Multiclass discriminant analysis via adaptive weighted scheme

Under homoscedastic Gaussian assumption, it is demonstrated that conventional LDA is formulated by maximizing the weighted arithmetic mean of the Kullback–Leibler (KL) divergences between different classes. However, the calculation of projection directions is dominated by class pairs with large KL divergence, which causes class pairs with small KL divergence overlapping in the low-dimensional subspace when the dimensionality of subspace is strictly lower than c−1, wherein c is the class number. Therefore, the classification accuracy is degraded significantly when dealing with classification task. In this paper, we propose a novel method, namely Multiclass Discriminant Analysis via Adaptive Weighted Scheme (MDAAWS), to alleviate the problem mentioned above by assigning weights to all between-class pairs adaptively. Since the proposed problem is a challenging task, an iterative algorithm is exploited to solve it and the corresponding theoretical analysis is presented as well. Extensive experiments conducted on various data sets demonstrate the effectiveness of MDAAWS when compared with some state-of-the-art supervised dimensionality reduction methods.