Efficient Minimax Clustering Probability Machine by Generalized Probability Product Kernel

Minimax Probability Machine (MPM), learning a decision function by minimizing the maximum probability of misclassification, has demonstrated very promising performance in classification and regression. However, MPM is often challenged for its slow training and test procedures. Aiming to solve this problem, we propose an efficient model named Minimax Clustering Probability Machine (MCPM). Following many traditional methods, we represent training data points by several clusters. Different from these methods, a Generalized Probability Product Kernel is appropriately defined to grasp the inner distributional information over the clusters. Incorporating clustering information via a non-linear kernel, MCPM can fast train and test in classification problem with promising performance. Another appealing property of the proposed approach is that MCPM can still derive an explicit worst-case accuracy bound for the decision boundary. Experimental results on synthetic and real data validate the effectiveness of MCPM for classification while attaining high accuracy.