Pareto discriminant analysis

摘要: Linear Discriminant Analysis (LDA) is a popular tool for multiclass discriminative dimensionality reduction. However, LDA suffers from two major problems: (1) It only optimizes the Bayes error case of unimodal Gaussian classes with equal covariances (assuming full rank matrices) and, (2) The extension maximizes sum pairwise distances between classes, and does not “simultaneously” maximize each distance classes. This typically results in serious overlapping projected space that are “close” input space. To solve these problems, this paper proposes Pareto (PARDA). Firstly, PARDA explicitly models as multidimensional sample covariance. Secondly, decomposes problem to set objective functions representing different Unlike existing extensions Fisher discriminant analysis (FDA) simultaneously distance, thus encouraging all equidistant other lower dimensional Solving multiobjective optimization – optimizing more than one, possibly conflicting, resulting solution known be “Pareto Optimal”. Experimental on synthetic data, several image data sets UCI repository show positive favor when compared standard state-of-the-art LDA.