{
  "abstract": "In this work, we introduce a new clustering method, namely T-ARC (Topology-Aware Randomized Clustering), that corrects the geometric bias of K-means by embedding topological information directly into the optimization objective. Building on the assumption that the data admits an underlying hidden structure modeled via a latent graph, the idea is to uncover this information through the interplay between the standard K-means data-fidelity term and a graph-cut penalty, which discourages cluster assignments inconsistent with the connectivity structure of the data. To render this coupling tractable, the latent graph is modeled as a random realization from a Stochastic Block Model (SBM), whose scalar parameter is optimized within a Distributionally Robust Optimization (DRO) framework, yielding a closed-form proximal update. Both SBM and DRO are informed by a persistence-based similarity matrix derived from zero-dimensional persistent homology ($H_0$), which translates the multiscale connectivity structure of the data into a pairwise topological prior. The overall optimization proceeds via Block Coordinate Descent; convergence is established through a global Lyapunov functional: the deterministic blocks satisfy monotonic descent, while the stochastic graph update satisfies descent in expectation, so that the expected energy converges. Experiments on synthetic datasets with non-convex geometries and on random subsets of Fashion-MNIST show that T-ARC recovers latent topological structures where K-means fails, achieving the highest accuracy on curved and interleaved clusters while remaining competitive, and markedly more stable than K-means, on real data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39466",
  "author_total": 5,
  "authors": [
    {
      "name": "Serena Grazia De Benedictis"
    },
    {
      "name": "Andersen Ang"
    },
    {
      "name": "Nicoletta Del Buono"
    },
    {
      "name": "Flavia Esposito"
    },
    {
      "name": "Laura Selicato"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/85tkdd7rr72gy.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39466",
  "fulltext_url": null,
  "id": "85tkdd7rr72gy",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.39466",
  "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",
      "cs.LG"
    ],
    [
      "arxiv",
      "math.AT"
    ],
    [
      "arxiv",
      "math.OC"
    ],
    [
      "openalex",
      "1703|Topological and Geometric Data Analysis"
    ]
  ],
  "openalex": "W7215111545",
  "pdf_url": "https://arxiv.org/pdf/2609.39466",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/85tkdd7rr72gy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2609.39466",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39466"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AT",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.OC",
      "subfield": "optimisation-control"
    }
  ],
  "title": "T-ARC: Topology-Aware Randomized Clustering via Distributionally Robust Stochastic Block Models",
  "title_text": "T-ARC: Topology-Aware Randomized Clustering via Distributionally Robust Stochastic Block Models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/85tkdd7rr72gy",
  "venue": "arXiv",
  "versions": []
}