We study in this paper the improvement of one-class support vector machines (OC-SVM) through sparse representation techniques for unsupervised anomaly detection. As Dictionary Learning (DL) became recently a common analysis technique that reveals hidden sparse patterns of data, our approach uses this insight to endow unsupervised detection with more control on pattern finding and dimensions. We introduce a new anomaly detection model that unifies the OC-SVM and DL residual functions into a single composite objective, subsequently solved through K-SVD-type iterative algorithms. A closed-form of the alternating K-SVD iteration is explicitly derived for the new composite model and practical implementable schemes are discussed. The standard DL model is adapted for the Dictionary Pair Learning (DPL) context, where the usual sparsity constraints are naturally eliminated. Finally, we extend both objectives to the more general setting that allows the use of kernel functions. The empirical convergence properties of the resulting algorithms are provided and an in-depth analysis of their parametrization is performed while also demonstrating their numerical performance in comparison with existing methods.

翻译：本文研究通过稀疏表示技术改进一类支持向量机（OC-SVM）以实现无监督异常检测。鉴于字典学习（DL）近年来已成为揭示数据隐藏稀疏模式的常用分析技术，我们的方法利用这一洞见，赋予无监督检测在模式发现和维度控制方面更强的能力。我们提出了一种融合OC-SVM与DL残差函数为单一复合目标的异常检测新模型，并通过K-SVD型迭代算法求解。明确推导了该复合模型交替K-SVD迭代的闭式解，并讨论了实际可行的实现方案。标准DL模型被适配至字典对学习（DPL）框架中，从而自然消除了常规稀疏性约束。最终，我们将两种目标函数扩展至更具一般性的核函数应用场景。本文给出了所得算法的经验收敛性质，深入分析了其参数化特性，并通过与现有方法的数值性能对比验证了其有效性。