Linear discriminant analysis with worst between-class separation and average within-class compactness

Abstract

Linear discriminant analysis (LDA) is one of the most popular supervised dimensionality reduction (DR) techniques and obtains discriminant projections by maximizing the ratio of average-case between-class scatter to averagecase within-class scatter. Two recent discriminant analysis algorithms (DAS), minimal distance maximization (MDM) and worst-case LDA (WLDA), get projections by optimizing worst-case scatters. In this paper, we develop a new LDA framework called LDA with worst between-class separation and average within-class compactness (WSAC) by maximizing the ratio of worst-case between-class scatter to averagecase within-class scatter. This can be achieved by relaxing the trace ratio optimization to a distance metric learning problem. Comparative experiments demonstrate its effectiveness. In addition, DA counterparts using the local geometry of data and the kernel trick can likewise be embedded into our framework and be solved in the same way.

Keywords

dimensionality reduction / linear discriminant analysis / the worst separation / the average compactness

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2014 Higher Education Press and Springer-Verlag Berlin Heidelberg