Dictionary-based online kernel principal subspace analysis with double orthogonality preservation

An adaptive online algorithm with a dictionary of observed signals for kernel principal subspace analysis is presented. A coefficient matrix for eigenfunctions is updated by a recursive least squares (RLS)-type algorithm and entries in the dictionary are adaptively added / removed preserving orthogonality of the eigenfunctions. It is shown that the orthogonalization can be implemented by analytically solvable (generalized) eigenvalues of 2×2 matrices, instead of the computation of the inverse squared root of matrix having the size of the dictionary. Numerical example is then illustrated to support the analysis.