The Catastrophic Failure of The k-Means Algorithm in High Dimensions, and How Hartigan's Algorithm Avoids It
Paper • 2602.09936 • Published
Dataset Viewer
The dataset viewer is not available for this split.
Cannot load the dataset split (in streaming mode) to extract the first rows.
Error code: StreamingRowsError
Exception: CastError
Message: Couldn't cast
files: list<item: struct<bytes: int64, path: string, sha256: string>>
child 0, item: struct<bytes: int64, path: string, sha256: string>
child 0, bytes: int64
child 1, path: string
child 2, sha256: string
generated_at: timestamp[s]
paper: struct<arxiv: string, openreview: string, title: string>
child 0, arxiv: string
child 1, openreview: string
child 2, title: string
upstream_code: struct<commit: string, repo: string>
child 0, commit: string
child 1, repo: string
verdict: string
trials: int64
below_threshold_negative_control: struct<sigma2: double, d: int64, lloyd_escape_wrong_point: string, lloyd_escape_wrong_point_rate: do (... 130 chars omitted)
child 0, sigma2: double
child 1, d: int64
child 2, lloyd_escape_wrong_point: string
child 3, lloyd_escape_wrong_point_rate: double
child 4, lloyd_keep_wrong_point: string
child 5, lloyd_keep_wrong_point_rate: double
child 6, theorem34_bound_rho_d4: double
child 7, interpretation: string
above_threshold: list<item: struct<sigma2: double, d: int64, lloyd_escape_wrong_point: string, lloyd_escape_wrong_poi (... 118 chars omitted)
child 0, item: struct<sigma2: double, d: int64, lloyd_escape_wrong_point: string, lloyd_escape_wrong_point_rate: do (... 106 chars omitted)
child 0, sigma2: double
child 1, d: int64
child 2, lloyd_escape_wrong_point: string
child 3, lloyd_escape_wrong_point_rate: double
child 4, lloyd_keep_wrong_point: string
child 5, lloyd_keep_wrong_point_rate: double
child 6, theorem34_bound_rho_d4: double
threshold: struct<paper_eq13_sigma: double, paper_eq13_sigma2: double, note: string>
child 0, paper_eq13_sigma: double
child 1, paper_eq13_sigma2: double
child 2, note: string
claim: string
to
{'claim': Value('string'), 'threshold': {'paper_eq13_sigma': Value('float64'), 'paper_eq13_sigma2': Value('float64'), 'note': Value('string')}, 'trials': Value('int64'), 'above_threshold': List({'sigma2': Value('float64'), 'd': Value('int64'), 'lloyd_escape_wrong_point': Value('string'), 'lloyd_escape_wrong_point_rate': Value('float64'), 'lloyd_keep_wrong_point': Value('string'), 'lloyd_keep_wrong_point_rate': Value('float64'), 'theorem34_bound_rho_d4': Value('float64')}), 'below_threshold_negative_control': {'sigma2': Value('float64'), 'd': Value('int64'), 'lloyd_escape_wrong_point': Value('string'), 'lloyd_escape_wrong_point_rate': Value('float64'), 'lloyd_keep_wrong_point': Value('string'), 'lloyd_keep_wrong_point_rate': Value('float64'), 'theorem34_bound_rho_d4': Value('float64'), 'interpretation': Value('string')}, 'verdict': Value('string')}
because column names don't match
Traceback: Traceback (most recent call last):
File "/src/services/worker/src/worker/utils.py", line 149, in get_rows_or_raise
return get_rows(
dataset=dataset,
...<4 lines>...
column_names=column_names,
)
File "/src/libs/libcommon/src/libcommon/utils.py", line 272, in decorator
return func(*args, **kwargs)
File "/src/services/worker/src/worker/utils.py", line 129, in get_rows
rows_plus_one = list(itertools.islice(safe_iter(ds, dataset=dataset), rows_max_number + 1))
File "/src/services/worker/src/worker/utils.py", line 489, in safe_iter
yield from ds.decode(False) if ds.features else ds
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2818, in __iter__
for key, example in ex_iterable:
^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2355, in __iter__
for key, pa_table in self._iter_arrow():
~~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 2380, in _iter_arrow
for key, pa_table in self.ex_iterable._iter_arrow():
~~~~~~~~~~~~~~~~~~~~~~~~~~~~^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 536, in _iter_arrow
for key, pa_table in iterator:
^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/iterable_dataset.py", line 419, in _iter_arrow
for key, pa_table in self.generate_tables_fn(**gen_kwags):
~~~~~~~~~~~~~~~~~~~~~~~^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 343, in _generate_tables
self._cast_table(pa_table, json_field_paths=json_field_paths),
~~~~~~~~~~~~~~~~^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
File "/usr/local/lib/python3.14/site-packages/datasets/packaged_modules/json/json.py", line 132, in _cast_table
pa_table = table_cast(pa_table, self.info.features.arrow_schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2369, in table_cast
return cast_table_to_schema(table, schema)
File "/usr/local/lib/python3.14/site-packages/datasets/table.py", line 2297, in cast_table_to_schema
raise CastError(
...<3 lines>...
