Robust linear discriminant analysis with a Laplacian assumption on projection distribution

Linear discriminant analysis (LDA) is typically carried out using Fisher's method, which relies heavily on the estimation of sample mean vectors and covariance matrices. However, Fisher LDA is vulnerable to outliers as it happens to other multivariate statistical methods. In this paper, we analyzed the optimal discriminant design based on the criterion of minimizing total misclassification rate, assuming that the projected samples follow Laplacian distribution. The corresponding optimization objective can be approximated as a linear programming problem. We illustrated the relations of our proposed discriminant to Fisher LDA and minimax probability machine (MPM) from the perspective of projection-pursuit. Experiments on 6 real world benchmark dataset from UCI repository validate the effectiveness of our method.