Direct Multicategory Proximal Support Vector Machine Classifier with Degenerate Eigenvalue Problem

Proximal Support Vector Machine Classification via Generalized Eigenvalues (GEPSVM) is a significant binary classifier. In this paper, a novel multicategory proximal support vector machine, namely Direct Multicategory Proximal Support Vector Machine Classifier (DMPSVM) is proposed. DMPSVM aims to simultaneously seek multiple planes and each plane is generated by an eigenvector corresponding to a smallest eigenvalue of each of the standard eigenvalue problems. Under the definition of the new optimization criterion, the differences of the DMPSVM algorithm from GEPSVM lie in four folds: (1) having geometrically more intuitive interpretability; (2) simultaneously obtaining the multiple planes by the corresponding standard eigenvalue problems; (3) that each plane only depends on its own class samples without additional attention to the others; and (4) exempting from the choice of regularization parameter as in GEPSVM. Finally, we also discuss DMPSVM´s degenetate eigenvalue problem. The effectiveness of the DMPSVM is demonstrated by tests on some benchmark datasets.