Fusing Dictionary Learning and Support Vector Machines for Unsupervised
  Anomaly Detection
Paul Irofti Iulian-Andrei Hîji Andrei Pătraşcu Nicolae Cleju
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.