The following paper proposes a set of novel feature selection criteria that can be applied to kernel Principal Component Analysis (kPCA) outcome to derive discriminative feature spaces for complex classification problems, such as biometric recognition tasks. The proposed class-separation criteria that are used to evaluate distributions of samples, which are projected onto nonlinear most discriminative directions, are modifications of Fisher Linear Discriminant (FLD). The modifications include reformulation of a basic class separation index that addresses the case of multi-modal class distributions and introduction of information regarding sample distribution skewness into the corresponding feature assessment criterion. It has been shown that class discrimination performance of the proposed scheme is better than in case of an application of a basic FLD scheme.