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Use of the Zero-Norm with Linear Models and Kernel Methods

MPG-Autoren
http://pubman.mpdl.mpg.de/cone/persons/resource/persons84311

Weston,  J
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons83901

Elisseeff,  A
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons84193

Schölkopf,  B
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Zitation

Weston, J., Elisseeff, A., Schölkopf, B., & Tipping, M. (2003). Use of the Zero-Norm with Linear Models and Kernel Methods. Journal of Machine Learning Research, 3, 1439-1461. Retrieved from http://jmlr.csail.mit.edu/papers/volume3/weston03a/weston03a.pdf.


Zitierlink: http://hdl.handle.net/11858/00-001M-0000-0013-DCE0-C
Zusammenfassung
We explore the use of the so-called zero-norm of the parameters of linear models in learning. Minimization of such a quantity has many uses in a machine learning context: for variable or feature selection, minimizing training error and ensuring sparsity in solutions. We derive a simple but practical method for achieving these goals and discuss its relationship to existing techniques of minimizing the zero-norm. The method boils down to implementing a simple modification of vanilla SVM, namely via an iterative multiplicative rescaling of the training data. Applications we investigate which aid our discussion include variable and feature selection on biological microarray data, and multicategory classification.