Universum Support Vector Machine -A generalized approach

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# Universum Support Vector Machine -A generalized approach - PowerPoint PPT Presentation

Universum Support Vector Machine -A generalized approach. Junfeng He with help from Professor Tony Jebara, Gerry Tesauro and Vladimir Naumovich Vapnik. SVM for Classification. Universum SVM for Classification. Idea: Contradiction on Universum. Universum SVM for Classification.

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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
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).
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…
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