The Oja depth (simplicial volume depth) is one of the classical statistical techniques for measuring the central tendency of data in multivariate space. Despite the widespread emergence of object data like images, texts, matrices or graphs, a well-developed and suitable version of Oja depth for object data is lacking. To address this shortcoming, a novel measure of statistical depth, the metric Oja depth applicable to any object data, is proposed. Two competing strategies are used for optimizing metric depth functions, i.e., finding the deepest objects with respect to them. The performance of the metric Oja depth is compared with three other depth functions (half-space, lens, and spatial) in diverse data scenarios. Keywords: Object Data, Metric Oja depth, Statistical depth, Optimization, Metric statistics

翻译：Oja深度（单纯形体积深度）是衡量多元空间数据集中趋势的经典统计技术之一。尽管图像、文本、矩阵或图等对象数据日益普及，但目前仍缺乏一种成熟且适用的Oja深度版本用于对象数据。为弥补这一不足，本文提出了一种新的统计深度度量——度量Oja深度，该深度适用于任何对象数据。我们采用两种竞争策略来优化度量深度函数，即寻找相对于这些函数的最深对象。在多种数据场景下，将度量Oja深度的性能与其他三种深度函数（半空间深度、透镜深度和空间深度）进行比较。关键词：对象数据，度量Oja深度，统计深度，优化，度量统计