A globally optimal fast iterative linear maximum likelihood classifier.

A novel iterative linear classification algorithm is developed from a maximum likelihood (ML) linear classifier. The main contribution of this paper is the discovery that a well-known maximum likelihood linear classifier with regularization is the solution to a contraction mapping for an acceptable range of values of the regularization parameter. Hence, a novel iterative scheme is proposed that converges to a fixed point, the globally optimum solution. To the best of our knowledge, this formulation has not been discovered before. Furthermore, the proposed iterative solution converges to a fixed point at a rate faster than the traditional gradient descent technique. The performance of the proposed iterative solution is compared to conventional gradient descent methods on linear and non-linearly separable data in terms of both convergence speed and overall classification performance.