1. An interconnecting neural network system comprising: a neural network unit that includes a plurality of neurons, each of the neurons outputting an excitation strength according to a similarity between an input vector and a centroid vector based on a kernel function; and a network control unit that constructs an artificial neural network structure by interconnecting neurons relating to each other among the neurons in the neural network unit via a weight, wherein each of the neurons in the neural network unit outputs an excitation strength according to a similarity between an input vector and a centroid vector based on a kernel function when the each neuron is excited by the input vector applied from an outside, and outputs a pseudo excitation strength obtained based on an excitation strength output from the other neuron when the each neuron is excited in a chain reaction to excitation of the other neuron connected to the each neuron.