Principal Component Analysis over Continuous Subspaces and Intersection of Half-Spaces

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 de ned by convex combinations of sample data and polyhedral regions de ned by intersection of half spaces The applications of these ideas in practice are simple and shown to be very e ective in providing much superior generalization properties than conventional PCA for appearance based recognition applications