Multikernel adaptive filters with multiple dictionaries and regularization

We discuss a method of regularization and a construction method of dictionary which have a high degree of freedom within the framework of multikernel adaptive filtering. The multikernel adaptive filter is an extension of the kernel adaptive filter using multiple kernels. Hence, it has offers higher performance than the kernel adaptive filter. In this paper, we focus on the fact that the multikernel adaptive filter determines a subspace in the sum of multiple reproducing kernel Hilbert spaces (RKHSs) associated with different kernels. Based on this, we propose a novel method to individually select appropriate input signals in order to construct dictionary which determines the subspace. Furthermore, based on the fact that any unknown filter is an element in RKHS, we propose L₂ regularization in order to avoid overadaptation. Also, we derive an algorithm that fixes the dictionary size in order to construct an efficient adaptive algorithm. Numerical examples show the efficiency of the proposed method.