Novel Fisher discriminant classifiers

At the present, several applications need to classify high dimensional points belonging to highly unbalanced classes. Unfortunately, when the training set cardinality is small compared to the data dimensionality (''small sample size'' problem) the classification performance of several well-known classifiers strongly decreases. Similarly, the classification accuracy of several discriminative methods decreases when non-linearly separable, and unbalanced, classes are treated. In this paper we firstly survey state of the art methods that employ improved versions of Linear Discriminant Analysis (LDA) to deal with the above mentioned problems; secondly, we propose a family of classifiers based on the Fisher subspace estimation, which efficiently deal with the small sample size problem, non-linearly separable classes, and unbalanced classes. The promising results obtained by the proposed techniques on benchmark datasets and the comparison with state of the art predictors show the efficacy of the proposed techniques.