Document Type

Journal Article

Department/Unit

Department of Computer Science

Title

Learning low-rank Mercer kernels with fast-decaying spectrum

Language

English

Abstract

Low-rank representations have received a lot of interest in the application of kernel-based methods. However, these methods made an assumption that the spectrum of the Gaussian or polynomial kernels decays rapidly. This is not always true and its violation may result in performance degradation. In this paper, we propose an effective technique for learning low-rank Mercer kernels (LMK) with fast-decaying spectrum. What distinguishes our kernels from other classical kernels (Gaussian and polynomial kernels) is that the proposed always yields low-rank Gram matrices whose spectrum decays rapidly, no matter what distribution the data are. Furthermore, the LMK can control the decay rate. Thus, our kernels can prevent performance degradation while using the low-rank approximations. Our algorithm has favorable in scalability-it is linear in the number of data points and quadratic in the rank of the Gram matrix. Empirical results demonstrate that the proposed method learns fast-decaying spectrum and significantly improves the performance. © 2011 Elsevier B.V.

Keywords

Fast-decaying spectrum, Low-rank kernel, Spectrum of gram matrices

Publication Date

2011

Source Publication Title

Neurocomputing

Volume

74

Issue

17

Start Page

3028

End Page

3035

Publisher

Elsevier

DOI

10.1016/j.neucom.2011.04.021

ISSN (print)

09252312

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