P-neuron: a neuron with a center

A neuron widely used for learning is based on an inner product of a weight vector and an input vector and a threshold function, which represents a step-like surface in a hyperspace. The proposed neuron decides the position and sharpness of the step by three parameters: the normal vector, the center position vector, and the sharpness. The center position vector makes it easy to control the step position in the input vector space and to produce active neurons. Moreover, the gradient descent method based on those P-neuron parameters achieves efficient use of many neurons. This method modifies the normal vector, not only by the input vector, but also by the difference between the center position and the input vector, and it produces neurons with various normal vectors. As a result, the number of neurons necessary for training is drastically reduced. Simulation results from some basic training problems show the good performance of the proposed neuron