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Journal Article

#### A Direct Method for Building Sparse Kernel Learning Algorithms

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##### Citation

Wu, M., Schölkopf, B., & BakIr, G. (2006). A Direct Method for Building Sparse
Kernel Learning Algorithms.* Journal of Machine Learning Research,* *7*,
603-624. Retrieved from http://jmlr.csail.mit.edu/papers/volume7/wu06a/wu06a.pdf.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-D217-6

##### Abstract

Many Kernel Learning Algorithms(KLA), including Support Vector Machine (SVM), result in a Kernel Machine (KM), such as a kernel classifier, whose key component is a weight vector in a feature space implicitly introduced by a positive definite kernel function. This weight vector is usually obtained by solving a convex optimization problem. Based on this fact we present a direct method to build Sparse Kernel Learning Algorithms (SKLA) by adding one more constraint to the original convex optimization problem, such that the sparseness of the resulting KM is explicitly controlled while at the same time the performance of the resulting KM can be kept as high as possible. A gradient based approach is provided to solve this modified optimization problem. Applying this method to the SVM results in a concrete algorithm for building Sparse Large Margin Classifiers (SLMC). Further analysis of the SLMC algorithm indicates that it essentially finds a discriminating subspace that can be spanned by
a small number of vectors, and in this subspace, the different classes of data are linearly well separated. Experimental results over several classification benchmarks demonstrate the effectiveness of our approach.