Reverse nearest neighbors Bhattacharyya bound linear discriminant analysis for multimodal classification

Recently, an effective improvement of linear discriminant analysis (LDA) called L2-norm linear discriminant analysis via the Bhattacharyya error bound estimation (L2BLDA) was proposed in its adaptability and nonsingularity. However, L2BLDA assumes all samples from the same class are independently identically distributed (i.i.d.). In real world, this assumption sometimes fails. To solve this problem, in this paper, reverse nearest neighbor (RNN) technique is imbedded into L2BLDA and a novel linear discriminant analysis named RNNL2BLDA is proposed. Rather than using classes to construct within-class and between-class scatters, RNNL2BLDA divides each class into subclasses by using RNN technique, and then defines the scatter matrices on these classes that may contain several subclasses. This makes RNNL2BLDA get rid of the i.i.d.assumption in L2BLDA and applicable to multimodal data, which have mixture of Gaussian distributions. In addition, by setting a threshold in RNN, RNNL2BLDA achieves robustness. RNNL2BLDA can be solved through a simple standard generalized eigenvalue problem. Experimental results on an artificial data set, some benchmark data sets as well as two human face databases demonstrate the effectiveness of the proposed method.