Impact of feature correlations on separation between bivariate normal distributions

The impact of feature correlations on class separation has received limited attention from researchers. Previous reports treat the problem from the viewpoint of multi-classifier fusion and are partially inconsistent in their conclusions. In this paper we show that these ambiguities are the result of incompatible basic assumptions, and that the conclusions from prior art hold only for specific configurations of class-conditional distributions. We show that the impact of feature correlations on class separation between two bivariate normal distributions can be positive or negative, and that it can only be gauged in the context of the parameters of involved marginals. The findings reported in this paper are of importance for the practice of feature extraction, feature selection, and in multi-classifier fusion.