Pith Number

pith:H5IJS6UU

pith:2024:H5IJS6UU64HQGMSKLM7SVRUSL4

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Computing k-means in mixed precision

Erin Carson, Xiaobo Liu, Xinye Chen

Lloyd's k-means remains stable when distance computations drop to lower precision.

arxiv:2407.12208 v3 · 2024-07-16 · math.NA · cs.NA

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\usepackage{pith}
\pithnumber{H5IJS6UU64HQGMSKLM7SVRUSL4}

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3 Author claim open · sign in to claim

4 Citations open

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✓ 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

We confirm the stability of the widely used distance computation formula. We propose a mixed-precision framework for k-means computation and investigate the effects of low-precision distance computation within the framework. Through extensive simulations on various data clustering and image segmentation tasks, we verify the applicability and robustness of the mixed precision k-means method.

C2weakest assumption

The simulations on the chosen datasets and tasks are representative of the numerical behavior that will occur in other k-means workloads; the paper does not provide a general proof that low-precision distance computation remains stable for arbitrary data distributions or cluster counts.

C3one line summary

Mixed-precision Lloyd's k-means remains stable and effective for normalized data in clustering and image segmentation tasks, with care needed for unnormalized data to avoid overflow.

Receipt and verification

First computed	2026-05-26T02:03:46.394219Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

3f50997a94f70f03324a5b3f2ac6925f237ac0804722d273fbd0010392da7d5c

Aliases

arxiv: 2407.12208 · arxiv_version: 2407.12208v3 · doi: 10.48550/arxiv.2407.12208 · pith_short_12: H5IJS6UU64HQ · pith_short_16: H5IJS6UU64HQGMSK · pith_short_8: H5IJS6UU

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/H5IJS6UU64HQGMSKLM7SVRUSL4 \
  | 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: 3f50997a94f70f03324a5b3f2ac6925f237ac0804722d273fbd0010392da7d5c

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "e3dfddfb633750079e163782644a8cfe51de1e6260ba83f569301e629a67c1fb",
    "cross_cats_sorted": [
      "cs.NA"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2024-07-16T22:48:35Z",
    "title_canon_sha256": "d531839e4ef0286488fab95813b30f748cc00a964c7a5d5ae66d67bbe4aa08d9"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2407.12208",
    "kind": "arxiv",
    "version": 3
  }
}