Metric Oja Depth, New Statistical Tool for Estimating the Most Central Objects

TL;DR

This paper introduces the metric Oja depth, a new statistical depth measure for object data, addressing the lack of suitable multivariate central tendency tools for complex data types.

Contribution

It proposes a novel metric Oja depth applicable to object data and compares its performance with existing depth functions across various scenarios.

Findings

Metric Oja depth effectively measures centrality in object data.

It outperforms some existing depth functions in diverse data scenarios.

Optimization strategies for the metric depth are developed and evaluated.

Abstract

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