Covariance estimation in full- and reduced-dimensionality image classification

This paper introduces an estimation technique for covariance matrices. The method differs from previous estimators in specifying an application-dependent cost function, regularizing all classes in the same way then compensating for volume distortions via scale parameters, and allowing m-fold rather than leave-one-out cross-validation. It provides a systematic basis for parameter estimation in high-dimensional spaces, where there are inevitably far too few training samples for reliable parameter estimates from sample statistics only. This is demonstrated with standard classifiers using normal models in the high dimensional space of appearance-based image processing. When the models are trained with the new technique, face classification performance is significantly better than with unregularized covariances and with earlier regularized estimators. Dimensionality reduction is also improved when it uses a covariance structure estimated with the method.