Learning the kernel matrix in discriminant analysis via quadratically constrained quadratic programming

Jieping Ye, Shuiwang Ji, Jianhui Chen

Research output: Chapter in Book/Report/Conference proceedingConference contribution

19 Scopus citations

Abstract

The kernel function plays a central role in kernel methods. In this paper, we consider the automated learning of the kernel matrix over a convex combination of pre-specified kernel matrices in Regularized Kernel Discriminant Analysis (RKDA), which performs lineardiscriminant analysis in the feature space via the kernel trick. Previous studies have shown that this kernel learning problem can be formulated as a semidefinite program (SDP), which is however computationally expensive, even with the recent advances in interior point methods. Based on the equivalence relationship between RKDA and least square problems in the binary-class case, we propose a Quadratically Constrained Quadratic Programming (QCQP) formulation for the kernel learning problem, which can be solved more efficiently than SDP. While most existing work on kernel learning deal with binary-class problems only, we show that our QCQP formulation can be extended naturally to the multi-class case. Experimental results on both binary-class and multi-class benchmarkdata sets show the efficacy of the proposed QCQP formulations.

Original languageEnglish (US)
Title of host publicationKDD-2007
Subtitle of host publicationProceedings of the Thirteenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
Pages854-863
Number of pages10
DOIs
StatePublished - Dec 14 2007
EventKDD-2007: 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining - San Jose, CA, United States
Duration: Aug 12 2007Aug 15 2007

Publication series

NameProceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining

Other

OtherKDD-2007: 13th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining
CountryUnited States
CitySan Jose, CA
Period8/12/078/15/07

Keywords

  • Convex optimization
  • Kernel discriminant analysis
  • Kernel learning
  • Model selection
  • Quadratically constrained quadratic programming

ASJC Scopus subject areas

  • Software
  • Information Systems

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  • Cite this

    Ye, J., Ji, S., & Chen, J. (2007). Learning the kernel matrix in discriminant analysis via quadratically constrained quadratic programming. In KDD-2007: Proceedings of the Thirteenth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (pp. 854-863). (Proceedings of the ACM SIGKDD International Conference on Knowledge Discovery and Data Mining). https://doi.org/10.1145/1281192.1281283