sklearn.cluster
.KMeans¶

class
sklearn.cluster.
KMeans
(n_clusters=8, init=’kmeans++’, n_init=10, max_iter=300, tol=0.0001, precompute_distances=’auto’, verbose=0, random_state=None, copy_x=True, n_jobs=1, algorithm=’auto’)[source]¶ KMeans clustering
Read more in the User Guide.
Parameters:  n_clusters : int, optional, default: 8
The number of clusters to form as well as the number of centroids to generate.
 init : {‘kmeans++’, ‘random’ or an ndarray}
Method for initialization, defaults to ‘kmeans++’:
‘kmeans++’ : selects initial cluster centers for kmean 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 kmeans 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 kmeans algorithm for a single run.
 tol : float, default: 1e4
Relative tolerance with regards to inertia to declare convergence
 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
 verbose : int, default 0
Verbosity mode.
 random_state : int, RandomState instance or None (default)
Determines random number generation for centroid initialization. Use an int to make the randomness deterministic. See Glossary.
 copy_x : boolean, optional
When precomputing 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 Ccontiguous. 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 Ccontiguous which may cause a significant slowdown.
 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”
Kmeans algorithm to use. The classical EMstyle 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_ : array, [n_clusters, n_features]
Coordinates of cluster centers
 labels_ :
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 minibatches. For large scale learning (say n_samples > 10k) MiniBatchKMeans is probably much faster than the default batch implementation.
Notes
The kmeans 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 kmeans method?’ SoCG2006)
In practice, the kmeans 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
ofmax_iter
),labels_
andmeans_
will not be consistent, i.e. themeans_
will not be the means of the points in each cluster. Also, the estimator will reassignlabels_
after the last iteration to makelabels_
consistent withpredict
on the training set.Examples
>>> from sklearn.cluster import KMeans >>> import numpy as np >>> X = np.array([[1, 2], [1, 4], [1, 0], ... [4, 2], [4, 4], [4, 0]]) >>> kmeans = KMeans(n_clusters=2, random_state=0).fit(X) >>> kmeans.labels_ array([0, 0, 0, 1, 1, 1], dtype=int32) >>> kmeans.predict([[0, 0], [4, 4]]) array([0, 1], dtype=int32) >>> kmeans.cluster_centers_ array([[1., 2.], [4., 2.]])
Methods
fit
(X[, y, sample_weight])Compute kmeans clustering. fit_predict
(X[, y, sample_weight])Compute cluster centers and predict cluster index for each sample. fit_transform
(X[, y, sample_weight])Compute clustering and transform X to clusterdistance space. get_params
([deep])Get parameters for this estimator. predict
(X[, sample_weight])Predict the closest cluster each sample in X belongs to. score
(X[, y, sample_weight])Opposite of the value of X on the Kmeans objective. set_params
(**params)Set the parameters of this estimator. transform
(X)Transform X to a clusterdistance space. 
__init__
(n_clusters=8, init=’kmeans++’, n_init=10, max_iter=300, tol=0.0001, precompute_distances=’auto’, verbose=0, random_state=None, copy_x=True, n_jobs=1, algorithm=’auto’)[source]¶

fit
(X, y=None, sample_weight=None)[source]¶ Compute kmeans clustering.
Parameters:  X : arraylike or sparse matrix, shape=(n_samples, n_features)
Training instances 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 Ccontiguous.
 y : Ignored
 sample_weight : arraylike, shape (n_samples,), optional
The weights for each observation in X. If None, all observations are assigned equal weight (default: None)

fit_predict
(X, y=None, sample_weight=None)[source]¶ Compute cluster centers and predict cluster index for each sample.
Convenience method; equivalent to calling fit(X) followed by predict(X).
Parameters:  X : {arraylike, sparse matrix}, shape = [n_samples, n_features]
New data to transform.
 y : Ignored
 sample_weight : arraylike, shape (n_samples,), optional
The weights for each observation in X. If None, all observations are assigned equal weight (default: None)
Returns:  labels : array, shape [n_samples,]
Index of the cluster each sample belongs to.

fit_transform
(X, y=None, sample_weight=None)[source]¶ Compute clustering and transform X to clusterdistance space.
Equivalent to fit(X).transform(X), but more efficiently implemented.
Parameters:  X : {arraylike, sparse matrix}, shape = [n_samples, n_features]
New data to transform.
 y : Ignored
 sample_weight : arraylike, shape (n_samples,), optional
The weights for each observation in X. If None, all observations are assigned equal weight (default: None)
Returns:  X_new : array, shape [n_samples, k]
X transformed in the new space.

get_params
(deep=True)[source]¶ Get parameters for this estimator.
Parameters:  deep : boolean, optional
If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:  params : mapping of string to any
Parameter names mapped to their values.

predict
(X, sample_weight=None)[source]¶ Predict the closest cluster each sample in X belongs to.
In the vector quantization literature, cluster_centers_ is called the code book and each value returned by predict is the index of the closest code in the code book.
Parameters:  X : {arraylike, sparse matrix}, shape = [n_samples, n_features]
New data to predict.
 sample_weight : arraylike, shape (n_samples,), optional
The weights for each observation in X. If None, all observations are assigned equal weight (default: None)
Returns:  labels : array, shape [n_samples,]
Index of the cluster each sample belongs to.

score
(X, y=None, sample_weight=None)[source]¶ Opposite of the value of X on the Kmeans objective.
Parameters:  X : {arraylike, sparse matrix}, shape = [n_samples, n_features]
New data.
 y : Ignored
 sample_weight : arraylike, shape (n_samples,), optional
The weights for each observation in X. If None, all observations are assigned equal weight (default: None)
Returns:  score : float
Opposite of the value of X on the Kmeans objective.

set_params
(**params)[source]¶ Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects (such as pipelines). The latter have parameters of the form
<component>__<parameter>
so that it’s possible to update each component of a nested object.Returns:  self

transform
(X)[source]¶ Transform X to a clusterdistance space.
In the new space, each dimension is the distance to the cluster centers. Note that even if X is sparse, the array returned by transform will typically be dense.
Parameters:  X : {arraylike, sparse matrix}, shape = [n_samples, n_features]
New data to transform.
Returns:  X_new : array, shape [n_samples, k]
X transformed in the new space.