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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)


  • Only suitable for two-label classification

  • Can we generalize universum SVM to both classification and regression?


  • 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.


  • 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).

L 2 version
L2 version

L 2 version1
L2 version


  • 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].


  • 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…

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 !