All-in-one multicategory least squares nonparallel hyperplanes support vector machine

In this study, the algorithmic implementation of multi-category nonparallel hyperplane support vector machines is described. First, a least square version of Nonparallel Hyperplane Support Vector Machine (NHSVM) is developed for binary classification problems. Solution of the primal problem corresponding to the proposed NHSVM reduces to a system of linear equations as opposed to a quadratic programming problem in NHSVM. This formulation results in a much simpler and faster approach for constructing a nonparallel hyperplane binary classifier, termed as Least Squares Nonparallel Hyperplane Support Vector Machine (LSNHSVM). Further, LSNHSVM is generalized to solve multi- category classification problems. This multi-class classifier is the named as Multicategory Least Squares Nonparallel Hyperplane Support Vector Machine (MLSNHSVM). Unlike most of the previous methods that usually cast a multi-category classification problem into a series of multiple independent binary classification problem, MLSNHSVM constructs a direct multi-category classifier by solving a system of linear equations. The proposed MLSNHSVM is in close accordance with the principle of solving multi-category problems directly. Experimental results demonstrate that MLSNHSVM has significantly higher classification accuracy as compared to other multi-class classifiers and is considerably efficient than multi-class SVM in terms of computational time.