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Efficiently Learning the Metric with Side-Information

  • Tijl De Bie
  • Michinari Momma
  • Nello Cristianini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2842)

Abstract

A crucial problem in machine learning is to choose an appropriate representation of data, in a way that emphasizes the relations we are interested in. In many cases this amounts to finding a suitable metric in the data space. In the supervised case, Linear Discriminant Analysis (LDA) can be used to find an appropriate subspace in which the data structure is apparent. Other ways to learn a suitable metric are found in [6] and [11]. However recently significant attention has been devoted to the problem of learning a metric in the semi-supervised case. In particular the work by Xing et al. [15] has demonstrated how semi-definite programming (SDP) can be used to directly learn a distance measure that satisfies constraints in the form of side-information. They obtain a significant increase in clustering performance with the new representation. The approach is very interesting, however, the computational complexity of the method severely limits its applicability to real machine learning tasks. In this paper we present an alternative solution for dealing with the problem of incorporating side-information. This side-information specifies pairs of examples belonging to the same class. The approach is based on LDA, and is solved by the efficient eigenproblem. The performance reached is very similar, but the complexity is only O(d 3) instead of O(d 6) where d is the dimensionality of the data. We also show how our method can be extended to deal with more general types of side-information.

Keywords

Canonical Correlation Analysis Neural Information Processing System Generalize Eigenvalue Problem Rayleigh Quotient Generalize Eigenvector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Tijl De Bie
    • 1
  • Michinari Momma
    • 2
  • Nello Cristianini
    • 3
  1. 1.Department of Electrical Engineering ESAT-SCDKatholieke Universiteit LeuvenLeuvenBelgium
  2. 2.Department of Decision Sciences and Engineering SystemsRensselaer Polytechnic InstituteTroyUSA
  3. 3.Department of StatisticsUniversity of California, DavisDavisUSA

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