Support Vector machine
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Transcript of Support Vector machine
SEN – 935 DATA MINING
Anandha L Ranganathan
Support Vector Machine
17. Support Vector Machine 1
Pre 1980s - Almost all learning methods learned linear decision surfaces. - Linear learning methods have nice theoretical properties
1980s - Almost all learning methods learned linear decision surfaces. - Linear learning methods have nice theoretical properties
1990’s - Efficient learning algorithms for non-linear functions based on
computational learning theory developed - Nice theoretical properties.
History
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Two independent developments within last decade
– Computational learning theory– New efficient separability of non-linear functions that use “kernel
functions”
The resultant learning algorithm is optimization algorithm rather than a greedy search.
What is greedy search ?
History
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Find largest sum by traversing through path.
Greedy search
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Find largest sum by traversing through path.
Greedy search
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Find largest sum by traversing through path.
Greedy search
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A system receives data as input. Output a function that can be predict some
features of future data.
Learning Theory
f x yest
f(x,w,b) = sign(w. x - b)
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Not affected by local minima. Do not suffer from the curse of dimensionality. Have modular design that allows one to
separately implement and design other component.
Various properties of the SVM solution help avoid over fitting, even in very high dimensional feature spaces
Features of SVM's
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Support vectors are data points that lie closes to the decision surface.
But they are difficult to classify. They have direct bearing of optimum location
on the surface.
Support Vectors
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d1 and d2 are 2 vectors. And sum of their distance is d1+d2=q.
d1=2x+5y and d2=3x+2y q=d1+d2=5x+7y
Vector Space – Primer
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Computing the inner products between the vectors in the featured space.
Kernal – Primer
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Linear Classifiers
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How would you classify this data?
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How would you classify this data?
Linear Classifiers
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How would you classify this data?
Linear Classifiers
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How would you classify this data?
Linear Classifiers
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How would you classify this data?
Linear Classifiers
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Any of these would be fine..
..but which is best?
Linear Classifiers
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Classifier Margin
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denotes -1 Define the margin of a linear classifier as the width that the boundary could be increased by before hitting a datapoint.
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Maximum Margin
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denotes -1 The maximum margin linear classifier is the linear classifier with the maximum margin.
This is the simplest kind of SVM (Called an LSVM)
Linear SVM17. Support Vector Machine 19
Formulating SVM
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Formulating SVM
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Formulating SVM
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Idea: map to higher dimensional feature space
Kernal - polynomial
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License Plate Recognition
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Pre-process the image of number plate. Segment the image into several parts of
which each contains only a single character.
License Plate Recognition
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Extract the feature vector of each normalized candidate
Recognizes the single character (a digit or a letter) by the set of SVMs trained in advance.
License Plate Recognition
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License Plate Recognition
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License Plate Recognition
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License Plate Recognition
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License Plate Recognition
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License Plate Recognition
If there are no more unclassified samples, then STOP. Otherwise, then repeat the process of recognition of character.
Add these test samples into their corresponding database for further training.
Recognize number plate by bringing all characters used together
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SVM is widely used as classify spam detection in the market.
It supports for Linear and Non-Linear spectrum.
Conclusion
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http://www.cs.ucf.edu/courses/cap6412/fall2009/papers/Berwick2003.pdf
http://physiology.med.cornell.edu/people/banfelder/qbio/resources_2011/2011_Leslie.pdf
http://physiology.med.cornell.edu/people/banfelder/qbio/resources_2011/2011_Leslie.pdf
http://www.cs.columbia.edu/~kathy/cs4701/documents/jason_svm_tutorial.pdf
http://www.slideshare.net/analog76/savedfiles?s_title=svm-12978262&user_login=wltongxing
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