{
  "abstract": "Nested dichotomies (NDs) reduce multiclass classification to a tree of binary classifiers. Tree structure can change accuracy, bias, and variance, but the full space of structures has not been mapped in aggregate. We introduce ndscape, a two-dimensional mapping of ND structures based on depth-weighted structural tokens. We use this embedding to conduct what is, to our knowledge, the first bias-variance analysis across the ND structure space. In simulations with 6 to 10 classes, NDs with similar tree structures exhibit similar squared bias, variance, and squared probability loss, regardless of whether the binary classifier is logistic regression or a decision tree. Variance, however, follows mean root-to-leaf depth when logistic regression is used at each node, so flatter, more balanced NDs are more stable, whereas with decision-tree node models, variance is not associated with depth and differs little across ND structures. On six datasets with 6 to 19 classes, held-out accuracy, log loss, and prediction variance remain spatially organised on the same topology-only map. None of the six standard construction heuristics tested selects a tree from the best-performing cluster on any dataset, although some select high-performing individual trees. The ndscape embedding turns ND selection from one opaque construction step into a readable comparison of class groupings, exposing the upper-level splits that distinguish high-performing and stable regions.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18050",
  "author_total": 3,
  "authors": [
    {
      "name": "Maxwell Dix-Matthews"
    },
    {
      "name": "Melinda Hodkiewicz"
    },
    {
      "name": "Adriano Polpo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cyk9rccqfa2z6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18050",
  "fulltext_url": null,
  "id": "cyk9rccqfa2z6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18050",
  "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"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Machine Learning and Data Classification"
    ]
  ],
  "openalex": "W7221814804",
  "pdf_url": "https://arxiv.org/pdf/2610.18050",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cyk9rccqfa2z6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:26Z",
      "native_id": "2610.18050",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18050"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ME",
      "subfield": "statistics"
    }
  ],
  "title": "ndscape: a structural map of the nested dichotomy space",
  "title_text": "ndscape: a structural map of the nested dichotomy space",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:26Z",
  "url": "https://research.draconitic.com/paper/cyk9rccqfa2z6",
  "venue": "arXiv",
  "versions": []
}