Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.18412 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910028646055936 |
|---|---|
| author | Lyu, Lingfeng Zhou, Doudou |
| author_facet | Lyu, Lingfeng Zhou, Doudou |
| contents | Ranking or assessing centrality in multivariate and non-Euclidean data is difficult because there is no canonical order and many depth notions become computationally fragile in high-dimensional or structured settings. We introduce a preference-based notion of centrality defined through population proximity comparisons with respect to a random reference draw, yielding a metric-intrinsic statistical functional that is well-defined on general metric spaces. Because the induced pairwise preferences may be non-transitive, we map them to a coherent one-dimensional score via a Bradley--Terry--Luce cross-entropy projection, viewed as a calibrated aggregation device rather than a correctly specified model. We develop two finite-sample estimators a convex M-estimator and a fast spectral estimator based on a comparison operator, and establish identifiability and consistency under mild conditions. Simulations and real-data examples, including high-dimensional and functional observations, illustrate that the proposed scores provide stable, interpretable rankings aligned with the underlying preference centrality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_18412 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Preference-based Centrality and Ranking in General Metric Spaces Lyu, Lingfeng Zhou, Doudou Methodology Ranking or assessing centrality in multivariate and non-Euclidean data is difficult because there is no canonical order and many depth notions become computationally fragile in high-dimensional or structured settings. We introduce a preference-based notion of centrality defined through population proximity comparisons with respect to a random reference draw, yielding a metric-intrinsic statistical functional that is well-defined on general metric spaces. Because the induced pairwise preferences may be non-transitive, we map them to a coherent one-dimensional score via a Bradley--Terry--Luce cross-entropy projection, viewed as a calibrated aggregation device rather than a correctly specified model. We develop two finite-sample estimators a convex M-estimator and a fast spectral estimator based on a comparison operator, and establish identifiability and consistency under mild conditions. Simulations and real-data examples, including high-dimensional and functional observations, illustrate that the proposed scores provide stable, interpretable rankings aligned with the underlying preference centrality. |
| title | Preference-based Centrality and Ranking in General Metric Spaces |
| topic | Methodology |
| url | https://arxiv.org/abs/2601.18412 |