A K-Medoids based Point-Process Modeling on Neural Spike Transformation using Binless Kernel

A neural prosthesis is designed to compensate for cognitive functional losses by modeling the information transmission among cortical areas. Existing methods generally build a generalized linear model to approximate the nonlinear transformation among two areas, and use the temporal information of the neural spike with low efficiency. It is essential to efficiently model the nonlinearity embedded in spike generation and transmission for the real-time. This paper proposes a nonlinear point-process model to describe spike-in and spike-out transformation using the theory of reproducing kernel Hilbert space (RKHS) and the binless kernel on spike trains. The binless kernel efficiently maps exact spike timing information to the RKHS to describe nonlinear transformations with global minimum regardless of the weight initialization. A streaming K-medoids algorithm is introduced to select typical and important features in this nonlinear binless kernel for further modeling. We test our model on the nonlinearly generated synthetic neural spike trains, and compare with the existing spike transformation methods, such as Volterra model and staged point-process model. The results show that our model has higher goodness-of-fit evaluated by Kolmogorov-Smirnov test and less variance on the prediction results, which indicates the potential better modeling approach for neural prosthesis application.