Institut Fayol – Mines St Etienne

Offre stage Master recherche en Génie Mathématique et Industriel

Anomaly detection methods in a signal processing context

Méthodes de détection d’anomalies dans un contexte de traitement du signal

1 Project description
Anomaly detection [2] poses the challenge of identifying patterns in data that deviate from the expected behavior. Anomalies often contain crucial information, sometimes of a critical nature, requiring appropriate exploitation. Anomaly detection is of paramount importance in various sectors such as cybersecurity, healthcare, finance, and manufacturing, given the substantial volume of currently available data.
In the industrial sector, data is typically collected from sensors, measuring instruments, and other data collection devices that record measurements at regular intervals over time. These data, referred to as time series, encompass information about variables such as temperature, pressure, production, energy consumption, and others, depending on the specific industrial context. Traditional anomaly detection methods, such as threshold and rule-based systems [2], often rely on assumptions (e.g., the assumption of the probability distribution of data, the availability of labeled data, etc.) that may occasionally become impractical in real-world scenarios[7].
Furthermore, in the context of signal processing, time-frequency representations provide the ability to visualize and manipulate the content of a signal by simultaneously considering two dimensions: time (appearance, evolution, extinction) and frequency characteristics (frequency concept). These representations, rooted in a solid mathematical theory, are widely used for processing data that evolves over time, such as audio signals. The goal of this internship is to develop methods for detecting anomalies in time series based on their time-frequency representation [3, 5].

The main objectives of this project are:
• Explore the possibility of treating spectrograms (the square modulus of a time-frequency representation) as images. Subsequently, implement image processing and statistical learning methods for anomaly detection [1].
• Leverage the properties of the time-frequency plane to formalize an anomaly detection criterion. This involves, for example, developing specific metrics based on the characteristics of time-frequency representations to identify anomalies.
• Approximate the distribution of time-frequency representations. This approach would enable a more accurate modeling of the behavior of time series in the time-frequency domain, thereby facilitating anomaly detection.
• Extend probabilistic anomaly detection approaches to the case of time-frequency representations [6]. This would require adapting existing probabilistic models to account for the specific characteristics of data in the time-frequency domain [4].
• Broaden the application of these methods to multivariate contexts by considering temporal data from various different sources.

Keywords: anomaly detection, time-frequency analysis, time series, statistical learning.

2 Basic information
• Internship duration: 5 months
• Starting date: as soon as possible and no later than March 31, 2024
• Location: École des Mines de Saint-Étienne (EMSE), Institut Henri Fayol, Saint-Étienne, France
• Indemnities: Legal amount (
• Supervisors: Marina Krémé, EMSE/LIMOS, Anis Hoayek, EMSE/LIMOS,

3 Candidate profile
• 2nd-year of MSc and/or 3rd-year of an engineering school,
• Strong background in applied mathematics,
• Proficiency in statistics learning
• Strong programming skills in Python
• Proficiency in the English language
• Additionally, skills in signal processing will be highly appreciated.

4 Application
To apply, candidates must send, their CV and a cover letter to Marina Krémé ( and Anis Hoayek (


[1] Jinwon An and Sungzoon Cho. Variational autoencoder based anomaly detection using reconstruction probability. 2015.
[2] Varun Chandola, Arindam Banerjee, and Vipin Kumar. Anomaly detection: A survey. ACM Computing Surveys, 41(3):1–58, July 2009.
[3] François Auger Franz Hlawatsch. Time-Frequency Analysis: Concepts and Methods. Wiley, January 2008.
[4] Anis S. Hoayek, Gilles R. Ducharme, and Zaher Khraibani. Distribution-free inference in record series. Extremes, 20(3):585–603, February 2017.
[5] A. Marina Kreme, Valentin Emiya, Caroline Chaux, and Bruno Torresani. Time-frequency fading algorithms based on gabor multipliers. IEEE Journal of Selected Topics in Signal Processing, 15(1):65–77, January 2021.
[6] Anis Hoayek Michel Kamel and Mireille Batton-Hubert. Anomaly detection based on system log data. International Conference on Linked Data Quality and Anomaly Detection, 2023.
[7] Sebastian Schmidl, Phillip Wenig, and Thorsten Papenbrock. Anomaly detection in time series: a comprehensive evaluation. Proceedings of the VLDB Endowment, 15(9):1779–1797, May 2022.


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