Multiple testing for outlier detection in functional data

Clémentine Barreyre (1) , Béatrice Laurent (2) , Jean-Michel Loubes (2) , Bertrand Cabon (1) , Loïc Boussouf (1)

1 Airbus Defence and Space [Toulouse]
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We propose a novel procedure for outlier detection in functional data, in a semi-supervised framework. As the data is functional, we consider the coefficients obtained after projecting the observations onto orthonormal bases (wavelet, PCA). A multiple testing procedure based on the two-sample test is defined in order to highlight the levels of the coefficients on which the outliers appear as significantly different to the normal data. The selected coefficients are then called features for the outlier detection, on which we compute the Local Outlier Factor to highlight the outliers. This procedure to select the features is applied on simulated data that mimic the behaviour of space telemetries, and compared with existing dimension reduction techniques.

Mots clés: Two sample tests; Outlier detection; Functional data; Local Outlier Factor; Multiple testing

Domaines: Machine Learning [stat.ML]; Méthodologie [stat.ME]; Applications [stat.AP]

Clémentine Barreyre, Béatrice Laurent, Jean-Michel Loubes, Bertrand Cabon, Loïc Boussouf. Multiple testing for outlier detection in functional data. 2017. ⟨hal-01651191⟩