Joni VIRTA, University of Turku, Finland

Will give a presentation on

Spatial depth for object data

Abstract:

In the first part of the talk we give a brief introduction to the concepts of statistical depth and object data. In summary, statistical depth measures assign high (low) values for points located near (far away from) the bulk of the data distribution, allowing quantifying their centrality/outlyingness. Whereas, object data refers to samples of data where the observations reside in an arbitrary metric space, instead of the space R^p.

In the second part of the talk we describe a novel measure of statistical depth, the metric spatial depth, for object data. This depth measure is shown to have highly interpretable geometric properties, making it appealing in object data analysis where standard descriptive statistics are difficult to compute. The proposed measure reduces to the classical spatial depth in a Euclidean space. In addition to studying its theoretical properties, to provide intuition on the concept, we explicitly compute metric spatial depths in several different metric spaces. Finally, we showcase the practical usefulness of the metric spatial depth in outlier detection, non-convex depth region estimation and classification.

Related preprint: https://arxiv.org/abs/2306.09740