An Approximate Version of Kernel PCA

Abstract

We propose an analog of kernel principal component analysis (kernel PCA). Our algorithm is based on an approximation of PCA which uses Gram-Schmidt orthonormalization. We combine this approximation with support vector machine kernels to obtain a nonlinear generalization of PCA. By using our approximation to PCA we are able to provide a more easily computed (in the case of many data points) and readily interpretable version of kernel PCA. After demonstrating our algorithm on some examples, we explore its use in applications to fluid flow and microarray data