A Quadratically Constrained MAP Classifier Using the Mixture of Gaussians Models as a Weight Function

In this paper, we propose classifiers derived from quadratically constrained maximum a posteriori (QCMAP) estimation. The QCMAP consists of the maximization of the expectation of a cost function, which is derived from the maximum a posteriori probability and a quadratic constraint. This criterion is highly general since its forms include least squares regressions and a support vector machine. Furthermore, the criterion provides a novel classifier, the “Gaussian QCMAP.” The QCMAP procedure still has large theoretical interest and its full extensibility has yet to be explored. In this paper, we propose using the mixture of Gaussian distributions as the QCMAP weight function. The mixture of Gaussian distributions has wide-ranging applicability, and encompasses forms, such as a normal distribution model and a kernel density model. We propose four types of mixture of Gaussian functions for QCMAP classifiers, and conduct experiments to demonstrate their advantages.