Multivariate Functional Outlier Detection using the FastMUOD Indices

TL;DR

This paper introduces FastMUOD indices for outlier detection in functional data, proposing new adaptations for multivariate cases and demonstrating the effectiveness of random projections through extensive testing.

Contribution

It develops and evaluates FastMUOD-based methods for multivariate functional outlier detection, including novel adaptations and the use of random projections.

Findings

Random projections improve outlier detection performance.

FastMUOD effectively detects different types of outliers.

Proposed methods outperform some existing techniques.

Abstract

We present definitions and properties of the fast massive unsupervised outlier detection (FastMUOD) indices, used for outlier detection (OD) in functional data. FastMUOD detects outliers by computing, for each curve, an amplitude, magnitude and shape index meant to target the corresponding types of outliers. Some methods adapting FastMUOD to outlier detection in multivariate functional data are then proposed. These include applying FastMUOD on the components of the multivariate data and using random projections. Moreover, these techniques are tested on various simulated and real multivariate functional datasets. Compared with the state of the art in multivariate functional OD, the use of random projections showed the most effective results with similar, and in some cases improved, OD performance.