Dynamics of projective adaptive resonance theory model: The foundation of PART algorithm

Projective adaptive resonance theory (PART) neural network developed by Cao and Wu recently has been shown to be very effective in clustering data sets in high dimensional spaces. The PART algorithm is based on the assumptions that the model equations of PART (a large scale and singularly perturbed system of differential equations coupled with a reset mechanism) have quite regular computational performance. This paper provides a rigorous proof of these regular dynamics of the PART model when the signal functions are special step functions, and provides additional simulation results to illustrate the computational performance of PART.