Outliers Detection in Functional Data
Résumé
The modern technologies ease the collection of massive data at high frequency. From a statistical point of view, these data can be considered as functional data: discrete observations of random functions. One of the key problems in functional data analysis, is the detection of outliers. For this purpose, we propose a robust method based on contaminated Gaussian mixture models [1]. This model allows both to group and to detect outliers in multivariate functional data. A mixture of multivariate contaminated Gaussian distributions [2] is a Gaussian mixture where each cluster has two components: one, with a large prior probability, represents normal observations, and the other, with a small prior probability, represents outliers. Dimension reduction methods based on [3], are used to introduce parsimony into the model. An ECM (Expectation-Conditional Maximization) algorithm is proposed for model inference and the choice of hyper-parameters is addressed through model selection. The model performs efficiently on simulated data. It also helps to correctly detect outliers in the industrial data sets which motivated this work.
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