The  Weizmann  Institute  of  Science
Faculty of Mathematics and Computer Science
 

Vision and Robotics Seminar

Anat Levin
School of Computer Science and Engineering
The Hebrew University
 

will speak on
 

Principal Component Analysis Over Continuous Subspaces
and Intersection of Half-spaces

Abstract:
Principal Component Analysis (PCA) is one of the most popular techniques for dimensionality reduction of multivariate data points with application are as covering many branches of science. The fundamental technique has been extended in a variety of ways including non-linear variants of PCA, combination of local linear PCA, mixture models for PCA, and probabilistic models for PCA. However, conventional 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 work we extend conventional PCA by proposing techniques for constructing the covariance matrix of uniformly sampled continuous regions in parameter space.  These regions include polytops defined by convex combinations of sample data, and polyhedral regions defined by the intersection of half spaces.  The application of these ideas in practice are simple and shown to be very effective in providing much superior generalization properties than conventional PCA for appearance-based recognition applications.

Joint work with Amnon Shashua.

The lecture will take place in the
Lecture Hall, Room 1, Ziskind Building
on Thursday, June 6, 2002
at noon