Assessing centrality or ranking observations in multivariate or non-Euclidean spaces is challenging because such data lack an intrinsic order and many classical depth notions lose resolution in high-dimensional or structured settings. We propose a preference-based framework that defines centrality through population pairwise proximity comparisons: a point is central if a typical draw from the underlying distribution tends to lie closer to it than to another. This perspective yields a well-defined statistical functional that generalizes data depth to arbitrary metric spaces. To obtain a coherent one-dimensional representation, we study a Bradley-Terry-Luce projection of the induced preferences and develop two finite-sample estimators based on convex M-estimation and spectral aggregation. The resulting procedures are consistent, scalable, and applicable to high-dimensional and non-Euclidean data, and across a range of examples they exhibit stable ranking behavior and improved resolution relative to classical depth-based methods.

翻译：评估多元或非欧几里得空间中观测值的中心性或排序具有挑战性，因为此类数据缺乏内在顺序，且许多经典深度概念在高维或结构化场景下会丧失分辨能力。我们提出一种基于偏好的框架，该框架通过总体成对邻近性比较来定义中心性：若从基础分布中抽取的典型样本更倾向于靠近某点而非另一点，则该点被视为中心。这一视角导出了一个定义明确的统计泛函，将数据深度推广至任意度量空间。为获得一致的一维表示，我们研究了诱导偏好的Bradley-Terry-Luce投影，并基于凸M估计与谱聚合开发了两种有限样本估计器。所得方法具有一致性、可扩展性，适用于高维与非欧几里得数据，且在一系列示例中展现出相较于经典深度方法更稳定的排序行为与更高的分辨能力。