1. Kernels in Pattern Recognition

2. A Langur - Baboon Binary Problem http://www.tribuneindia.co m/2006/20060712/himplu s4.jpg … HA HA HA … http://www.sickworld.net/ db4/00381/sickworld.net/ _uimages/baboons.jpg

3. Representation of Binary Data

4. Concept of Kernels Idea proposed by Aizerman in 1964. Feature … space … dimensionality … transformation such that The dot product exists {i.e. is not infinite} in higher dimension & Data is linearly separable.

5. Dot Product The scalar value signifies the amount of projection of a in the direction of b The scalar value also signifies the degree of similarity between a and b Adopted from http://www.netcomuk.co.u k/~jenolive/vect6.html

6. A Geometrical Interpretation Mapping Mapping data from low dimension to high dimension. Data is linearly separable in higher dimension. Separable hyperplane defined by a normal or weight vector.

7. Cross Product Normal vector or Weight vector i.e. perpendicular to the hyperplane. http://www.netcomuk.co.uk/~je nolive/vect8.html Area covered while moving a to b in counterclockwise direction moves the vector upwards... Like tightening of a screw This vector is perpendicular to the plane in which a and b lie.

8. Importance of dot product & kernel == dot product Classification requires computation of dot product between normal of hyperplane and test point. Often, normal is expressed as a linear combination of points in higer dimension. Dot products signify on which side of the hyperplane the test point lies – act of classification Dot product computation expensive and transformation not easy to find, so propose a kernel function, whose scalar value is equivalent to the dot product in higer dimensional plane.

9. Geometrical Interpretation of Importance of dot product & kernel == dot product

10. How does a kernel look like? A Planner View from Top

11. How does a kernel look like? An Isometric View from different Side angles

12. The End

13. Vapnick proposes Support Vector Machines

14. An Apple – Orange Binary Problem http://en.wikipedia.org /wiki/Image:Apples.jp g http://en.wikipedia.org /wiki/Image:Ambersw eet_oranges.jpg

15. Representation of Binary Data

16. Separable Case

17. The Lagrangian Optimize Subject to Differentiate w.r.t w  weight vector b  the constant alpha  Lagrangian parameter

18. Non-Separable Case

19. The Lagrangian Optimize Subject to Differentiate w.r.t w  weight vector b  the constant alpha  Lagrangian parameter xi  another Lagrangian paramer

20. Finally … after some mental mathematical harrasment we get: Optimized values of weight vector and b values. And Then Use it to classify new test examples …

21. In The End If SVMs can’t help classify…  then DITCH them and classify apples and oranges by eating them yourself...