Least squares twin support vector hypersphere (LS-TSVH) for pattern recognition

The twin support vector hypersphere (TSVH) is a novel efficient pattern recognition tool, because it determines a pair of hyperspheres by solving two related SVM-type problems, each of which is smaller than in a classical SVM. In this paper we formulate a least squares version for this classifier, termed as the least squares twin support vector hypersphere (LS-TSVH). This formulation leads to extremely simple and fast algorithm for generating binary classifier based on a pair of hyperspheres. Due to equality type constraints in the formulation, the solution follows from solving two sets of nonlinear equations, instead of the two dual quadratic programming problems (QPPs) for TSVH. We show that the two sets of nonlinear equations are solved using the well-known Newton downhill algorithm. The effectiveness of proposed LS-TSVH is demonstrated by experimental results on several artificial and benchmark datasets.