Exponential Multi-Modal Discriminant Feature Fusion for Small Sample Size

Multi-modal Canonical Correlation Analysis (MCCA) is an important information fusion method, and some discriminant variations of MCCA have been proposed. However, the variations suffer from the Small Sample Size (SSS) problem and the absence of cross-modal discriminant scatters. Thus we propose a novel exponential multi-modal discriminant feature fusion method for a small amount of training samples, i.e. exponential multi-modal discriminant correlation analysis. In the method, we construct a discriminative integration scatter of all the modalities by constraining the aggregation towards cross-modal discriminative centroids. Besides, the method gives a decomposition-based matrix exponential strategy. The strategy can solve the SSS problem and improve the robustness of noises, and we further provide corresponding theoretical proofs and some intuitive analysis. The method can learn correlation fusion features with well discriminative power from a small amount of samples. Encouraging experimental results show the effectiveness and robustness of our method.