Multi-regularization Parameters Estimation for Gaussian Mixture Classifier based on MDL Principle

Regularization is a solution to solve the problem of unstable estimation of covariance matrix with a small sample set in Gaussian classifier. And multi-regularization parameters estimation is more difficult than single parameter estimation. In this paper, KLIM_L covariance matrix estimation is derived theoretically based on MDL (minimum description length) principle for the small sample problem with high dimension. KLIM_L is a generalization of KLIM (Kullback-Leibler information measure) which considers the local difference in each dimension. Under the framework of MDL principle, multi-regularization parameters are selected by the criterion of minimization the KL divergence and estimated simply and directly by point estimation which is approximated by two-order Taylor expansion. It costs less computation time to estimate the multi-regularization parameters in KLIM_L than in RDA (regularized discriminant analysis) and in LOOC (leave-one-out covariance matrix estimate) where cross validation technique is adopted. And higher classification accuracy is achieved by the proposed KLIM_L estimator in experiment.