Multiple testing for outlier detection in functional data
This addresses outlier detection for functional data, such as space telemetries, but appears incremental as it builds on existing dimension reduction and outlier detection techniques.
The authors tackled outlier detection in functional data by proposing a semi-supervised method that uses multiple testing on projected coefficients to select features, then applies Local Outlier Factor, achieving results on simulated space telemetry data.
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.