Discriminatory Data Mapping by Matrix-Based Supervised Learning Metrics

  • M. Strickert
  • P. Schneider
  • J. Keilwagen
  • T. Villmann
  • M. Biehl
  • B. Hammer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5064)

Abstract

Supervised attribute relevance detection using cross-comparisons (SARDUX), a recently proposed method for data-driven metric learning, is extended from dimension-weighted Minkowski distances to metrics induced by a data transformation matrix Ω for modeling mutual attribute dependence. Given class labels, parameters of Ω are adapted in such a manner that the inter-class distances are maximized, while the intra-class distances get minimized. This results in an approach similar to Fisher’s linear discriminant analysis (LDA), however, the involved distance matrix gets optimized, and it can be finally utilized for generating discriminatory data mappings that outperform projection pursuit methods with LDA index. The power of matrix-based metric optimization is demonstrated for spectrum data and for cancer gene expression data.

Keywords

Supervised feature characterization adaptive matrix metrics attribute dependence modeling projection pursuit LDA 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • M. Strickert
    • 1
  • P. Schneider
    • 2
  • J. Keilwagen
    • 1
  • T. Villmann
    • 3
  • M. Biehl
    • 2
  • B. Hammer
    • 4
  1. 1.Leibniz Institute of Plant Genetics and Crop Plant Research Gatersleben 
  2. 2.Institute for Mathematics and Computing ScienceUniversity of Groningen 
  3. 3.Research group Computational IntelligenceUniversity of Leipzig 
  4. 4.Institute of Computer ScienceTechnical University of Clausthal 

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