Fusing Dictionary Learning and Support Vector Machines for Unsupervised Anomaly Detection

TL;DR

This paper introduces a novel unsupervised anomaly detection method that combines dictionary learning and support vector machines, enhancing pattern discovery and detection accuracy through a unified optimization framework.

Contribution

The paper proposes a new model unifying OC-SVM and dictionary learning residuals, with explicit iterative algorithms and kernel extensions, advancing unsupervised anomaly detection techniques.

Findings

The proposed algorithms converge empirically and are practically implementable.

The method outperforms existing approaches in numerical experiments.

Kernel extensions improve detection flexibility and accuracy.

Abstract

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.