Kernel discrimination via oblique projection

Classifier design plays a paramount role in pattern recognition. Previously, we set the problem in the framework of function approximation, wherein a classifier is assumed to be an element of a reproducing kernel Hilbert space continuously defined on the pattern feature space, and adopted orthogonal projection criteria for classifier design. In practice, subspaces spanned by features of different classes are not necessarily orthogonal to each other. And thus we consider here to discriminate a pattern class called the target class from other classes, by obliquely projecting a pattern feature vector onto the subspace spanned by the training pattern features of the target class, along the subspace spanned by those of other classes. In addition, we extend the discrimination algorithm to a nonlinear version using the related reproducing kernel. Experimental results on face recognition are presented to demonstrate the feasibility of the presented algorithm for pattern classification.