Multiplex depth for network-valued data and applications

The demand for analyzing network-valued data is growing in various research areas. To facilitate robust analysis of such data, we introduce a novel depth concept called multiplex depth, which generalizes Tukey’s depth for multivariate data to the realm of network data. This depth is applicable to both binary and weighted networks, enabling data ordering and outlier detection. We study the depth-related properties of multiplex depth and establish the consistency of sample depth and depth-based median estimators. Furthermore, we devise efficient computational algorithms to facilitate the practical implementation. To assess the effectiveness of our approach, we conduct a comprehensive evaluation using both simulated data and a neuroscience-derived dataset of brain networks. This evaluation takes into account crucial tasks such as data ranking, center estimation, and outlier detection, ensuring a thorough and rigorous analysis of our methodology. Supplementary materials for this article are available online.