A1 Refereed original research article in a scientific journal
Measure of shape for object data
Authors: Virta, Joni
Publisher: Taylor & Francis
Publication year: 2025
Journal: Journal of Nonparametric Statistics
Journal name in source: Journal of Nonparametric Statistics
ISSN: 1048-5252
eISSN: 1026-7654
DOI: https://doi.org/10.1080/10485252.2025.2517775
Web address : https://www.tandfonline.com/doi/full/10.1080/10485252.2025.2517775
Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/499357973
Object data analysis is concerned with statistical methodology for datasets whose elements reside in an arbitrary, unspecified metric space. In this work we propose the object shape, a novel measure of shape/symmetry for object data. The object shape is easy to compute and interpret, owing to its intuitive interpretation as interpolation between two extreme forms of symmetry. As one major part of this work, we apply object shape in various metric spaces and show that it manages to unify several pre-existing, classical forms of symmetry. We also propose a new visualisation tool called the peeling plot, which allows using the object shape for outlier detection and principal component analysis of object data.
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Funding information in the publication:
This work was supported by the Research Council of Finland under Grants 347501, 353769.
