Multiplex Depth for Network-Valued Data and Applications
提出一种名为多重深度的新概念，将Tukey深度从多变量数据推广到网络数据，支持二值和加权网络的数据排序与异常值检测，并通过模拟和脑网络数据验证其有效性。
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 paper are available online.