A regularized pairwise multi-classification knowledge-based machine and applications

This paper presents a novel knowledge-based linear classification model for multi-category discrimination of sets or objects with prior knowledge. The prior knowledge is in the form of multiple polyhedral sets belonging to one or more categories or classes and it is introduced as additional constraints into the formulation of the Tikhonov linear least squares multi-class support vector machine model. The resulting formulation leads to a least squares problem that can be solved using matrix methods or iterative methods. Investigations include the development of a linear knowledge-based classification model extended to the case of multi-categorical discrimination and expressed as a single unconstrained optimization problem. Advantages of this formulation include explicit expressions for the classification weights of the classifier(s) and its ability to incorporate and handle prior knowledge directly to the classifiers. In addition it can provide fast solutions to the optimal classification weights for multi-categorical separation without the use of specialized solver-software. To evaluate the model, data and prior knowledge from the Wisconsin breast cancer prognosis and two-phase flow regimes in pipes were used to train and test the proposed formulation.