Heteroscedastic Max-min Distance Analysis

Many discriminant analysis methods such as LDA and HLDA actually maximize the average pairwise distances between classes, which often causes the class separation problem. Max-min distance analysis (MMDA) addresses this problem by maximizing the minimum pairwise distance in the latent subspace, but it is developed under the homoscedastic assumption. This paper proposes Heteroscedastic MMDA (HMMDA) methods that explore the discriminative information in the difference of intra-class scatters for dimensionality reduction. WHMMDA maximizes the minimal pairwise Chenoff distance in the whitened space. OHMMDA incorporates this objective and the minimization of class compactness into a trace quotient formulation and imposes an orthogonal constraint to the final transformation, which can be solved by a bisection search algorithm. Two variants of OHMMDA are further proposed to encode the margin information. Experiments on several UCI Machine Learning datasets and the Yale Face database demonstrate the effectiveness of the proposed HMMDA methods.