Edgewise Outliers of Network Indexed Signals

We consider models for network-indexed multivariate data, also known as graph signals, involving a dependence between variables as well as across graph nodes. The dependence across nodes is typically established through the entries of the Laplacian matrix by imposing a distribution that relates the graph signal from one node to the next. Based on such distributional assumptions of the graph signal, we focus on outliers detection and introduce the new 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 Minimum Covariance Determinant (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 involving French departmental election data.