Learning low-rank Mercer kernels with fast-decaying spectrum

Binbin Pan, Jianhuang Lai*, Pong Chi YUEN

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)3028-3035
Number of pages8
JournalNeurocomputing
Volume74
Issue number17
DOIs
Publication statusPublished - Oct 2011

Scopus Subject Areas

  • Computer Science Applications
  • Cognitive Neuroscience
  • Artificial Intelligence

User-Defined Keywords

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

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