DMCA
Sparse Greedy Matrix Approximation for Machine Learning (2000)
| Citations: | 222 - 10 self |
BibTeX
@INPROCEEDINGS{Smola00sparsegreedy,
author = {Alex J. Smola and Bernhard Schölkopf},
title = {Sparse Greedy Matrix Approximation for Machine Learning},
booktitle = {},
year = {2000},
pages = {911--918},
publisher = {Morgan Kaufmann}
}
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Abstract
In kernel based methods such as Regularization Networks large datasets pose signi- cant problems since the number of basis functions required for an optimal solution equals the number of samples. We present a sparse greedy approximation technique to construct a compressed representation of the design matrix. Experimental results are given and connections to Kernel-PCA, Sparse Kernel Feature Analysis, and Matching Pursuit are pointed out. 1. Introduction Many recent advances in machine learning such as Support Vector Machines [Vapnik, 1995], Regularization Networks [Girosi et al., 1995], or Gaussian Processes [Williams, 1998] are based on kernel methods. Given an m-sample f(x 1 ; y 1 ); : : : ; (x m ; y m )g of patterns x i 2 X and target values y i 2 Y these algorithms minimize the regularized risk functional min f2H R reg [f ] = 1 m m X i=1 c(x i ; y i ; f(x i )) + 2 kfk 2 H : (1) Here H denotes a reproducing kernel Hilbert space (RKHS) [Aronszajn, 1950],...
Keyphrases
machine learning sparse greedy matrix approximation introduction many recent advance risk functional min f2h reg regularization network girosi optimal solution gaussian process williams compressed representation sparse kernel feature analysis support vector machine vapnik kernel method reproducing kernel hilbert space signi cant problem matching pursuit design matrix target value experimental result basis function sparse greedy approximation technique regularization network large datasets
