Incremental Kernel Principal Component Analysis

Abstract

The kernel principal component analysis (KPCA) has been applied in numerous image-related machine learning applications and it has exhibited superior performance over previous approaches, such as PCA. However, the standard implementation of KPCA scales badly with the problem size, making computations for large problems infeasible. Also, the "batch" nature of the standard KPCA computation method does not allow for applications that require online processing. This has somewhat restricted the domains in which KPCA can potentially be applied. This paper introduces an incremental computation algorithm for KPCA to address these two problems. The basis of the proposed solution lies in computing incremental linear PCA in the kernel induced feature space, and constructing reduced-set expansions to maintain constant update speed and memory usage. We also provide experimental results which demonstrate the effectiveness of the approach.