Ridge estimation of covariance matrix from data in two classes

Abstract

This paper deals with the problem of estimating a covariance matrix from the data in two classes: (1) good data with the covariance matrix of interest and (2) contamination coming from a Gaussian distribution with a different covariance matrix. The ridge penalty is introduced to address the problem of high-dimensional challenges in estimating the covariance matrix from the two-class data model. A ridge estimator of the covariance matrix has a uniform expression and keeps positive-definite, whether the data size is larger or smaller than the data dimension. Furthermore, the ridge parameter is tuned through a cross-validation procedure. Lastly, the proposed ridge estimator is verified with better performance than the existing estimator from the data in two classes and the traditional ridge estimator only from the good data.