Coupled Regularized Sample Covariance Matrix Estimator for Multiple Classes

The estimation of covariance matrices multiple classes with limited training data is a difficult problem. sample matrix (SCM) known to perform poorly when the number variables large compared available samples. In order reduce mean squared error (MSE) SCM, regularized (shrinkage) SCM estimators are often used. this work, we consider (RSCM) for multiclass problems that couple together two different target regularization: pooled (average) and scaled identity matrix. Regularization toward beneficial population covariances similar, whereas regularization guarantees positive definite. We derive MSE optimal tuning parameters as well propose method their under assumption class populations follow (unspecified) elliptical distributions finite fourth-order moments. performance proposed coupled RSCMs evaluated simulations in discriminant analysis (RDA) classification set-up on real data. results based three sets indicate comparable cross-validation but significant speed-up computation time.