2011 IEEE International Workshop on Machine Learning for Signal Processing September 18-21, 2011, Beijing, China 978-1-4577-1623-2/11/$26.00 c 2011 IEEE AN ADAPTIVE DECODER FROM SPIKE TRAINS TO MICRO-STIMULATION USING KERNEL LEAST-MEAN-SQUARES (KLMS) Lin Li, Il Memming Park, Sohan Seth, John S. Choi Joseph T. Francis, Justin C. Sanchez, and Jos´ e C. Pr´ ıncipe University of Florida, University of Miami SUNY Downstate Medical Center and NYU-Poly ABSTRACT This paper proposes a nonlinear adaptive decoder for so- matosensory 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 en- capsulates the statistical description of the point process that generates the spike trains, and bypasses the curse of dimensionality-resolution of the binned spike representa- tions. 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. Index Terms— Adaptive Neural decoder, KLMS, spike train, microstimulation 1. INTRODUCTION The rapid advance of microelectrode arrays and electrophys- iological recording techniques is promoting the simultaneous stimulation and recording of the spatiotemporal activities of hundreds of neurons. This opens up new opportunities to pre- cisely predict stimulus or reconstruct movement by observing and modeling neural responses at the single neuron or popu- lation level. Quantifying the information contained in neural spike trains is the fundamental step to design neural prosthet- ics and brain machine interfaces. In order to effectively apply machine learning algorithms to neural decoding, a significant step is to define an appropri- ate input space for the decoder. A variety of machine learning techniques have been applied on the discrete representations of spike train (binned data), such as statistical methods [1, 2], This work was supported in part by the U.S. National Science Founda- tion under Grant CNS-0540304, NSF Partnerships for Innovation Program 0650161, and Darpa project N66001-10-C-2008. kernel-based methods [3] etc. However, binned spike train representations (typically 50-100ms in duration) can impair the decoder time resolution of decoding models. Specifically, with a large bin size, a decoder will fail to reconstruct be- havior if it falls in a time range less than the bin size. For example, in the case of a somatosensory prosthesis, the time resolution of micro-stimulation signals used to create tactile sensation is small (0.2ms), which requires a small bin size (less than the width of the stimulus pulse). With such small bin size, the input space becomes sparse and dimensionality of the input space also becomes a problem. Alternatively, the vector of the spike times may be a more effective and accu- rate representation of spike trains. However, traditional ma- chine learning algorithms cannot be directly implemented on the vector of spike times because it exists in a space that has no natural metric [4]. However it is still possible to define positive definite functions in the spike train space [4]. To contend with such problems, the mathematical theory of reproducing kernel Hilbert space (RKHS) can be used to create a suitable inner product between two spike trains by using the nonlinear cross intensity kernel. This implicitly transforms a spike train into a continuous time function in the RKHS and opens up the possibility of applying any kernel- based machine learning algorithms directly on the spike time space. In addition to the representation space, another challenge of neural modeling is the complexity and noise inherent in the spike train structure due to the organization of the neural circuits and the functional links between the neural assem- blies [5]. It is essential that the model is capable of adaptively learning from new data to track nonstationarities. Therefore, this paper proposes an adaptive decoder with the KLMS al- gorithm [6] applied directly on the spike time input space, which performs adaptive nonlinear regression with a linear sample-by-sample adaption algorithm in the RKHS without converging to local minima, and can effectively track nonsta- tionarities. In this paper, this adaptive KLMS-based decoder of spike trains is applied to reconstruct continuous micro-stimulation for a sensory prosthesis on both synthetic and real data