A Fixed-Point Online Kernel Principal Component Extraction Algorithm

Kernel principal component analysis (KPCA) is a powerful and widely applied nonlinear feature extraction technique. However, as originally proposed, KPCA may be cumbersome or infeasible in large-scale datasets, which motivated the development of low-complexity iterative extraction algorithms, mainly aiming image processing applications. Recently, some online KPCA extraction algorithms were proposed, but most of them suffer from low-convergence speed. This paper proposes a new algorithm based on fixed-point iterative equations for KPCA extraction, expanding kernel components using a compact dictionary, dynamically built from data, according to a user-defined accuracy parameter. The algorithm relies on simple equations, can track nonstationary environments, and requires reduced storage, enabling its use in real-time applications operating in low-cost embedded hardware. Results involving open-access image datasets show improved accuracy and convergence speed, as well as permitted effective improvements in practical image applications, as compared to state-of-art online KPCA techniques.