A polyhedral conic functions based classification method for noisy data

Abstract

<p style='text-indent:20px;'>This paper presents a robust binary classification method, which is an extended version of the Modified Polyhedral Conic Functions (M-PCF) algorithm, earlier developed by Gasimov and Ozturk. The new version presented in this paper, has new features in comparison to the original algorithm. The mathematical model used in the new version, is relaxed by allowing some inaccuracies in an optimal way. By this way, it is aimed to reduce the overfitting and improve the generalization property. In the original version, the sublevel set of a separating function generated at every iteration, does not contain any element of the other set. This is changed in the new version, where the sublevel sets of separating functions generated by the new algorithm, are allowed to contain some elements from other set. On the other hand, the new algorithm uses a tolerance parameter which prevents generating "less productive separating functions". In the original version, the algorithm continues till all points of the "first" set are separated from the second one, where a separating function is generated if there still exist unseparated elements regardless the number of such elements. In the new version, the tolerance parameter is used to terminate iterations if there are only a few unseparated elements. By this way, it is aimed to improve the generalization property of the algorithm, and therefore the new version is called Parameterized Polyhedral Conic Functions (P-PCF) method. The performance and efficiency of the proposed algorithm is demonstrated on well-known datasets from the literature and on noisy data.</p>