)
datasets.table.CastError: Couldn't cast
files: list<item: struct<bytes: int64, path: string, sha256: string>>
child 0, item: struct<bytes: int64, path: string, sha256: string>
child 0, bytes: int64
child 1, path: string
child 2, sha256: string
generated_at: timestamp[s]
paper: struct<arxiv: string, openreview: string, title: string>
child 0, arxiv: string
child 1, openreview: string
child 2, title: string
upstream_code: struct<commit: string, repo: string>
child 0, commit: string
child 1, repo: string
verdict: string
trials: int64
below_threshold_negative_control: struct<sigma2: double, d: int64, lloyd_escape_wrong_point: string, lloyd_escape_wrong_point_rate: do (... 130 chars omitted)
child 0, sigma2: double
child 1, d: int64
child 2, lloyd_escape_wrong_point: string
child 3, lloyd_escape_wrong_point_rate: double
child 4, lloyd_keep_wrong_point: string
child 5, lloyd_keep_wrong_point_rate: double
child 6, theorem34_bound_rho_d4: double
child 7, interpretation: string
above_threshold: list<item: struct<sigma2: double, d: int64, lloyd_escape_wrong_point: string, lloyd_escape_wrong_poi (... 118 chars omitted)
child 0, item: struct<sigma2: double, d: int64, lloyd_escape_wrong_point: string, lloyd_escape_wrong_point_rate: do (... 106 chars omitted)
child 0, sigma2: double
child 1, d: int64
child 2, lloyd_escape_wrong_point: string
child 3, lloyd_escape_wrong_point_rate: double
child 4, lloyd_keep_wrong_point: string
child 5, lloyd_keep_wrong_point_rate: double
child 6, theorem34_bound_rho_d4: double
threshold: struct<paper_eq13_sigma: double, paper_eq13_sigma2: double, note: string>
child 0, paper_eq13_sigma: double
child 1, paper_eq13_sigma2: double
child 2, note: string
claim: string
to
{'claim': Value('string'), 'threshold': {'paper_eq13_sigma': Value('float64'), 'paper_eq13_sigma2': Value('float64'), 'note': Value('string')}, 'trials': Value('int64'), 'above_threshold': List({'sigma2': Value('float64'), 'd': Value('int64'), 'lloyd_escape_wrong_point': Value('string'), 'lloyd_escape_wrong_point_rate': Value('float64'), 'lloyd_keep_wrong_point': Value('string'), 'lloyd_keep_wrong_point_rate': Value('float64'), 'theorem34_bound_rho_d4': Value('float64')}), 'below_threshold_negative_control': {'sigma2': Value('float64'), 'd': Value('int64'), 'lloyd_escape_wrong_point': Value('string'), 'lloyd_escape_wrong_point_rate': Value('float64'), 'lloyd_keep_wrong_point': Value('string'), 'lloyd_keep_wrong_point_rate': Value('float64'), 'theorem34_bound_rho_d4': Value('float64'), 'interpretation': Value('string')}, 'verdict': Value('string')}
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The Catastrophic Failure of the k-Means Algorithm in High Dimensions, and How Hartigan's Algorithm Avoids It
Summary
This repository provides the kmeansx library and scripts needed to reproduce the results of our paper, available as a preprint and accepted to ICML 2026 (ICML link TBA). Pre-computed results and reproduction scripts are available on Zenodo.
kmeansx implements Lloyd's and Hartigan's k-means algorithms in JAX, with a scikit-learn-style API. It also provides a wrapper around scikit-learn's Spectral Clustering and an SDP-based clustering implementation via CVXPY.
Installation
If you have a GPU and want to use it for computation, install JAX with CUDA support first:
pip install jax[cuda12]
Then install the package:
pip install .
Quick Start
kmeansx follows a scikit-learn-style API:
import kmeansx
import jax.random as jr
data = ... # array of shape (n_samples, n_features)
kmeans = kmeansx.KMeans(
n_clusters=...,
n_init=...,
max_iter=...,
init=..., # 'random', 'random_partition', or 'kmeans++'
algorithm=..., # 'Hartigan' or 'Lloyd'
)
result = kmeans.fit(
key=jr.key(seed),
data=data,
output="best", # 'best' returns the run with lowest k-means loss
# 'all' returns all runs with an extra batch dimension
)
print(result)
# KmeansSolution(centroids=..., labels=..., loss=...)
Repository Structure
src/kmeansx/
├── kmeans/ # Lloyd and Hartigan k-means implementations (JAX)
├── metrics/ # Clustering evaluation metrics
├── _other_algos/ # Spectral clustering (sklearn wrapper) and SDP clustering (CVXPY)
└── svd_utils.py # PCA and randomized SVD utilities
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