An effective cost-sensitive sparse online learning framework for imbalanced streaming data classification and its application to online anomaly detection

Class imbalance is one of the most challenging problems in streaming data mining due to its adverse impact on predictive capability of online models. Most of the existing approaches for online learning lack an effective mechanism to handle high-dimensional streaming data with skewed class distributions, resulting in deteriorated model performance and limited interpretability. In this paper, we develop a cost-sensitive regularized dual averaging (CSRDA) method to tackle this problem. Our proposed method substantially extends the influential regularized dual averaging method by formulating a new convex optimization function, in which four ℓ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ell _1$$\end{document}-norm regularized cost-sensitive objective functions are directly optimized, respectively. We then theoretically analyze CSRDA’s regret bounds and the bounds of primal variables, demonstrating that CSRDA and its variants can achieve a theoretical convergence in terms of the balanced cost and sparsity when handling severe imbalanced and high-dimensional streaming data. To validate the proposed methods, we conduct extensive experiments on six benchmark streaming datasets with varied imbalance ratios and three online anomaly detection tasks. The experimental results demonstrate that, compared to other baseline methods, CSRDA and its variants not only improve classification performance, but also successfully capture sparse features more effectively and hence potentially have a better model interpretability.