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It is widely recognized that the kernel-based learning scheme is one of powerful tools in the field of machine learning. Recently, learning with multiple kernels, instead of a single kernel, attracts much attention in this field. Although their efficacy was investigated in terms of practical sense, their theoretical grounds were not sufficiently discussed in the past studies. In our previous work,...
The existence and uniqueness conditions of quaternion reproducing kernel Hilbert spaces (QRKHS) are established in order to provide a mathematical foundation for the development of quaternion-valued kernel learning algorithms. This is achieved through a rigorous account of left quaternion Hilbert spaces, which makes it possible to generalise standard RKHS to quaternion RKHS. Quaternion versions of...
We present a novel estimation algorithm for filtering and regression with a number of advantages over existing methods. The algorithm has wide application in robotics as no assumptions are made about the underlying distributions, it can represent non-Gaussian multi-modal posteriors, and learn arbitrary non-linear models from noisy data. Our method is a generalisation of the Kernel Bayes' Rule that...
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