Diffusive method for multiple class data classification

A simple algorithm for multiple class data classification is proposed, which is based on the infinit speed of propagation and the strong maximum principle for the heat equation. In this method, solutions of the heat equation whose initial data are the characteristic function of the training dataset are considered. The classification is established by the sign of the difference of two solutions in a very short time interval. A numerical algorithm for discrete training data in high-dimensional feature space is proposed. As an application of the proposed method, numerical results on the classification of handwritten digits database are presented in this paper.