{
  "abstract": "The cyclic nature of many biological systems is frequently reflected in periodic gene expression patterns. Standard dimensionality reductions can reveal such variation but do not link a sample's position on a cycle to an ordering of the molecular features that define it. We introduce clrcycle, which applies a centered log-ratio transformation, learns a cyclic feature ordering by maximizing variance captured by the first Fourier mode, and projects samples onto the corresponding cosine and sine coordinates. The resulting two-dimensional geometry assigns each sample a phase and a radius measuring the magnitude of its projection onto the learned Fourier circle. Across a mouse circadian atlas, clrcycle recovers known temporal organization and reveals tissue-specific differences in rhythmic timing. In FUCCI-profiled single cells, clrcycle represents independently measured cell-cycle phase in two-dimensional coordinates more reliably than conventional two-dimensional embeddings. In human endometrium, a circular coordinate learned from 250 highly variable genes recovers menstrual-stage organization and can stage unseen endometrial biopsies. Together, these results establish clrcycle as powerful, explicitly circular dimensionality reduction technique to quantify high-dimensional cyclic variation across biological cycles.",
  "abstract_shown": true,
  "affiliations": [
    "California Institute of Technology"
  ],
  "article_type": "New results",
  "arxiv": null,
  "author_total": 3,
  "authors": [
    {
      "name": "N. P. Swarna"
    },
    {
      "name": "J. Emhemed"
    },
    {
      "affs": [
        0
      ],
      "name": "L. Pachter"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0tcawkppvcmsc.bib",
  "cited_by": 0,
  "doi": "10.64898/2026.10.22.761053",
  "fulltext_url": "https://www.biorxiv.org/content/10.64898/2026.10.22.761053v1.full",
  "id": "0tcawkppvcmsc",
  "issns": [],
  "landing_url": "https://www.biorxiv.org/content/10.64898/2026.10.22.761053v1",
  "language": null,
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "biorxiv",
      "bioinformatics"
    ],
    [
      "openalex",
      "1312|Single-cell and spatial transcriptomics"
    ]
  ],
  "openalex": "W7223862898",
  "pdf_url": "https://www.biorxiv.org/content/10.64898/2026.10.22.761053v1.full.pdf",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0tcawkppvcmsc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "10.64898/2026.10.22.761053",
      "source": "biorxiv",
      "url": "https://www.biorxiv.org/content/10.64898/2026.10.22.761053v1"
    }
  ],
  "subjects": [
    {
      "field": "biology",
      "origin": "biorxiv:bioinformatics",
      "subfield": "bioinformatics"
    }
  ],
  "title": "Dimensionality Reduction for Cyclic Compositional Data",
  "title_text": "Dimensionality Reduction for Cyclic Compositional Data",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/0tcawkppvcmsc",
  "venue": "bioRxiv",
  "versions": []
}