Many classification problems contain shape information from input features, such as monotonic, convex, and concave. In this research, we propose a new classifier, called Shape-Restricted Support Vector Machine (SR-SVM), which takes the component-wise shape information to enhance classification accuracy. There exists vast research literature on monotonic classification covering monotonic or ordinal shapes. Our proposed classifier extends to handle convex and concave types of features, and combinations of these types. While standard SVM uses linear separating hyperplanes, our novel SR-SVM essentially constructs non-parametric and nonlinear separating planes subject to component-wise shape restrictions. We formulate SR-SVM classifier as a convex optimization problem and solve it using an active-set algorithm. The approach applies basis function expansions on the input and effectively utilizes the standard SVM solver. We illustrate our methodology using simulation and real world examples, and show that SR-SVM improves the classification performance with additional shape information of input.
Piecewise Combination of Hyper-Sphere Support Vector Machine for Multi-Class Classification Problems
