026 Christoffel Function based Anomaly Detection for Satellite Telemetry

Job title:

026 Christoffel Function based Anomaly Detection for Satellite Telemetry

Company:

Centre National d’Etudes Spatiales

Job description

25-026 Christoffel Function based Anomaly Detection for Satellite TelemetryPostuler25-026 Christoffel Function based Anomaly Detection for Satellite Telemetry

• Doctorat, 36 mois
• Temps plein
• Indifférent
• Maitrise, IEP, IUP, Bac+4
• Command and Control

PostulerMissionAnomaly detection is an AI field that identifies data points or patterns deviating from the norm. It uses machine learning and statistical methods to learn from historical data, define “normal” behavior, and detect outliers indicating errors, security breaches, or failures. While supervised methods rely on labeled data, most applications lack labels, requiring unsupervised approaches where the algorithm identifies anomalies. The lack of labels complicates fine-tuning and evaluation, while the rarity of anomalies increases the risk of false positives or negatives. Streaming data is also challenging due to its dynamic nature and growing volume so that many approaches struggle with complex parameterization ‎[7].Anomaly detection in satellite telemetry is the chosen application for this thesis, as it fits well: onboard anomalies are rare, and methods must learn nominal behavior from current telemetry to detect weak signals that could indicate future failures during inference.A hybrid AI approach, leveraging the Christoffel function (CF) issued from the Christoffel-Darboux kernel, central in approximation theory with many potential uses in data science ‎[5], addressed the above issues, as demonstrated in Kévin Ducharlet’s PhD thesis ‎[1]. Two novel methods, DyCF and DyCG, were developed for detecting anomalies in data streams, as points in Euclidian space. DyCF handles concept drift, while DyCG eliminates the need for parameter tuning. Both methods excel in execution time and memory usage, often outperforming fine-tuned state-of-the-art approaches ‎[2], encouraging further research.First, some limitations of DyCF and DyCG should be addressed. Actually, determining the CF requires inverting the empirical moment matrix of the discrete measure supported by the observations. As the size of this matrix grows, numerical instabilities arise. Solutions, such as “Tychonov regularization” ‎‎[6] or changing the monomial basis used to build the matrix, should be explored.Scaling up DyCF and DyCG for high-dimensional datasets is also a key goal. If the issue stems from the moment matrix size, one solution could be to randomly select a subset of monomials to form it. Federated learning may also help, as it allows multiple devices to train models locally. Only model updates are sent to a central server, which aggregates them to improve a global model, then redistributes it for further training. Another promising approach is combining “shallow” and “deep” methods. For example, using k-Nearest-Neighbors in the feature space of neural networks has shown competitive performance in object detection and image classification by sampling virtual outliers from low-likelihood regions of the class-conditional distribution ‎[8]. This combination of methods could also be explored for CFl-based approaches.More ambitiously, the PhD thesis will investigate CF-based methods to detect “anomalous time-trajectories”, i.e., infinite-dimensional objects such as ‘points’ in the Hilbert space. The scientific challenges are to (i) manipulate a CF associated with a measure supported on trajectories, and (ii) score new trajectories over a time interval, rather than points in Euclidean space. Recent progress in this area will be consolidated and applied in the thesis ‎[3].Finally, the research will have to address data quality issues, such as inter-series or intra-series irregularities ‎[4], while also integrating business knowledge.The PhD thesis is in collaboration with CNES and LAAS-CNRS (DISCO and MAC teams), under the ANITI AI cluster, ADDX chair led by L. Travé-Massuyès and co-chaired by J.-B. Lasserre. D. Henrion will also participate.[1] Ducharlet, K., Travé-Massuyès, L., Lasserre, J. B., Le Lann, M. V., & Miloudi, Y. (2024). Leveraging the Christoffel function for outlier detection in data streams. Int. J. of Data Science and Analytics, 1-17[2] Ducharlet, K. (2023). Détection d’anomalies dans les flux de données pour une application dans les réseaux de capteurs, Doctoral dissertation, INSA de Toulouse[3] Henrion, D., & Lasserre, J. B. (2024). An infinite-dimensional Christoffel function and detection of abnormal trajectories. Preprint arXiv:2407.02019[4] Lacoquelle, C., Pucel, X., Travé-Massuyès, L., Reymonet, A., & Enaux B. (2022). Warped time series anomaly detection. Preprint arXiv:2404.12134[5] Lasserre, J. B., Pauwels, E., & Putinar, M. (2022). The Christoffel-Darboux kernel for data analysis (Vol. 38). Cambridge University Press[6] Marx, S., Pauwels, E., Weisser, T., Henrion, D., & Lasserre, J. B. (2021). Semi-algebraic approximation using Christoffel-Darboux kernel. Constructive Approximation, 1-39[7] Samariya, D., & Thakkar, A. (2023). A comprehensive survey of anomaly detection algorithms. Annals of Data Science, 10(3), 829-850[8] Sun, Y., Ming, Y., Zhu, X., & Li, Y. (2022, June). Out-of-distribution detection with deep nearest neighbors. In 39th Int. Conf. on Machine Learning, ICML. Baltimore, Maryland USA, 20827-20840For more Information about the topics and the co-financial partner (found by the lab !);contact Directeur de thèse –Then, prepare a resume, a recent transcript and a reference letter from your M2 supervisor/ engineering school director and you will be ready to apply online before March 14th, 2025 Midnight Paris time !

Expected salary

Location

Toulouse

Job date

Wed, 05 Feb 2025 07:05:30 GMT

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