Margin maximization for polyhedral conic classifiers

Generalization ability has a key role for successful prediction for classification algorithms. In literature, well known support vector machines tries to increase generalization ability via maximizing the value called margin, which is the largest distance between two parallel hyperplanes on the closest points of different data sets. In this research, polyhedral conic functions are reformulated as maximum margin separating hyperplane and, idea of margin maximization is adapted to conic surfaces. Based on this idea, two new approaches are proposed to maximize margin value for conic classifiers. In the first approach, conic functions are used in a same manner with kernel functions to obtain both hyperplane and conic classifiers. In the second approach, a distance based conic classifier is obtained by solving generalized eigen value problem. In addition to these, a penalized approach is also proposed to overcome overfitting problem of the polyhedral conic functions algorithm.