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Anomaly Detection in Multichannel Data Using Sparse Representation in RADWT Frames

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  • Daniela De Canditiis

    (Istituto per le Applicazioni del Calcolo, CNR-Rome, 00185 Rome, Italy)

  • Italia De Feis

    (Istituto per le Applicazioni del Calcolo, CNR-Naples, 80131 Naples, Italy)

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.

Suggested Citation

  • Daniela De Canditiis & Italia De Feis, 2021. "Anomaly Detection in Multichannel Data Using Sparse Representation in RADWT Frames," Mathematics, MDPI, vol. 9(11), pages 1-26, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1288-:d:568302
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    References listed on IDEAS

    as
    1. De Canditiis, Daniela & De Feis, Italia, 2019. "Simultaneous nonparametric regression in RADWT dictionaries," Computational Statistics & Data Analysis, Elsevier, vol. 134(C), pages 36-57.
    2. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    3. She, Yiyuan & Owen, Art B., 2011. "Outlier Detection Using Nonconvex Penalized Regression," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 626-639.
    4. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Multivariate functional outlier detection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 177-202, July.
    5. Mia Hubert & Peter Rousseeuw & Pieter Segaert, 2015. "Rejoinder to ‘multivariate functional outlier detection’," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(2), pages 269-277, July.
    6. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
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