class mars.learn.cluster.KMeans(n_clusters=8, init='k-means||', n_init=1, max_iter=300, tol=0.0001, verbose=0, random_state=None, copy_x=True, algorithm='auto', oversampling_factor=2, init_iter=5)[source]

K-Means clustering.

Read more in the User Guide.

  • n_clusters (int, default=8) – The number of clusters to form as well as the number of centroids to generate.

  • init ({'k-means++', 'k-means||', 'random'} or tensor of shape (n_clusters, n_features), default='k-means||') –

    Method for initialization, defaults 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.

    ’k-means||’: scalable k-means++.

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

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

  • n_init (int, default=1) – 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, default=300) – Maximum number of iterations of the k-means algorithm for a single run.

  • tol (float, default=1e-4) – Relative tolerance with regards to inertia to declare convergence.

  • verbose (int, default=0) – Verbosity mode.

  • random_state (int, RandomState instance, default=None) – Determines random number generation for centroid initialization. Use an int to make the randomness deterministic. See Glossary.

  • copy_x (bool, default=True) – 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.

  • algorithm ({"auto", "full", "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.

  • oversampling_factor (int, default=2) – Only work for kmeans||, used in each iteration in kmeans||.

  • init_iter (int, default=5) – Only work for kmeans||, indicates how may iterations required.


Coordinates of cluster centers. If the algorithm stops before fully converging (see tol and max_iter), these will not be consistent with labels_.


tensor of shape (n_clusters, n_features)


Labels of each point


tensor of shape (n_samples,)


Sum of squared distances of samples to their closest cluster center.




Number of iterations run.



See also


Alternative online implementation that does incremental updates of the centers positions using mini-batches. For large scale learning (say n_samples > 10k) MiniBatchKMeans is probably much faster than the default batch implementation.


The k-means problem is solved using either Lloyd’s or Elkan’s algorithm.

The average complexity is given by O(k n T), were n is the number of samples and T is the number of iteration.

The worst case complexity is given by O(n^(k+2/p)) with n = n_samples, p = n_features. (D. Arthur and S. Vassilvitskii, ‘How slow is the k-means method?’ SoCG2006)

In practice, the k-means algorithm is very fast (one of the fastest clustering algorithms available), but it falls in local minima. That’s why it can be useful to restart it several times.

If the algorithm stops before fully converging (because of tol or max_iter), labels_ and cluster_centers_ will not be consistent, i.e. the cluster_centers_ will not be the means of the points in each cluster. Also, the estimator will reassign labels_ after the last iteration to make labels_ consistent with predict on the training set.


>>> from mars.learn.cluster import KMeans
>>> import mars.tensor as mt
>>> X = mt.array([[1, 2], [1, 4], [1, 0],
...               [10, 2], [10, 4], [10, 0]])
>>> kmeans = KMeans(n_clusters=2, random_state=0, init='k-means++').fit(X)
>>> kmeans.labels_
array([1, 1, 1, 0, 0, 0], dtype=int32)
>>> kmeans.predict([[0, 0], [12, 3]])
array([1, 0], dtype=int32)
>>> kmeans.cluster_centers_
array([[10.,  2.],
       [ 1.,  2.]])
__init__(n_clusters=8, init='k-means||', n_init=1, max_iter=300, tol=0.0001, verbose=0, random_state=None, copy_x=True, algorithm='auto', oversampling_factor=2, init_iter=5)[source]

Initialize self. See help(type(self)) for accurate signature.


__init__([n_clusters, init, n_init, …])

Initialize self.

fit(X[, y, sample_weight, session, run_kwargs])

Compute k-means clustering.

fit_predict(X[, y, sample_weight, session, …])

Compute cluster centers and predict cluster index for each sample.

fit_transform(X[, y, sample_weight, …])

Compute clustering and transform X to cluster-distance space.


Get parameters for this estimator.

predict(X[, sample_weight, session, run_kwargs])

Predict the closest cluster each sample in X belongs to.

score(X[, y, sample_weight, session, run_kwargs])

Opposite of the value of X on the K-means objective.


Set the parameters of this estimator.

transform(X[, session, run_kwargs])

Transform X to a cluster-distance space.