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On the separation of classes: can the Fisher criterion be improved upon when classes have unequal variance–covariance structure?

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Abstract

A value of class separation can be used as a criterion to optimize data-analytical protocols for multivariate classification problems. The Fisher criterion assumes equal variance–covariance structure, an assumption which is often violated in real datasets. The practical consequences of using the Fisher criterion compared to exploiting the variance–covariance differences has not been studied previously. Here, we show that about 50 samples are required to benefit from using the unequal variance–covariance structures for estimating class separation in two dimensions and more samples are required in higher dimensions. The results show that the Fisher criterion is robust and accurate for selection between pre-treatments compared to a newly derived criterion called the Cooke criterion. Copyright © 2010 John Wiley & Sons, Ltd.