
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x1
x2 How would you classify these
points using a linear
discriminant function in order
to minimize the error rate?
Binary Classificationdenotes +1
denotes -1
Infinite number of answers!
Which one is the best?
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Binary Classification
“safe zone” We have to find out the
optimal hyperplane with the
maximum margin.
Margin is defined as the
width that the boundary
could be increased by before
hitting a data point
Why it is the best?
Robust to outliners and thus
strong generalization ability.
Margin
x1
x2
denotes +1
denotes -1
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Hard-margin SVM
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Minimise : 𝑄 𝑤, 𝑏 =1
2𝑤 2…….(2)
Subject to: 𝑦𝑖 𝑤𝑇𝑥𝑖 + 𝑏 ≥ 1 𝑓𝑜𝑟 𝑖 = (1,…… ,𝑀)…….(3)
Q(w, b,𝛼)=𝑊𝑇𝑊 − 𝑖=1𝑀 𝛼𝑖 𝑦𝑖 𝑤𝑇𝑥𝑖 + 𝑏 − 1 ……(4)
Where 𝛼 = (𝛼𝑖 , ……𝛼𝑀) and 𝛼𝑖 are the nonnegative Lagrange
multipliers.
• The optimal solution of (4) is given by the saddle
point.
• Where (4) is minimized with respect to w
• Maximized with respect to 𝛼𝑖 (≥ 0)
• Maximized or minimized with respect to b
according to the sign 𝑖=1𝑀 𝛼𝑖𝑦𝑖
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Soft- margin SVM
𝑦𝑖 𝑤𝑇𝑥𝑖 + 𝑏 ≥ 1 − 𝜉𝑖 𝑓𝑜𝑟 𝑖 = 1, …… ,𝑀 …….(7)
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Soft margin SVM
𝑚𝑖𝑛𝑖𝑚𝑖𝑠𝑒 𝑄 𝑤, 𝑏, 𝜉 =1
2𝑤 2 +
𝐶
𝑃 𝑖=1𝑀 𝜉𝑖
𝑃 ……..(5)
𝑆𝑢𝑏𝑗𝑒𝑐𝑡 𝑡𝑜 𝑦𝑖 𝑤𝑇𝑥𝑖 + 𝑏 ≥ 1 − 𝜉𝑖 𝑓𝑜𝑟 𝑖 = 1,…… ,𝑀 ….(6)
𝑄 𝑤, 𝑏, 𝛼, 𝛽
=1
2𝑤 2 + 𝐶
𝑖=1
𝑀
𝜉𝑖 −
𝑖=1
𝑀
𝛼𝑖 𝑦𝑖 𝑤𝑇𝑥𝑖 + 𝑏 − 1 + 𝜉𝑖 −
𝑖=1
𝑀
𝛽𝑖𝜉𝑖
……(7)
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Kernels
Types of Kernel Function
Polynomial
Radial Base function(RBF)
Sigmoid
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Multiclass Classification Initially SVM is Binary Classifier.
Most of the practical applications involve
multiclass classification.
One against One Approach.
If n is the number of classes, we generate
n(n-1)/2 models.
It is not practical for large-scale linear
classification.
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SVM Model
Margin Parameter (C) Selection
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SVM ModelKernel Parameter Selection
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K-fold Cross Validation Create a K-fold partition of the dataset.
For each of K experiments, use K-1 folds for training and the remaining one for testing.
The advantage of K-Fold Cross validation is that all the examples in the dataset are eventually used for both training and testing
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Hand Movement
Classification using
SVM
Data acquisition
using NI-Elvis
Feature selection using
Wavelate
Feature classification using SVM
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Data acquisition using NI-Elvis
Two connectors are
connected to Flexor
Digitorum supercialis
(FDS) muscle.
The readings are
taken for different
hand movements.
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Data acquisition using NI-Elvis
This is time verses
amplitude graph of hand
movement data.
Class 1 :open hand
Class 2 : closed hand
Class 3 :wrist flexion
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Results (training & testing)
Subject Training Accuracy (%) Testing Accuracy(%)
Male1 89.5833 86.3636
Male2 93.75 79.1667
Female 1 90 80
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Blackout Prediction
Using SVM
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Probabilistic Model
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Kernel Selection
Kernel Training Accuracy % Testing Accuracy%
Polynomial 100 94.44
Radial 100 100
Sigmoid 52.63 38.89
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Margin Parameter Selection
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Kernel Parameter
Selection
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Conclusion Results of first case study show that, single
channel surface Electromyogram analysis is
simple, less expensive and effective.
The second case study shows, using blackout
prediction model we can predict blackout before it
occurs.
Here output of SVM is given to emergency control
system, which initiates the prevention mechanism
against the blackout.
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Refferences1. “Support Vector Machines for Pattern
Classification” by Shigeo Abe
2. “Classification of low-level finger contraction from single channel Surface EMG” by Vijay Pal Singh and Dinesh Kant Kumar
3. “Fault Location in Power Distribution System with Distributed Generation Using Support Vector Machine,” by Agrawal, R.Thukaram
4. M. R. Ahsan, M. I. Ibrahimy, and O. O. Khalifa, “EMG signal classication for human computer interaction: A review,"European Journal of Scientic Research, vol. 33, no. 3, pp. 480-501, 2009.
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References 5. J. Kim, S. Mastnik, and E. Andr,”EMG-based
hand gesture recognition for realtime biosignalinterfacing,"13th international conference on Intelligent user interfaces, 2008, pp.3039.
6. K. Englehart and B. Hudgins, “A robust, real-time control scheme for multifunction myoelectric control,"Biomedical Engineering, IEEE Transactions on, vol. 50, no. 7, pp. 848854, 2003.
7. C Rudin, D Waltz, and R N Anderson, “Machine learning for the new york city power grid,"IEEETrans. on Pattern analysis and machine intelligence , VOL. 34, NO. 2, February 2011
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THANK YOU