Adaptive inverse control of neural spatiotemporal spike patterns with a reproducing kernel Hilbert space (RKHS) framework.
This paper proposes a nonlinear adaptive decoder for somatosensory micro-stimulation based on the kernel least mean square (KLMS) algorithm applied directly on the space of spike trains. Instead of using a binned representation of spike trains, we transform the vector of spike times into a function in reproducing kernel Hilbert space (RKHS), where the inner product of two spike time vectors is defined by a nonlinear cross intensity kernel. This representation encapsulates the statistical description of the point process that generates the spike trains, and bypasses the curse of dimensionality-resolution of the binned spike representations. We compare our method with two other methods based on binned data: GLM and KLMS, in reconstructing biphasic micro-stimulation. The results indicate that the KLMS based on RKHS for spike train is able to detect the timing, the shape and the amplitude of the biphasic stimulation with the best accuracy.