Nonlinear Manifold Based Discriminant Analysis for Face Recognition

Manifolds are mathematical spaces whose points have Euclidean neighborhoods, but whose global structure could be more complex. A one dimensional manifold has a neighborhood that resembles a line. A two dimensional one resembles a plane. If we consider a one dimensional example, most system neighborhoods cannot be represented optimally by a straight line. A multi-ordered nonlinear line would be better suited to represent most data. A learning algorithm to model the pipeline, based on Fischer Linear Discriminant (FLD), using least squares estimation is presented in this paper. Face patterns are known to show continuous variability. Yet face images of one individual tend to cluster together and can be considered as a neighborhood. Such similar patterns form a pipeline in state space that can be used for pattern classification. Multiple patterns can be trained by having separate lines for each pattern. Face points are now projected onto a low-dimensional mean nonlinear pipe-line, thus providing an easy intuitive way to place new points. Given a test point/face, the classification problem is now simplified to checking the nearest neighbors. This can be done by finding the minimum distance pipe-line from the test-point. The proposed representation of a face image results in improved accuracy when compared to the classical point representation.