Adaptive KPCA Modeling of Nonlinear Systems

This paper proposes an adaptive algorithm for kernel principal component analysis (KPCA). Compared to existing work: (i) the proposed algorithm does not rely on assumptions, (ii) combines the up- and downdating step to become a single operation, (iii) the adaptation of the eigendecompsition can, computationally, reduce to O(N) and (iv) the proposed algorithm is more accurate. To demonstrate these benefits, the proposed adaptive KPCA, or AKPCA, algorithm is contrasted with existing work in terms of accuracy and efficiency. The article finally presents an application to an industrial data set showing that the adaptive algorithm allows modeling time-varying and non-stationary process behavior.