KERNEL-BASED TENSOR PARTIAL LEAST SQUARES FOR RECONSTRUCTION OF LIMB MOVEMENTS

We present a new supervised tensor regression method based on multi-way array decompositions and kernel ma-chines. The main issue in the development of a kernel-based framework for tensorial data is that the kernel functions have to be defined on tensor-valued input, which here is defined based on multi-mode product kernels and probabilistic gen-erative models. This strategy enables taking into account the underlying multilinear structure during the learning process. Based on the defined kernels for tensorial data, we develop a kernel-based tensor partial least squares approach for regres-sion. The effectiveness of our method is demonstrated by a real-world application, i.e., the reconstruction of 3D move-ment trajectories from electrocorticography signals recorded from a monkey brain. Index Terms — Tensors, kernels, partial least squares, ECoG, motion trajectory 1