New Interior-Point Approach for One- and Two-Class Linear Support Vector Machines Using Multiple Variable Splitting

Abstract Multiple variable splitting is a general technique for decomposing problems by using copies of variables and additional linking constraints that equate their values. The resulting large optimization problem can be solved with specialized interior-point method exploits the structure computes Newton direction combination direct iterative solvers (i.e. Cholesky factorizations preconditioned conjugate gradients linear systems related to, respectively, subproblems new constraints). present work applies this to solving real-world binary classification novelty (or outlier) detection means of, two-class one-class support vector machines (SVMs). Unlike previous approaches SVMs, which were practical only low-dimensional points, proposal also deal high-dimensional data. compared state-of-the-art SVMs are based on either algorithms (such as SVM-OOPS) or specific developed machine learning community LIBSVM LIBLINEAR). computational results show that, competitive not against methods—and much more efficient than they data—but LIBSVM, whereas LIBLINEAR generally outperformed proposal. For consistently all other approaches, in terms solution time quality.