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Support Vector Machine

SEN – 935 DATA MINING

∗ Anandha L Ranganathan
∗
17. Support Vector Machine

1
History


Pre 1980s
−
−


−
−


−
−

17. Support Vector Machine

- 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.

2
History



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 ?

17. Support Vector Machine

3
Greedy search



Find largest sum by traversing through path.

17. Support Vector Machine

4
Greedy search



Find largest sum by traversing through path.

17. Support Vector Machine

5
Greedy search



Find largest sum by traversing through path.

17. Support Vector Machine

6
Learning Theory




A system receives data as input.
Output a function that can be predict some features of
future data.

α



x

f

yest

f(x,w,b) = sign(w. x - b)

17. Support Vector Machine

7
Features of SVM's






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

17. Support Vector Machine

8
Support Vectors






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.

17. Support Vector Machine

9
Vector Space – Primer






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

17. Support Vector Machine

10
Kernal – Primer


Computing the inner products between the vectors
in the featured space.

17. Support Vector Machine

11
Linear Classifiers
denotes +1
denotes -1

How would you
classify this data?

17. Support Vector Machine

12
Linear Classifiers
denotes +1
denotes -1

How would you
classify this data?

17. Support Vector Machine

13
Linear Classifiers
denotes +1
denotes -1

How would you
classify this data?

17. Support Vector Machine

14
Linear Classifiers
denotes +1
denotes -1

How would you
classify this data?

17. Support Vector Machine

15
Linear Classifiers
denotes +1
denotes -1

How would you
classify this data?

17. Support Vector Machine

16
Linear Classifiers
denotes +1
denotes -1

Any of these would be
fine..
..but which is best?

17. Support Vector Machine

17
Classifier Margin
denotes +1

Define the margin of
a linear classifier as
the width that the
boundary could be
increased by before
hitting a datapoint.

denotes -1

17. Support Vector Machine

18
Maximum Margin

denotes +1

The maximum
margin linear
classifier is the linear
classifier with the
maximum margin.

denotes -1

This is the simplest
kind of SVM (Called
an LSVM)

17. Support Vector Machine

19

Linear SVM
Formulating SVM

17. Support Vector Machine

20
Formulating SVM

17. Support Vector Machine

21
Formulating SVM

17. Support Vector Machine

22
Kernal - polynomial


Idea: map to higher dimensional feature space

17. Support Vector Machine

23
License Plate Recognition

17. Support Vector Machine

24
License Plate Recognition

∗ Pre-process the image of number plate.
∗ Segment the image into several parts of which each
contains only a single character.

17. Support Vector Machine

25
License Plate Recognition

∗ 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.

17. Support Vector Machine

26
License Plate Recognition

17. Support Vector Machine

27
License Plate Recognition

17. Support Vector Machine

28
License Plate Recognition

17. Support Vector Machine

29
License Plate Recognition

17. Support Vector Machine

30
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

17. Support Vector Machine

31
Conclusion




SVM is widely used as classify spam detection in the
market.
It supports for Linear and Non-Linear spectrum.

17. Support Vector Machine

32








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=svm12978262&user_login=wltongxing

17. Support Vector Machine

33

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Support Vector machine