Fuzzy linear proximal support vector machines for multi-category data classification

Given a data set, each point of which is labelled with one of M labels, we propose a multi-category extension of fuzzy proximal support vector machines, where a fuzzy membership is assigned to each data point. Patterns are classified by assigning them to the nearest of M parallel planes, which are proximal to one of the M-categories and separate a category from the rest. The algorithm is simple and fast as no quadratic or linear programming problem is solved. Effectively, only the solution of a linear system of equations is needed.