A novel linear discriminant analysis based on alternate ratio sum minimization

Linear discriminant analysis (LDA) and its variants are popular supervised dimension reduction methods, which have been widely used to handle high-dimensional data. Since most of previous LDA methods are developed based on the trace ratio (TR) criterion, they usually obtain the low-dimensional data feature with weak discriminative ability, due to the projections with small variance. The ratio sum (RS) criterion was developed to alleviate this drawback. However, the conventional ratio sum is formulated to maximize the arithmetic mean of items which suffers from the domination of the largest objectives and might deteriorate the recognition accuracy in practical applications. In this paper, a novel ratio sum minimization based linear discriminant analysis (RSM-LDA) method is proposed in this paper. Specifically, a new ratio sum minimization (RSM) criterion is developed, which is based on the properties of the harmonic mean and effectively avoids the dominance problem to discover more discriminative features of the data. However, obtaining a closed solution for the RSM-LDA problem is challenging. For this purpose, three optimization methods are used to solve the optimization problem of RSM-LDA, and the inherent relationships between the methods are discussed. Experimental results demonstrate that the proposed RSM-LDA method has better performance in classification tasks on several datasets, when compared with some comparison methods based dimensionality reduction methods. In addition, combined with other experimental results, the effectiveness of RSM-LDA was verified.