Renewable ℓ 1-Regularized Linear Support Vector Machine with High-Dimensional Streaming Data

The rapid growth of modern data collection methods brings new challenges for existing classification problems and the storage of huge datasets in memory. The need to develop online update methods is becoming increasingly pressing. In this paper, we study the renewable estimation process for a linear support vector machine (SVM) in high-dimensional online settings. The proposed renewable estimation process, which includes online ℓ1-regularized and online debiased procedures, is feasible for handling high-dimensional streaming data since the online estimators are updated by integrating current new data batches with summary statistics of historical data, rather than re-accessing the entire raw dataset. Theoretically, we prove the convergence rates of the proposed online estimators under mild conditions. Numerical studies confirm the effectiveness of the proposed methods. Supplementary materials for this paper are available online.