Universum Support Vector Machine -A generalized approach

1. Universum Support Vector Machine-A generalized approach Junfeng He with help from Professor Tony Jebara, Gerry Tesauro and Vladimir Naumovich Vapnik

2. SVM for Classification

3. Universum SVM for Classification • Idea: Contradiction on Universum

4. Universum SVM for Classification • Approximation: If is close to zero, then a small change in will cause a contradiction on universum data

5. Universum SVM for Classification

6. Universum SVM for Classification • Dual form: (With U as ε-insenstive function)

7. Problem • Only suitable for two-label classification • Can we generalize universum SVM to both classification and regression?

8. Idea • View regression as many two-label classification problems: For any given y, For this two-lable classification problem, using the idea of universum SVM, the loss function should be: • With all possible y, the total loss function on universum data:

9. Generalized Universum Support Vector Machine For two classification, i.e., y = {+1,-1}, if p(y=+1)=p(y=-1) = 0.5, degenerated as Universum SVM:

11. Generalized Support Vector Machine

12. Dual form Replacing by , we get the kernel version.

13. Property • Suitable for both classification and regresson. • Without the universum part traditional SVR. • Sparse in training data, not sparse in universum data ( because of loss function).

14. L2 version

15. L2 version

16. Dual form

17. Property • Suitable for both regression and classification . • Without the universum part LS-SVM. • For classification y={+1,-1}, if E = 0, degenerated to Universum LS-SVM [Fabian Sinz 2007].

18. Property • Not sparse in training or universum data. Because of loss function: • It can be used for online learning. can be computed based on

19. Experiments - male/female face classification • Yale Face Dataset Training: male 250 female168 Test: male 171 female 168 Universum: 1700. Created by: a * male + (1-a) * female Classification Error on Test Set

20. More experiments • Coming soon…

21. Thank You! 谢谢！ ありがとう ！ Vielen Dank！ Kop Koon Ka! 謝謝！ Merci beaucoup ！ 감사합니다 ！ Spasiba ！ Ευχαριστίες ! شكور！ Grazias ！ Köszönöm！ Obrigado ！

22. Q & A?