An adaptive method for combined covariance estimation and classification

In this paper a family of adaptive covariance estimators is proposed to mitigate the problem of limited training samples for application to hyperspectral data analysis in quadratic maximum likelihood classification. These estimators are the combination of adaptive classification procedures and regularized covariance estimators. In these proposed estimators, the semi-labeled samples (whose labels are determined by a decision rule) are incorporated in the process of determining the optimal regularized parameters and estimating those supportive covariance matrices that formulate final regularized covariance estimators. In all experiments with simulated and real remote sensing data, these proposed combined covariance estimators achieved significant improvement on statistics estimation and classification accuracy over conventional regularized covariance estimators and an adaptive Maximum Likelihood classifier (MLC). The degree of improvement increases with dimensions, especially for ill-posed or very ill-posed problems where the total number of training samples is smaller than the number of dimensions.