Adaptive kernel principal component analysis

An adaptive kernel principal component analysis (AKPCA) method, which has the flexibility to accurately track the kernel principal components (KPC), is presented. The contribution of this paper may be divided into two parts. First, KPC are recursively formulated to overcome the batch nature of standard kernel principal component analysis (KPCA). This formulation is derived from the recursive eigendecomposition of kernel covariance matrix and indicates the KPC variation caused by the new data. Second, kernel covariance matrix is correctly updated to adapt to the changing characteristics of data. In this adaptive method, the KPC is adaptively adjusted without re-eigendecomposing the kernel Gram matrix. The proposed method not only maintains constant update speed and memory usage as the data-size increases, but also alleviates sub-optimality of the KPCA method for non-stationary data. Experiments for simulation data and real applications are detailed to assess the utility of the proposed method. The results demonstrate that our approach yields improvements in terms of both computational speed and approximation accuracy.