Recursion-Free Online Multiple Incremental/Decremental Analysis Based on Ridge Support Vector Learning

 Abstract—This study presents a rapid multiple incremental and decremental mechanism based on Weight-Error Curves (WECs) for support-vector analysis. To handle rapidly increasing amounts of data, recursion-free computation is proposed for predicting the Lagrangian multipliers of new samples. This study examines the characteristics of Ridge Support Vector Models, including Ridge Support Vector Machines and Regression, subsequently devising a recursion-free function derived from WECs. With this proposed function, all of the new Lagrangian multipliers can be computed at once without using any gradual step sizes. Moreover, such a function can relax a constraint, where the increment of new multiple Lagrangian multipliers should be the same in the previous work, thereby easily satisfying the requirement of Karush–Kuhn–Tucker (KKT) conditions. The proposed mechanism no longer requires typical time-consuming bookkeeping strategies, which compute the step size by checking all the training samples in each incremental round. Experiments were carried out on open datasets for evaluating our work. The results showed that the computational speed was successfully enhanced, better than the baselines. Besides, the accuracy still remained. These findings revealed that the proposed method was appropriate for incremental/decremental learning, thereby demonstrating the effectiveness of the proposed idea.