Anomaly Detection in Multichannel Data Using Sparse Representation in RADWT Frames

Daniela De Canditiis,Italia De Feis

doi:10.3390/math9111288

Daniela De Canditiis, Italia De Feis

Open Access

https://doi.org/10.3390/math9111288

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Abstract

We introduce a new methodology for anomaly detection (AD) in multichannel fast oscillating signals based on nonparametric penalized regression. Assuming the signals share similar shapes and characteristics, the estimation procedures are based on the use of the Rational-Dilation Wavelet Transform (RADWT), equipped with a tunable Q-factor able to provide sparse representations of functions with different oscillations persistence. Under the standard hypothesis of Gaussian additive noise, we model the signals by the RADWT and the anomalies as additive in each signal. Then we perform AD imposing a double penalty on the multiple regression model we obtained, promoting group sparsity both on the regression coefficients and on the anomalies. The first constraint preserves a common structure on the underlying signal components; the second one aims to identify the presence/absence of anomalies. Numerical experiments show the performance of the proposed method in different synthetic scenarios as well as in a real case.

Highlights

Detection (AD) is an important problem that has received much attention in recent years
We model the nominal shape as K multiple signals from K channels sharing a joint sparse representation into a special dictionary, and we add a possible anomaly term of any form and shape to each signal component
The idea we develop in our work is the following: a linear model is applied to simultaneously estimate the signal by using its sparse representation in this special dictionary and detect potential anomalies modeled as residuals in this sparse representation

Summary

Introduction

Detection (AD) is an important problem that has received much attention in recent years. Reference [5] is devoted to novelty detection, where the distinction with the word anomaly is that the former considers, as normal, the data after their detection Another important and very recent paper is the one by Thudumu et al [7], which reviews AD in the context of big data where a curse of dimensionality occurs, bringing the failure of different methodologies. We model the nominal shape as K multiple signals from K channels sharing a joint sparse representation into a special dictionary, and we add a possible anomaly term of any form and shape to each signal component This framework represents situations where we expect similar shapes for the components of the signal, but some components can undergo anomaly behavior for some unpredictable reason. The authors propose detecting anomalies by simultaneously estimating both the nominal signal and its residual using nonconvex penalized regression with the constraint on the outliers vector.

The Data Model and Problem Setting

Implementation

Gj denoting the reduction of design

Synthetic Data

Real Data

Conclusions