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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. 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

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
  • Idea: Contradiction on Universum
universum svm for classification1
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 classification3
Universum SVM for Classification
  • Dual form: (With U as ε-insenstive function)
problem
Problem
  • Only suitable for two-label classification
  • Can we generalize universum SVM to both classification and regression?
slide8
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
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
Dual form

Replacing by , we get the kernel version.

property
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).
property1
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].

property2
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
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
More experiments
  • Coming soon…
slide21
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 !