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.

本研究通过稀疏表示技术改进了一类支持向量机（OC-SVM）用于无监督异常检测，提出了一种将 OC-SVM 和 DL 残差函数融合为单一复合目标的新异常检测模型，并通过 K-SVD 类型的迭代算法进行求解，同时将 DL 模型适应于字典对学习（DPL）上下文中，进一步扩展这两个目标以允许使用核函数，并对其参数进行了深入分析，通过与现有方法的比较展示了数值性能。

融合字典学习和支持向量机的无监督异常检测

Fusing Dictionary Learning and Support Vector Machines for Unsupervised  Anomaly Detection

Anomaly detection is defined as the problem of finding data points that do
not follow the patterns of the majority. Among the various proposed methods for
solving this problem, classification-based methods, including one-class Support
Vector Machines (SVM) are considered effective and state-of-the-art. The
one-class SVM method aims to find a decision boundary to distinguish between
normal data points and anomalies using only the normal data. On the other hand,
most real-world problems involve some degree of uncertainty, where the true
probability distribution of each data point is unknown, and estimating it is
often difficult and costly. Assuming partial distribution information such as
the first and second-order moments is known, a distributionally robust
chance-constrained model is proposed in which the probability of
misclassification is low. By utilizing a mapping function to a higher
dimensional space, the proposed model will be capable of classifying
origin-inseparable datasets. Also, by adopting the kernel idea, the need for
explicitly knowing the mapping is eliminated, computations can be performed in
the input space, and computational complexity is reduced. Computational results
validate the robustness of the proposed model under different probability
distributions and also the superiority of the proposed model compared to the
standard one-class SVM in terms of various evaluation metrics.

基于分类的方法在异常检测中十分有效，本论文提出了一种分布稳健的概率约束模型，利用核函数的方法来分类难以分离的数据集，并且在验证中显示了该模型的鲁棒性和优越性。