Online Learning Algorithms for Double-Weighted Least Squares Twin Bounded Support Vector Machines

Twin support vector machine with two nonparallel classifying hyperplanes and its extensions have attracted much attention in machine learning and data mining. However, the prediction accuracy may be highly influenced when noise is involved. In particular, for the least squares case, the intractable computational burden may be incurred for large scale data. To address the above problems, we propose the double-weighted least squares twin bounded support vector machines and develop the online learning algorithms. By introducing the double-weighted mechanism, the linear and nonlinear double-weighted learning models are proposed to reduce the influence of noise. The online learning algorithms for solving the two models are developed, which can avoid computing the inverse of the large scale matrices. Furthermore, a new pruning mechanism which can avoid updating the kernel matrices in every iteration step for solving nonlinear model is also developed. Simulation results on three UCI data with noise demonstrate that the online learning algorithm for the linear double-weighted learning model can get least computation time as well considerable classification accuracy. Simulation results on UCI data and two-moons data with noise demonstrate that the nonlinear double-weighted learning model can be effectively solved by the online learning algorithm with the pruning mechanism.