Adaptive weighted multiclass linear discriminant analysis

In this paper, we propose a novel linear dimension reduction method called Adaptive Weighted Multiclass Linear Discriminant Analysis (AWMLDA). The proposed approach is based on the Fisher’s linear discriminant analysis (FLDA), which maximizes the ratio of the sum of the between-class scatter and the within-class scatter. Since the projection direction of FLDA overemphasized the large class distances that causing the classes with small distances are still closed in the subspace, the solution of FLDA is suboptimal for the multiclass problem. In the proposed method, firstly our method learn the transform matrix by measuring the between-class scatter and the within-class scatter of every pairwise classes rather than the sum measurement, and we use the square root of the inverse covariance matrix ∑^−1/2 to replace the original within-class matrix. The method of AWMLDA considers every distances of each pairwise, unlike MMDA [1] and WLDA [2] considered the minimum between/maximum within class distances respectively. Secondly, we assign the weights for each pairwise to balance the distances between each pairwise in the subspace and they can be updated with the Cauchy-Schwarz inequality adaptively. The distances of weighted pairwise are more close in the subspace such that the neighboring classes can be separated as well. Finally, we derive an efficient algorithm to solve the optimization problem, and give the theoretical analysis in detail. Experimental results demonstrate the effectiveness of AWMLDA when compared with some other well-known multiclass LDA methods.