 Asymptotic error bounds for kernel-based Nyström low-rank approximation matricesLo-Bin Chang, Zhidong Bai, Su-Yun Huang and Chii-Ruey Hwang Journal of Multivariate Analysis, 2013, vol. 120, issue C, 102-119 Abstract: 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 Nyström low-rank approximation. It uses a reduced kernel K̂, which is n×m, consisting of m columns (say columns i1,i2,⋯,im) randomly drawn from K. This approximation takes the form K≈K̂U−1K̂T, where U is the reduced m×m matrix formed by rows i1,i2,⋯,im of K̂. 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 Nyström low-rank approximation matrix. Keywords: Nyström approximation; Kernel Gram matrix; Spectrum decomposition; Asymptotic error bound; Wishart random matrix (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:120:y:2013:i:c:p:102-119 Ordering information: This journal article can be ordered from DOI: 10.1016/j.jmva.2013.05.006 Access Statistics for this article Journal of Multivariate Analysis is currently edited by de Leeuw, J. More articles in Journal of Multivariate Analysis from Elsevier |
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