Online Learning Approach Based on Recursive Formulation for Twin Support Vector Machine and Sparse Pinball Twin Support Vector Machine

In this paper, an online approach was proposed for twin support vector machine motivated by online learning algorithms for double-weighted least squares twin bounded support vector machines. In many applications for training, data are available online, and batch training methods are not suitable because of space and time requirements. For the online method proposed in this paper, the online learning method was created by recursive relation of twin support vector machine in two linear and nonlinear cases, which avoids calculating inverse matrices in every repetition step. Thus, only the inverse matrix in the initial step must be calculated, and every repetition step is calculated recursively from the previous step, which causes the training time to decrease without losing accuracy. Moreover, for studying the effectiveness of the proposed approach, this online approach was used for sparse pinball twin support vector machine, and simulation results indicated this online approach not only did not reduce accuracy but also, for some datasets, increased accuracy for online cases.