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Linear discriminant analysis with worst between-class separation and average within-class compactness
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Journal Article
Linear discriminant analysis with worst between-class separation and average within-class compactness
2014
Overview
Linear discriminant analysis （LDA） is one of the most popular supervised dimensionality reduction （DR） tech- niques and obtains discriminant projections by maximizing the ratio of average-case between-class scatter to average- case within-class scatter. Two recent discriminant analysis algorithms （DAS）, minimal distance maximization （MDM） and worst-case LDA （WLDA）, get projections by optimiz- ing 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 maximiz- ing the ratio of worst-case between-class scatter to average- case within-class scatter. This can be achieved by relaxing the trace ratio optimization to a distance metric learning prob- lem. 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 frame- work and be solved in the same way.
Publisher
Higher Education Press,Springer Nature B.V
Subject
