Spike Train Online Learning For Spiking Neurons Based On Kernel Methods

The artificial neural networks(ANNs) have been researched extensively and have successfully been used in many application areas. In recent years, spiking neural networks(SNNs) have received considerable amount of attention from researchers which are more biologically interpretable,especially the theoretical research of SNNs learning algorithm. From the perspective of learning manners on the spike train, the supervised learning algorithm can be divided into offline and online learning. The traditional SNNs mostly use the offline learning algorithm, the traditional SNNs mostly use the offline learning algorithm, which are generally applicable to the static data learning, and the online learning algorithm has more advantages to process real-time data. However, due to the discontinuity in the spike process, the formulation of efficient supervised learning algorithms for spiking neurons is difficult and remains an important problem in the research area.In this paper, firstly, introduce the modeling method of the spiking neurons and several common neuron models, and present the learning rule of synaptic weights adjustment and the online learning algorithm for spiking neurons based on the linear spike train kernel which use Widrow-Hoff(WH) learning rule. We conduct experiments analyzed to the algorithm by the performance comparison of different kernel functions, the learning process of spike trains and the learning performance of different parameter settings. The experiment results show that our proposed method has higher learning accuracy and flexibility than the offline learning method in the same conditions to the large-scale data sets and the learning problems of complex environment.Furthermore, the spike train expressed by the simple kernel function is linear in the postsynaptic neuron from the perspective of synapses information transmission process, because it ignores the performance of the dendrites. Therefore, we put forward two more biological interpretability the nonlinear learning rule of synaptic weights adjustment and two online learning algorithms for spiking neurons based on the nonlinear spike train kernel, which is based on the two kinds of spike train nonlinear mechanisms for spiking neurons. The effect of different kernel functions, the learning process of spike trains, different number of synaptic inputs, different firing rates of the spike trains, and different length of the desired output spike trains on the performance of the learning algorithm is also analyzed. The effect of different kernel functions, the learning process of spike trains, different number of synaptic inputs, different firing rates of the spike trains, and different length of the desired output spike trains on the performance of the learning algorithm is also analyzed. The experiment results show that our proposed algorithms have higher precision flexibility than the linear process in the same situation.Finally, because each of the kernel functions has different spatial mapping feature, it will have a greater difference in performance in different application scenarios, however, both of the linear and nonlinear online learning algorithms use a single kernel function based on feature space, so this paper will consider combining multiple kernels to obtain a more stable and efficient learning manners on the spike train kernel. Then this paper will introduce multiple kernel learning algorithms in the support vector machine to the online learning rules of spike train. In this paper, we adopt direct sum kernel learning mechanism and product kernel learning mechanism in the composite kernels method to combine with the different kernel functions, and propose spike train online learning for spiking neurons based on multiple kernel methods. The effect of different firing rates of the spike trains, different length of the desired output spike trains and different number of synaptic inputs on the performance of the learning algorithm is also analyzed. The simulation experiment shows that the algorithm has higher precision and more stable learning performance.