{
  "abstract": "Spatial clustering increasingly involves complex objects, including probability distributions, networks, and structured matrices, for which conventional parametric likelihoods may be difficult to specify. We construct a generalized likelihood by exponentiating a cluster-specific Bregman loss on fixed representations of the responses, avoiding the need to specify a parametric sampling model for each response class. Each cluster is associated with an unknown representative, and the generalized likelihood measures within-cluster homogeneity through the Bregman divergence between the represented observations and that representative. A prior family matched to the Bregman geometry yields conjugate generalized posterior updates and permits exact marginalization of the cluster-specific representatives. The resulting collapsed scores combine within-cluster Bregman dispersion with uncertainty in the representatives, while a spanning-tree partition prior restricts posterior partition support to spatially contiguous clusters. This collapsed representation also leads to a tractable MCMC algorithm for posterior computation. The framework accommodates multiple complex-object response classes within a common inferential construction. We establish posterior consistency for the spatial partition and cluster-specific representatives under infill-domain asymptotics. Simulation studies with different complex-object responses demonstrate accurate recovery of spatial partitions and cluster-specific representatives. We further analyze racial-composition distributions across spatial units in Houston, illustrating geographically coherent clusters with distinct demographic compositions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04166",
  "author_total": 2,
  "authors": [
    {
      "name": "Srijato Bhattacharyya"
    },
    {
      "name": "Huiyan Sang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e431kq7epxmga.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04166",
  "fulltext_url": null,
  "id": "e431kq7epxmga",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04166",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "stat.ME"
    ],
    [
      "openalex",
      "1702|Bayesian Methods and Mixture Models"
    ]
  ],
  "openalex": "W7220711123",
  "pdf_url": "https://arxiv.org/pdf/2610.04166",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e431kq7epxmga.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:16Z",
      "native_id": "2610.04166",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04166"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "Consistent Spatial Clustering of Complex Objects via Bregman Geometry",
  "title_text": "Consistent Spatial Clustering of Complex Objects via Bregman Geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:16Z",
  "url": "https://research.draconitic.com/paper/e431kq7epxmga",
  "venue": "arXiv",
  "versions": []
}