  Using precise times of every spike, spiking supervised learning has more
effects on complex spatial-temporal pattern than supervised learning only
through neuronal firing rates. The purpose of spiking supervised learning after
spatial-temporal encoding is to emit desired spike trains with precise times.
Existing algorithms of spiking supervised learning have excellent performances,
but mechanisms of them still have some problems, such as the limitation of
neuronal types and complex computation. Based on an online regulative mechanism
of biological synapses, this paper proposes an online supervised learning
algorithm of multiple spike trains for spiking neural networks. The proposed
algorithm with a spatial-temporal transformation can make a simple direct
regulation of synaptic weights as soon as firing time of an output spike is
obtained. Besides, it is also not restricted by types of spiking neuron models.
Relationship among desired output, actual output and input spike trains is
firstly analyzed and synthesized to simply select a unit of pair-spike for a
direct regulation. And then a computational method is constructed based on
simple triple spikes using this direct regulation. Compared with other learning
algorithms, results of experiments show that proposed algorithm has higher
learning accuracy and efficiency.
