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In recent years, neuroscientists have discovered that the neural information is encoded by spike trains with precise times. Supervised learning algorithm based on the precise times for spiking neurons becomes an important research field. Although many existing algorithms have the excellent learning ability, most of their mechanisms still have some complex computations and certain limitations. Moreover, the discontinuity of spiking process also makes it very difficult to build an efficient algorithm. This paper proposes a supervised learning algorithm for spiking neurons using the kernel function of spike trains based on a unit of pair-spike. Firstly, we comprehensively divide the intervals of spike trains. Then, we construct an optimal selection and computation method of spikes based on the unit of pair-spike. This method avoids some wrong computations and reduces the computational cost by using each effective input spike only once in every epoch. Finally, we use the kernel function defined by an inner product operator to solve the computing problem of discontinue spike process and multiple output spikes. The proposed algorithm is successfully applied to many learning tasks of spike trains, where the effect of our optimal selection and computation method is verified and the influence of learning factors such as learning kernel, learning rate, and learning epoch is analyzed. Moreover, compared with other algorithms, all experimental results show that our proposed algorithm has the higher learning accuracy and good learning efficiency.

A Supervised Learning Algorithm for Spiking Neurons Using Spike Train Kernel Based on a Unit of Pair-Spike