Atom dimension adaptation for infinite set dictionary learning

TL;DR

This paper introduces an adaptive method for adjusting set-atom sizes in dictionary learning, enhancing signal representation and anomaly detection, especially for dependency anomalies, outperforming existing techniques.

Contribution

It proposes a novel algorithm for adaptively tuning set-atom sizes in Gaussian and cone dictionary learning, improving both representation accuracy and anomaly detection.

Findings

Reduces representation error compared to previous methods.

Improves detection of dependency anomalies.

Outperforms state-of-the-art anomaly detection techniques.

Abstract

Recent work on dictionary learning with set-atoms has shown benefits in anomaly detection. Instead of viewing an atom as a single vector, these methods allow building sparse representations with atoms taken from a set around a central vector; the set can be a cone or may have a probability distribution associated to it. We propose a method for adaptively adjusting the size of set-atoms in Gaussian and cone dictionary learning. The purpose of the algorithm is to match the atom sizes with their contribution in representing the signals. The proposed algorithm not only decreases the representation error, but also improves anomaly detection, for a class of anomalies called `dependency'. We obtain better detection performance than state-of-the-art methods.