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. 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

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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


Svm for classification

SVM for Classification


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 classification2

Universum SVM for Classification


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?


Universum support vector machine a generalized approach

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:


Generalized support vector machine

Generalized Support Vector Machine


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).


L 2 version

L2 version


L 2 version1

L2 version


Dual form1

Dual form


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…


Universum support vector machine a generalized approach

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 !


Universum support vector machine a generalized approach

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