Feature weighted mahalanobis distance: Improved robustness for Gaussian classifiers

Gaussian classifiers are strongly dependent on their underlying distance method, namely the Mahalanobis distance. Even though widely used, in the presence of noise this distance measure loses dramatically in performance, due to equal summation of the squared distances over all features. The features with large distance can mask all the other features so that the classification considers only these features, neglecting the information provided by the other features. To overcome this drawback we propose to weight the different features in the Mahalanobis distance according to their distances after the variance normalization. The idea behind this is to give less weight to noisy features and high weight to noise free features which are more reliable. Thereafter, we replace the traditional distance measure in a Gaussian classifier with the proposed. In a series of experiments we show the improved noise robustness of Gaussian classifiers by the proposed modifications in contrast to the traditional approach.