sklearn.cluster.k_means(X, n_clusters, sample_weight=None, init='k-means++', precompute_distances='auto', n_init=10, max_iter=300, verbose=False, tol=0.0001, random_state=None, copy_x=True, n_jobs=None, algorithm='auto', return_n_iter=False)[source]

K-means clustering algorithm.

Read more in the User Guide.

Xarray-like or sparse matrix, shape (n_samples, n_features)

The observations to cluster. It must be noted that the data will be converted to C ordering, which will cause a memory copy if the given data is not C-contiguous.


The number of clusters to form as well as the number of centroids to generate.

sample_weightarray-like, shape (n_samples,), optional

The weights for each observation in X. If None, all observations are assigned equal weight (default: None)

init{‘k-means++’, ‘random’, or ndarray, or a callable}, optional

Method for initialization, default to ‘k-means++’:

‘k-means++’ : selects initial cluster centers for k-mean clustering in a smart way to speed up convergence. See section Notes in k_init for more details.

‘random’: choose k observations (rows) at random from data for the initial centroids.

If an ndarray is passed, it should be of shape (n_clusters, n_features) and gives the initial centers.

If a callable is passed, it should take arguments X, k and and a random state and return an initialization.

precompute_distances{‘auto’, True, False}

Precompute distances (faster but takes more memory).

‘auto’ : do not precompute distances if n_samples * n_clusters > 12 million. This corresponds to about 100MB overhead per job using double precision.

True : always precompute distances

False : never precompute distances

n_initint, optional, default: 10

Number of time the k-means algorithm will be run with different centroid seeds. The final results will be the best output of n_init consecutive runs in terms of inertia.

max_iterint, optional, default 300

Maximum number of iterations of the k-means algorithm to run.

verboseboolean, optional

Verbosity mode.

tolfloat, optional

The relative increment in the results before declaring convergence.

random_stateint, RandomState instance or None (default)

Determines random number generation for centroid initialization. Use an int to make the randomness deterministic. See Glossary.

copy_xbool, optional

When pre-computing distances it is more numerically accurate to center the data first. If copy_x is True (default), then the original data is not modified, ensuring X is C-contiguous. If False, the original data is modified, and put back before the function returns, but small numerical differences may be introduced by subtracting and then adding the data mean, in this case it will also not ensure that data is C-contiguous which may cause a significant slowdown.

n_jobsint or None, optional (default=None)

The number of jobs to use for the computation. This works by computing each of the n_init runs in parallel.

None means 1 unless in a joblib.parallel_backend context. -1 means using all processors. See Glossary for more details.

algorithm“auto”, “full” or “elkan”, default=”auto”

K-means algorithm to use. The classical EM-style algorithm is “full”. The “elkan” variation is more efficient by using the triangle inequality, but currently doesn’t support sparse data. “auto” chooses “elkan” for dense data and “full” for sparse data.

return_n_iterbool, optional

Whether or not to return the number of iterations.

centroidfloat ndarray with shape (k, n_features)

Centroids found at the last iteration of k-means.

labelinteger ndarray with shape (n_samples,)

label[i] is the code or index of the centroid the i’th observation is closest to.


The final value of the inertia criterion (sum of squared distances to the closest centroid for all observations in the training set).


Number of iterations corresponding to the best results. Returned only if return_n_iter is set to True.