Edgewise outliers of network indexed signals

TL;DR

This paper introduces the concept of edgewise outliers in network indexed multivariate data, deriving detection rules and thresholds, and proposing a robust edgewise MCD algorithm for improved outlier detection.

Contribution

It presents a novel framework for detecting edgewise outliers in network data and develops a robust MCD algorithm tailored for this purpose.

Findings

Edgewise outliers can be effectively detected using derived distribution thresholds.

The robust edgewise MCD algorithm improves outlier detection accuracy.

Application on real data demonstrates practical utility of the method.

Abstract

We consider models for network indexed multivariate data involving a dependence between variables as well as across graph nodes. In the framework of these models, we focus on outliers detection and introduce the concept of edgewise outliers. For this purpose, we first derive the distribution of some sums of squares, in particular squared Mahalanobis distances that can be used to fix detection rules and thresholds for outlier detection. We then propose a robust version of the deterministic MCD algorithm that we call edgewise MCD. An application on simulated data shows the interest of taking the dependence structure into account. We also illustrate the utility of the proposed method with a real data set.