{
  "abstract": "Spectral clustering commonly assigns communities by clustering a low-dimensional representation, whereas likelihood refinement can improve an initial assignment using the observed edges. We ask whether sharp community-recovery accuracy can be retained when the refinement no longer accesses individual edges. We develop spectral likelihood-ratio clustering for stochastic block models using one regularized adjacency eigensystem and the original vertex degrees. The method estimates connection probabilities and updates each vertex's label by a likelihood-ratio classifier on reconstructed rows. The refinement accepts any sufficiently accurate initialization, including one computed from the same graph. Its expected misclassification proportion is bounded by a constant times the error of a raw-edge oracle classifier, plus the probability that initialization misses the required accuracy. Repeated k-means++ on the retained spectral coordinates supplies one complete procedure with a constant-factor oracle guarantee. The oracle knows the model parameters and the other labels. The guarantee holds for a fixed number of communities, comparable positive block probabilities and community sizes, and a nondegenerate normalized block matrix. It allows arbitrarily slowly diverging expected degrees under the stated upper sparsity condition. We explain the likelihood-ratio construction first, then the regularization and exact-degree correction required by the general result. The proof combines sharp local testing, truncated spectral-row estimates and leave-one-out comparisons.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40531",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhixin Zhou"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dbgvnvtaee9y0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40531",
  "fulltext_url": null,
  "id": "dbgvnvtaee9y0",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40531",
  "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",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40531",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dbgvnvtaee9y0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40531",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40531"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Rate-Optimal Spectral Likelihood-Ratio Clustering in Stochastic Block Models",
  "title_text": "Rate-Optimal Spectral Likelihood-Ratio Clustering in Stochastic Block Models",
  "type": "preprint",
  "updated_at": "2026-11-01T12:21:00Z",
  "url": "https://research.draconitic.com/paper/dbgvnvtaee9y0",
  "venue": "arXiv",
  "versions": []
}