Regularized covariance estimators for hyperspectral data classification and its application to feature extraction

The main purpose of this work is to find an improved regularized covariance estimator of each class with the advantages of LOOC, and BLOOC, which are useful for high dimensional pattern recognition problems. The searching ranges of LOOC and BLOOC are between the linear combinations of three pair covariance estimators. The first proposed covariance estimator (mixed-LOOC1) extended the searching range and is a general case of LOOC and BLOOC. By observing that the optimal value of leave-one-out likelihood function of LOOC usually occurs at near the end point of the parameter domain, the second covariance estimator (mixed-LOOC2), which needs less computation, was proposed. Using the proposed covariance estimator to improve the linear feature extraction methods when the multivariate data are singular or nearly so is demonstrated.