Two-dimensional Bhattacharyya bound linear discriminant analysis with its applications

The recently proposed L2-norm linear discriminant analysis criterion based on Bhattacharyya error bound estimation (L2BLDA) was an effective improvement over linear discriminant analysis (LDA) and was used to handle vector input samples. When faced with two-dimensional (2D) inputs, such as images, converting two-dimensional data to vectors, regardless of the inherent structure of the image, may result in some loss of useful information. In this paper, we propose a novel two-dimensional Bhattacharyya bound linear discriminant analysis (2DBLDA). 2DBLDA maximizes the matrix-based between-class distance, which is measured by the weighted pairwise distances of class means and minimizes the matrix-based within-class distance. The criterion of 2DBLDA is equivalent to optimizing the upper bound of the Bhattacharyya error. The weighting constant between the between-class and within-class terms is determined by the involved data that make the proposed 2DBLDA adaptive. The construction of 2DBLDA avoids the small sample size (SSS) problem, is robust, and can be solved through a simple standard eigenvalue decomposition problem. The experimental results on image recognition and face image reconstruction demonstrate the effectiveness of 2DBLDA.