Pith Number

pith:7IQ5ROQX

pith:2026:7IQ5ROQXRFVW6A5AMGZSLKSC22

not attested not anchored not stored refs resolved

Beyond Explained Variance: A Cautionary Tale of PCA

Gionni Marchetti

PCA scatterplots can falsely suggest clusters in data that actually form a simple ring with no clusters.

arxiv:2605.13520 v1 · 2026-05-13 · cond-mat.stat-mech · cs.LG

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\usepackage{pith}
\pithnumber{7IQ5ROQXRFVW6A5AMGZSLKSC22}

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Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

our analysis based on t-SNE and persistent homology (PH) reveals a ring-like structure with no evident clustering and intrinsic dimensionality equal to one. We further propose a generative probabilistic-geometric model in which the data are sampled uniformly from a unit circle. Under this model, pairwise cosine distances follow an arcsine distribution, in qualitative agreement with the observed U-shaped distribution

C2weakest assumption

That the proposed generative model of uniform sampling from a unit circle is the appropriate description of the data-generating process and that qualitative agreement between the arcsine distribution and the observed distances constitutes independent support rather than post-hoc fitting.

C3one line summary

PCA suggested clustering in fossil teeth data on a nonlinear manifold, but t-SNE and persistent homology show a ring structure with no clustering, supported by a unit-circle generative model whose arcsine distance distribution matches observations qualitatively.

References

57 extracted · 57 resolved · 1 Pith anchors

[1] To this end, various heuristics exist 2004

[2] Pearson, Philosophical Magazine Series 12, 559 (1901) 1901

[3] Hotelling, Journal of Educational Psychology24, 498 (1933) 1933

[4] I. T. Jolliffe,Principal Component Analysis, Springer Series in Statistics (Springer, New York, NY, 2002), 2nd ed., ISBN 978-0-387-95442-4, springer Science+Business Media New York; eBook ISBN: 978-0- 2002

[5] Shlens , title = 2014 · arXiv:1404.1100

Receipt and verification

First computed	2026-05-18T02:44:24.395181Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

fa21d8ba17896b6f03a061b325aa42d6828c1fdf930e00996c515cb0883d070f

Aliases

arxiv: 2605.13520 · arxiv_version: 2605.13520v1 · doi: 10.48550/arxiv.2605.13520 · pith_short_12: 7IQ5ROQXRFVW · pith_short_16: 7IQ5ROQXRFVW6A5A · pith_short_8: 7IQ5ROQX

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/7IQ5ROQXRFVW6A5AMGZSLKSC22 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: fa21d8ba17896b6f03a061b325aa42d6828c1fdf930e00996c515cb0883d070f

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "efec67830e03f908c7a4897f44fc9795632c2e6b3be7c3444d7fbc8a37f19c96",
    "cross_cats_sorted": [
      "cs.LG"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "cond-mat.stat-mech",
    "submitted_at": "2026-05-13T13:37:31Z",
    "title_canon_sha256": "8e1a924b6e7a85906999aa77cc2050a2cd2ed21cc268a2da32e34da389b87c9a"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2605.13520",
    "kind": "arxiv",
    "version": 1
  }
}