Incremental generalized multiple maximum scatter difference with applications to feature extraction

In this paper, we propose a new algorithm to implement the generalized multiple maximum scatter difference (GMMSD). Due to enhanced features of this algorithm over the original GMMSD, we named it GMMSD+. By employing a different projection from both the range of the between-class scatter matrix and the null space of the within-class scatter matrix, GMMSD+ can divide the centroid vector of each class into two components: intrinsic common component (ICC) and discriminant difference component (DCC), and then automatically discards ICC which contains little discriminative information, while keeping DCC which contains the true discriminative power. Next, we introduce a practical implementation of GMMSD+, which can accurately and efficiently update the discriminant vectors with new training samples incrementally, eliminating the complete re-computation of the training process. Our experiments demonstrate that incremental version of GMMSD+(IGMMSD+) eliminates the complete re-computation of the training process when new training samples are presented, leading to significantly reduced computational cost.