In several pattern recognition problems, particularly in image recognition ones, there are often a large number of features available, but the number of training samples for each pattern is significantly less than the dimension of the feature space. This statement implies that the sample group covariance matrices often used in the Gaussian maximum probability classifier are singular. A common s...

Covariances play a fundamental role in the theory of time series and they are critical quantities that are needed in both spectral and time domain analysis. Estimation of covariance matrices is needed in the construction of confidence regions for unknown parameters, hypothesis testing, principal component analysis, prediction, discriminant analysis among others. In this paper we consider both l...

In this paper we present diierent approaches to structur-ing covariance matrices within statistical classiiers. This is motivated by the fact that the use of full covariance matrices is infeasible in many applications. On the one hand, this is due to the high number of model parameters that have to be estimated, on the other hand the computational complexity of a classiier based on full covaria...

This paper studies the effect of covariance regularization for classification of high-dimensional data. This is done by fitting a mixture of Gaussians with a regularized covariance matrix to each class. Three data sets are chosen to suggest the results are applicable to any domain with high-dimensional data. The regularization needs of the data when pre-processed using the dimensionality reduct...