Analytic center of spherical shells and its application to analytic center machine

The two-case pattern recognition problem aims to find the best way of linearly separate two different classes of data points with a good generalization performance. In the context of learning machines proposed to solve the pattern recognition problem, the analytic center machine (ACM) uses the analytic center cutting plane method restricted to spherical shells. In this work we prove existence and uniqueness of the analytic center of a spherical surface, which guarantees the well definedness of ACM problem. We also propose and analyze new primal, dual and primal-dual formulations based on interior point methods for the analytic center machine. Further, we provide a complexity bound on the number of iterations for the primal approach.