sklearn.cluster.k_means(X, n_clusters, 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=1, algorithm=’auto’, return_n_iter=False)[source]

K-means clustering algorithm.

Read more in the User Guide.


X : array-like or sparse matrix, shape (n_samples, n_features)

The observations to cluster.

n_clusters : int

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

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’: generate k centroids from a Gaussian with mean and variance estimated from the data.

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_init : int, 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_iter : int, optional, default 300

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

verbose : boolean, optional

Verbosity mode.

tol : float, optional

The relative increment in the results before declaring convergence.

random_state : int, RandomState instance or None, optional, default: None

If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.

copy_x : boolean, optional

When pre-computing distances it is more numerically accurate to center the data first. If copy_x is True, then the original data is not modified. 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.

n_jobs : int

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

If -1 all CPUs are used. If 1 is given, no parallel computing code is used at all, which is useful for debugging. For n_jobs below -1, (n_cpus + 1 + n_jobs) are used. Thus for n_jobs = -2, all CPUs but one are used.

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_iter : bool, optional

Whether or not to return the number of iterations.


centroid : float ndarray with shape (k, n_features)

Centroids found at the last iteration of k-means.

label : integer ndarray with shape (n_samples,)

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

inertia : float

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

best_n_iter : int

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