Contributions à la détection d'anomalies interprétable à l'aide de la profondeur des données

Abnormal events are subjects of interest in various fields of application, such as industry, finance and medicine, when they provide information that differs from the general trend. We can see that the arrival of new interconnected sensors, more powerful and in greater numbers, is leading to an increase in the mass of data available for analysis, requiring innovative methods to solve modern challenges. On the one hand, the growing volume of samples requires faster algorithms, while potential data contamination calls for reliable and robust techniques. On the other hand, it is becoming complicated but necessary to interpret certain decisions made by these new tools, as their complexity has increased when coupled with a large quantity of data.The first part of this thesis focuses on the use of data depths, which measure the centrality of data, in the context of anomaly detection. The development of these methods in recent years, particularly their implementation via numerical approximations coupled with optimisation procedures, has made it possible to extend their use to large-scale datasets. We carry out several comparisons with recognised and widely applied methods in this field, while providing experimental (visual) tools to facilitate parameterisation and thus facilitate their use by practitioners.In the second part, we propose a new method for visualising multivariate data based on reducing the dimensionality of the input space with the aim of better visual separation of abnormal observations (=anomalies) in the sense of data depths. Abnormal Component Analysis (ACA) consists in searching for a new orthogonal basis in an unsupervised way to represent the data while providing interpretation opportunities on the input variables responsible for anomalies of interest. The detailed algorithm, together with certain details enabling users to use it, is followed by applications on real data sets to demonstrate the relevance of the technique.Finally, the last part extends the ACA reasoning to functional data in order to take advantage of the continuous nature of many observed phenomena (time series, frequency analysis, etc.). This extension makes use of dictionaries of functions with various properties to extract significant information from different types of anomalies, which are also described using real data sets. This extension proves to be effective for obtaining a "summary" visualisation of the functional data, complemented by an interpretation obtained using the functions employed.