Polyhedral separation approaches for pattern classification problems

In the last twenty years a remarkable research work has been performed in the area of data analysis and machine learning, mainly tackling problems of clustering and classification type. This work deals with pattern classification, which consists in categorizing data into different classes on the basis of their similarities. From the mathematical point of view, classification reduces to finding separation surfaces in the sample space, where the objects (samples) are represented through their attributes. If the sets are linearly separable then one hyperplane provides complete separation, however, in many real-world applications, this is not the case. In most datasets, in fact, classes are disjoint but their convex hulls intersect. In this situation, the decision boundary between the classes is nonlinear and it can be approximated by using for example piecewise linear functions. In this work we present some nonlinear models for classification problems of supervised, semisupervised and Multiple Instance Learning (MIL) type, by tackling polyhedral separation approaches.