標題: Asymptotic error bounds for kernel-based Nystrom low-rank approximation matrices
作者: Chang, Lo-Bin
Bai, Zhidong
Huang, Su-Yun
Hwang, Chii-Ruey
應用數學系
Department of Applied Mathematics
關鍵字: Nystrom approximation;Kernel Gram matrix;Spectrum decomposition;Asymptotic error bound;Wishart random matrix
公開日期: 1-九月-2013
摘要: Many kernel-based learning algorithms have the computational load scaled with the sample size n due to the column size of a full kernel Gram matrix K. This article considers the Nystrom low-rank approximation. It uses a reduced kernel (K) over cap, which is n x m, consisting of m columns (say columns i(1), i(2),..., i(m)) randomly drawn from K. This approximation takes the form K approximate to (K) over capU(-1)(K) over cap (T), where U is the reduced m x m matrix formed by rows, i(1),i(2),..., i(m) of (K) over cap. Often m is much smaller than the sample size n resulting in a thin rectangular reduced kernel, and it leads to learning algorithms scaled with the column size m. The quality of matrix approximations can be assessed by the closeness of their eigenvalues and eigenvectors. In this article, asymptotic error bounds on eigenvalues and eigenvectors are derived for the Nystrom low-rank approximation matrix. (C) 2013 Elsevier Inc. All rights reserved.
URI: http://dx.doi.org/10.1016/j.jmva.2013.05.006
http://hdl.handle.net/11536/22103
ISSN: 0047-259X
DOI: 10.1016/j.jmva.2013.05.006
期刊: JOURNAL OF MULTIVARIATE ANALYSIS
Volume: 120
Issue: 
起始頁: 102
結束頁: 119
顯示於類別:期刊論文


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