Browsing by Author "Huang, Su-Yun"

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Asymptotic error bounds for kernel-based Nystrom low-rank approximation matrices
(2013-09-01)
Chang, Lo-Bin
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Bai, Zhidong
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Huang, Su-Yun
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Hwang, Chii-Ruey
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應用數學系
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.
Multiclass support vector classification via coding and regression
(2010-03-01)
Chen, Pei-Chun
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Lee, Kuang-Yao
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Lee, Tsung-Ju
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Lee, Yuh-Jye
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Huang, Su-Yun
The multiclass classification problem is considered and resolved through coding and regression. There are various coding schemes for transforming class labels into response scores. An equivalence notion of coding schemes is developed, and the regression approach is adopted for extracting a low-dimensional discriminant feature subspace. This feature subspace can be a linear subspace of the column span of original input data or kernel-mapped feature data. The classification training and prediction are carried out in this feature subspace using a linear classifier, which lead to a simple and computationally light but yet powerful toolkit for classification. Experimental results, including prediction ability and CPU time comparison with LIBSVM, show that the regression-based approach is a competent alternative for the multiclass problem. (C) 2009 Elsevier B.V. All rights reserved.