[BUG] `KMeans.transform` returns squared distances instead of Euclidean distances

[apiqwe]

Describe the bug

cuml.cluster.KMeans.transform() returns squared Euclidean distances to cluster centers, while sklearn.cluster.KMeans.transform() returns Euclidean distances.

For the first transformed sample, the distances to the two centers should be sqrt(2) and sqrt(242). cuML instead returns 2 and 242, respectively. Every cuML output value is the square of the corresponding scikit-learn distance.

Steps/Code to reproduce bug

cuML reproducer:

import numpy as np
from cuml.cluster import KMeans

model = KMeans(n_clusters=2,init=np.array([[1., 1.],[11., 11.],]),n_init=1,).fit(np.array([[0., 0.],[1., 1.],[2., 2.],[10., 10.],[11., 11.],[12., 12.],]))

print(model.transform(np.array([[0., 0.],[10., 10.],])))

Output:

[[  2. 242.]
 [162.   2.]]

For comparison, the equivalent scikit-learn code:

import numpy as np
from sklearn.cluster import KMeans

model = KMeans(n_clusters=2,init=np.array([[1., 1.],[11., 11.],]),n_init=1,).fit(np.array([[0., 0.],[1., 1.],[2., 2.],[10., 10.],[11., 11.],[12., 12.],]))

print(model.transform(np.array([[0., 0.],[10., 10.],])))

Output:

[[ 1.41421356 15.55634919]
 [12.72792206  1.41421356]]

Expected behavior

KMeans.transform() should return the Euclidean distance from each sample to each cluster center, matching the established scikit-learn cluster-distance-space API.

For the fitted centers [1, 1] and [11, 11], the expected transformed matrix is:

[[sqrt(2),   sqrt(242)],
 [sqrt(162), sqrt(2)  ]]

which evaluates to:

[[ 1.41421356 15.55634919]
 [12.72792206  1.41421356]]

Environment details (please complete the following information):

• Environment location: Docker
• Linux Distro/Architecture: Ubuntu 24.04 / x86_64
• GPU Model/Driver: NVIDIA GeForce RTX 4090 / 595.71.05
• CUDA: 13.2
• Method of cuDF & cuML install: conda

conda list:

conda list
# packages in environment at /opt/conda/envs/rapids-26.08:
#
# Name                              Version          Build                                         Channel
# Name              Version       Build                                      Channel
python              3.14.6        h242f9ac_102_cp314                         conda-forge
numpy               2.4.6         py314h2b28147_0                            conda-forge
scipy               1.16.3        py314hf07bd8e_2                            conda-forge
scikit-learn        1.9.0         np2py314hf09ca88_0                         conda-forge
rapids              26.08.00      cuda13_260806_c2656556                     rapidsai
cuml                26.08.00      cuda13_cp311_abi3_260805_265b9da6          rapidsai
libcuml             26.08.00      cuda13_260805_265b9da6                     rapidsai
cudf                26.08.00      cuda13_cp311_abi3_260805_ff5b362d          rapidsai
libraft             26.08.00      cuda13_260805_ebf92684                     rapidsai
libraft-headers     26.08.00      cuda13_260805_ebf92684                     rapidsai
pylibraft           26.08.00      cuda13_cp311_abi3_260805_ebf92684          rapidsai
cuvs                26.08.01      cuda13_cp311_abi3_260806_25b1be43          rapidsai
libcuvs             26.08.01      cuda13_260806_25b1be43                     rapidsai
cupy                14.1.1        py314hdea9c46_0                            conda-forge
cupy-core           14.1.1        py314hcd3b49b_0                            conda-forge
numba               0.64.0        py314h8169c2f_0                            conda-forge
numba-cuda          0.30.4        py314h42812f9_0                            conda-forge
rmm                 26.08.00      cuda13_cp311_abi3_260805_42d059f1          rapidsai
librmm              26.08.00      cuda13_260805_42d059f1                     rapidsai
cuda-version        13.3           hcbadf70_3                                 conda-forge
cuda-bindings       13.3.1        py314h42812f9_1                            conda-forge
cuda-cudart         13.3.29       hecca717_0                                 conda-forge
cuda-nvrtc          13.3.33       hecca717_0                                 conda-forge
libcublas           13.6.0.2      h676940d_0                                 conda-forge
libcusolver         12.2.6.9      h676940d_0                                 conda-forge
libcusparse         12.8.2.51     hecca717_0                                 conda-forge
libcurand           10.4.3.29     h676940d_0                                 conda-forge

Additional context

The model is deterministic because the initial centers are provided explicitly and n_init=1. Fitting leaves the two centers at [1, 1] and [11, 11].

The relationship between the outputs is exact:

1.41421356 ** 2 = 2
15.55634919 ** 2 = 242
12.72792206 ** 2 = 162

This suggests that cuML exposes the internal squared-distance matrix without applying the final square root required by the scikit-learn-compatible transform() contract.

The cuML KMeans documentation describes this method as transforming input into cluster-distance space and refers users to scikit-learn's KMeans API. Returning squared distances changes magnitudes and can silently affect downstream estimators that consume transformed features.

[Hashim1999164]

I will take this. transform should return Euclidean distances to match sklearn.