Dictionary Learning with Uniform Sparse Representations for Anomaly Detection

TL;DR

This paper explores how dictionary learning with uniform sparse representations can effectively detect anomalies in datasets by modeling the majority of samples and identifying deviations.

Contribution

It introduces a specific dictionary learning formulation using a K-SVD-type algorithm for anomaly detection based on uniform sparse representations.

Findings

Efficient discrimination of anomalies from regular data points.

Successful modeling of the majority subspace in datasets.

Numerical simulations demonstrate the method's effectiveness.

Abstract

Many applications like audio and image processing show that sparse representations are a powerful and efficient signal modeling technique. Finding an optimal dictionary that generates at the same time the sparsest representations of data and the smallest approximation error is a hard problem approached by dictionary learning (DL). We study how DL performs in detecting abnormal samples in a dataset of signals. In this paper we use a particular DL formulation that seeks uniform sparse representations model to detect the underlying subspace of the majority of samples in a dataset, using a K-SVD-type algorithm. Numerical simulations show that one can efficiently use this resulted subspace to discriminate the anomalies over the regular data points.