Learning kernels from indefinite similarities

  • Authors:
  • Yihua Chen;Maya R. Gupta;Benjamin Recht

  • Affiliations:
  • University of Washington, Seattle, WA;University of Washington, Seattle, WA;California Institute of Technology, Pasadena, CA

  • Venue:
  • ICML '09 Proceedings of the 26th Annual International Conference on Machine Learning
  • Year:
  • 2009

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Abstract

Similarity measures in many real applications generate indefinite similarity matrices. In this paper, we consider the problem of classification based on such indefinite similarities. These indefinite kernels can be problematic for standard kernel-based algorithms as the optimization problems become non-convex and the underlying theory is invalidated. In order to adapt kernel methods for similarity-based learning, we introduce a method that aims to simultaneously find a reproducing kernel Hilbert space based on the given similarities and train a classifier with good generalization in that space. The method is formulated as a convex optimization problem. We propose a simplified version that can reduce overfitting and whose associated convex conic program can be solved efficiently. We compare the proposed simplified version with six other methods on a collection of real data sets.