{
  "abstract": "Spectral embedding methods are widely used for dimensionality reduction and clustering of high-dimensional datasets with intrinsic low-dimensional structures. Although many datasets of practical interest exhibit invariance under symmetries such as rotations, standard spectral embedding methods do not account for this, treating symmetry-related data points as unrelated. Our approach to this problem is to incorporate the symmetries directly into the affinity kernels used for spectral embedding. We analyze the case of a Riemannian data manifold $M$ with symmetries given by a compact Lie group~$G$ and prove that, under suitable conditions, graph Laplacians constructed from three types of invariant kernels converge pointwise to explicit second-order differential operators on the quotient space $M/G$. Our analysis implies improved convergence rates, as the effective dimension drops according to the dimension of the group. We validate our approach on datasets with $\\mathrm{SO}(2)$ or $\\mathrm{SO}(3)$ symmetry, and show that $G$-invariant spectral embedding recovers the intrinsic geometry of the data, in contrast to standard spectral embedding, which fails to do so even in the limit of infinite data.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.08987",
  "author_total": 6,
  "authors": [
    {
      "name": "Yeari Vigder"
    },
    {
      "name": "Paulina Hoyos"
    },
    {
      "name": "David Thong"
    },
    {
      "name": "Joakim andén"
    },
    {
      "name": "Joe Kileel"
    },
    {
      "name": "Amit Moscovich"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1mf2pf231xs9w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.08987",
  "fulltext_url": null,
  "id": "1mf2pf231xs9w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.08987",
  "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",
      "cs.NA"
    ],
    [
      "arxiv",
      "math.NA"
    ],
    [
      "arxiv",
      "math.ST"
    ],
    [
      "arxiv",
      "stat.TH"
    ],
    [
      "openalex",
      "1703|Topological and Geometric Data Analysis"
    ]
  ],
  "openalex": "W7168214239",
  "pdf_url": "https://arxiv.org/pdf/2607.08987",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1mf2pf231xs9w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2607.08987",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.08987"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NA",
      "subfield": "numerical-analysis"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.ST",
      "subfield": "statistics"
    }
  ],
  "title": "Group Invariant Spectral Embedding",
  "title_text": "Group Invariant Spectral Embedding",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:03Z",
  "url": "https://research.draconitic.com/paper/1mf2pf231xs9w",
  "venue": "arXiv",
  "versions": []
}