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Universum Support Vector Machine -A generalized approachPowerPoint Presentation

Universum Support Vector Machine -A generalized approach

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### Universum Support Vector Machine-A generalized approach

Junfeng He

with help from Professor Tony Jebara, Gerry Tesauro and Vladimir Naumovich Vapnik

Universum SVM for Classification

- Idea: Contradiction on Universum

Universum SVM for Classification

- Approximation: If is close to zero, then a small change in will cause a contradiction on universum data

Universum SVM for Classification

- Dual form: (With U as ε-insenstive function)

Problem

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

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:

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:

Dual form

Replacing by , we get the kernel version.

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).

L2 version

L2 version

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].

Property

- Not sparse in training or universum data.
Because of loss function:

- It can be used for online learning.
can be computed based on

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

More experiments

- Coming soon…

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 ！

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