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We propose a novel multikernel adaptive filtering algorithm based on the iterative projections in the sum space of reproducing kernel Hilbert spaces. We employ linear and Gaussian kernels, envisioning an application to partially-linear-system identification/estimation. The algorithm is derived by reformulating the hyperplane projection along affine subspace (HYPASS) algorithm in the sum space. The...
Learning based on kernel machines is widely known as a powerful tool for various fields of information science including signal processing such as function estimation from finite sampling points. One of central topics of kernel machines is model selection, especially selection of a kernel or its parameters. In our previous works, we investigated the generalization error of a model space itself corresponding...
In this paper, we discuss the moment problem of g-frames in Hilbert spaces. Firstly, we give the definition of moment problem which is based on operators, and discuss the necessary and sufficient conditions of the existence of its solution. Secondly, we discuss its best approximative solution by orthogonal projection when it has no exact solution.
Theoretical analyses on generalization error of a model space for kernel regressors with respect to training samples are given in this paper. In general, the distance between an unknown true function and a model space tends to be small with a larger set of training samples. However, it is not clarified that a larger set of training samples achieves a smaller difference at each point of the unknown...
During vector predictive coding of digital signal series, the vector signal series, obtained by grouping adjacent samples of sources signal series, can approximate to a vector autoregressive series with stable covariance. This paper, applying the orthogonal projection principle of Hilbert space, attempts to formulate a vector predictive coding strategy highly capable of parallel processing and to...
Orthogonal projections onto the intersection of subspaces are useful in signal processing algorithms including iterative decoding of linear dispersion codes for an unknown MIMO channels and equalization for wireless communication systems. The von Neumann-Halperin method of alternating projections (MAP) is an iterative algorithm for determining the orthogonal projection of a given vector in a Hilbert...
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