Multiple testing for outlier detection in functional data

TL;DR

This paper introduces a semi-supervised outlier detection method for functional data using multiple testing on basis coefficients, combined with Local Outlier Factor, demonstrating effectiveness on simulated space telemetry data.

Contribution

It presents a new outlier detection approach that combines multiple testing on basis coefficients with LOF, tailored for functional data in a semi-supervised setting.

Findings

Effective outlier detection on simulated space telemetry data

Comparison shows advantages over existing dimension reduction methods

Method identifies significant coefficient features for outlier detection

Abstract

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.