Analysis of Chernoff Criterion for Linear Dimensionality Reduction
Document Type
Conference Proceeding
Publication Date
12-1-2010
Journal / Book Title
IEEE
Abstract
Well known linear discriminant analysis (LDA) based on the Fisher criterion is incapable of dealing with heteroscedasticity in data. However, in many practical applications we often encounter heteroscedastic data, i.e., within class scatter matrices can not be expected to be equal. A technique based on the Chernoff criterion for linear dimensionality reduction has been proposed recently. The technique extends well-known Fisher's LDA and is capable of exploiting information about heteroscedasticity in the data. While the Chernoff criterion has been shown to outperform the Fisher's, a clear understanding of its exact behavior is lacking. In addition, the criterion, as introduced, is rather complex, thereby making it difficult to clearly state its relationship to other linear dimensionality techniques. In this paper, we show precisely what can be expected from the Chernoff criterion and its relations to the Fisher criterion and Fukunaga-Koontz transform. Furthermore, we show that a recently proposed decomposition of the data space into four subspaces is incomplete. We provide arguments on how to best enrich the decomposition of the data space in order to account for heteroscedasticity in the data.
DOI
10.1109/ICSMC.2010.5641971
Montclair State University Digital Commons Citation
Peng, Jing; Robila, Stefan; Fan, Wei; and Seetharaman, Guna, "Analysis of Chernoff Criterion for Linear Dimensionality Reduction" (2010). Department of Computer Science Faculty Scholarship and Creative Works. 116.
https://digitalcommons.montclair.edu/compusci-facpubs/116
Published Citation
Peng, J., Robila, S., Fan, W., & Seetharaman, G. (2010, October). Analysis of chernoff criterion for linear dimensionality reduction. In 2010 IEEE International Conference on Systems, Man and Cybernetics (pp. 3014-3021). IEEE.