Heteroscedastic Max-Min Distance Analysis for Dimensionality Reduction

Bing Su*, Xiaoqing Ding, Changsong Liu, Ying Wu

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Max-min distance analysis (MMDA) performs dimensionality reduction by maximizing the minimum pairwise distance between classes in the latent subspace under the homoscedastic assumption, which can address the class separation problem caused by the Fisher criterion but is incapable of tackling heteroscedastic data properly. In this paper, we propose two heteroscedastic MMDA (HMMDA) methods to employ the differences of class covariances. Whitened HMMDA extends MMDA by utilizing the Chernoff distance as the separability measure between classes in the whitened space. Orthogonal HMMDA (OHMMDA) incorporates the maximization of the minimal pairwise Chernoff distance and the minimization of class compactness into a trace quotient formulation with an orthogonal constraint of the transformation, which can be solved by bisection search. Two variants of OHMMDA further encode the margin information by using only neighboring samples to construct the intra-class and inter-class scatters. Experiments on several UCI datasets and two face databases demonstrate the effectiveness of the HMMDA methods.

Original languageEnglish (US)
Pages (from-to)4052-4065
Number of pages14
JournalIEEE Transactions on Image Processing
Issue number8
StatePublished - Aug 2018


  • Chernoff distance
  • Dimensionality reduction
  • class separation problem
  • max-min distance analysis
  • trace quotient

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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