Linear discriminant analysis with worst between-class separation and average within-class compactness
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 average-case 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 average-case 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.
Keywordsdimensionality reduction linear discriminant analysis the worst separation the average compactness
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- 10.Cai D. He X. Kun Z. Han J. Bao H. Local sensitive discriminant analysis. In Proceedings of the international joint conference on artificial intelligence. 2007, 141–146Google Scholar
- 12.Xu B. Huang K. Liu C. Dimensionality reduction by minimal distance maximization. In: Proceedings of 20th International Conference on Pattern Recognition, 2010, 569–572Google Scholar
- 13.Zhang Y. Yeung D. Worst-case linear discriminant analysis. In: Proceedings of Advances in Neural Information Processing Systems. 2010, 2568–2576Google Scholar
- 20.Frank A. Asuncion A. UCI Machine Learning Repository. http://archive.ics.uci.edu/ml
- 22.Martinez A. Benavente R. The AR-face database. Technical Report 24, CVC, 1998. http://www2.ece.ohiostate.edu/?aleix/ARdatabase.html Google Scholar
- 23.Nene S. Nayar S. Murase H. Columbia Object Image Library (COIL-20). Technical Report005, CUCS, 1996. http://www1.cs.columbia.edu/CAVE/software/softlib/coil-20.php Google Scholar