A new discriminant analysis based on boundary/non-boundary pattern separation

In this paper, we propose a new discriminant analysis, named as linear boundary discriminant analysis (LBDA), which increases the class separability by differently emphasizing the boundary and non-boundary patterns. This is achieved by defining two novel scatter matrices and solving eigenproblem on the criterion described by these scatter matrices. As a result, the classification performance using the extracted features can be improved. This effectiveness of LBDA is theoretically explained by reformulating scatter matrices in pairwise form. In addition, LBDA can extract larger number of features than original LDA. The experiments are conducted to show the performance of LBDA, and the result shows that LBDA can outperform other algorithms in most cases.