Abstract

Principal Component Analysis (PCA) is one of the most pop- ular techniques for dimensionality reduction of multivariate data points with application areas covering many branches of science. However, con- ventional PCA handles the multivariate data in a discrete manner only, i.e., the covariance matrix represents only sample data points rather than higher-order data representations. In this paper we extend conventional PCA by proposing techniques for constructing the covariance matrix of uniformly sampled continuous re- gions in parameter space. These regions include polytops defined by convex combinations of sample data, and polyhedral regions defined by intersection of half spaces. The applications of these ideas in practice are simple and shown to be very efiective in providing much superior generalization properties than conventional PCA for appearance-based recognition applications.