Maximum a Posteriori Based Kernel Classifier Trained by Linear Programming

We propose a new approach for classification problem based on the maximum a posteriori (MAP) estimation. The necessary and sufficient condition for the cost function to estimate a posteriori probability was obtained. It was clarified by the condition that a posteriori probability cannot be estimated by using linear programming. In this paper, a kernelized function of which result is the same as that of the MAP classifier is estimated. By relieving the problem from to estimate a posteriori probability to such a function, the freedom of cost function becomes wider. We propose a new cost function for such a function that can be solved by using linear programming. We conducted binary classification experiment by using 13 datasets from the UCI repository and compared the results to the well known methods. The proposed method outperforms the other methods for several datasets. We also explain the relation and the similarity between the proposed method and the support vector machine (SVM). Furthermore, the proposed method has other advantages for classification. Besides it can be solved by linear programming which has many excellent solvers, it does not have regularization parameter such as C in the cost function in SVM and its cost function is so simple that we can consider its various extensions for future work.