K-Means clustering.
Read more in the :ref:`User Guide <k_means>`.
Parameters ----------
n_clusters : int, default=8 The number of clusters to form as well as the number of centroids to generate.
init : 'k-means++', 'random'
or ndarray 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.
'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.
n_init : int, 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, 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.
precompute_distances : 'auto' or bool, default='auto' 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.
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 :term:`Glossary <random_state>`.
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.
n_jobs : int, 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 :obj:`joblib.parallel_backend` context. ``-1`` means using all processors. See :term:`Glossary <n_jobs>` for more details.
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.
Attributes ---------- cluster_centers_ : ndarray of shape (n_clusters, n_features) Coordinates of cluster centers. If the algorithm stops before fully converging (see ``tol`` and ``max_iter``), these will not be consistent with ``labels_``.
labels_ : ndarray of shape (n_samples,) Labels of each point
inertia_ : float Sum of squared distances of samples to their closest cluster center.
n_iter_ : int Number of iterations run.
See Also --------
MiniBatchKMeans 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.
Notes ----- 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.
Examples --------
>>> from sklearn.cluster import KMeans >>> import numpy as np >>> X = np.array([1, 2], [1, 4], [1, 0],
... [10, 2], [10, 4], [10, 0]
) >>> kmeans = KMeans(n_clusters=2, random_state=0).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.]
)