sklearn.cluster.KMeans — scikit-learn 1.2.2 documentation

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Read more in the User Guide .

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’}, callable or array-like of shape (n_clusters, n_features), default=’k-means++’

Method for initialization:

‘k-means++’ : selects initial cluster centroids using sampling based on an empirical probability distribution of the points’ contribution to the overall inertia. This technique speeds up convergence. The algorithm implemented is “greedy k-means++”. It differs from the vanilla k-means++ by making several trials at each sampling step and choosing the best centroid among them.

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

If an array 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, n_clusters and a random state and return an initialization.

n_init ‘auto’ or int, default=10

Number of times the k-means algorithm is run with different centroid seeds. The final results is the best output of n_init consecutive runs in terms of inertia. Several runs are recommended for sparse high-dimensional problems (see Clustering sparse data with k-means ).

When n_init='auto' , the number of runs depends on the value of init: 10 if using init='random' , 1 if using init='k-means++' .

New in version 1.2: Added ‘auto’ option for n_init .

Changed in version 1.4: Default value for n_init will change from 10 to 'auto' in version 1.4.

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 Frobenius norm of the difference in the cluster centers of two consecutive iterations to declare convergence.

verbose int, default=0

Verbosity mode.

random_state int, RandomState instance or None, 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. 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. Note that if the original data is not C-contiguous, a copy will be made even if copy_x is False. If the original data is sparse, but not in CSR format, a copy will be made even if copy_x is False.

algorithm {“lloyd”, “elkan”, “auto”, “full”}, default=”lloyd”

K-means algorithm to use. The classical EM-style algorithm is "lloyd" . The "elkan" variation can be more efficient on some datasets with well-defined clusters, by using the triangle inequality. However it’s more memory intensive due to the allocation of an extra array of shape (n_samples, n_clusters) .

"auto" and "full" are deprecated and they will be removed in Scikit-Learn 1.3. They are both aliases for "lloyd" .

Changed in version 0.18: Added Elkan algorithm

Changed in version 1.1: Renamed “full” to “lloyd”, and deprecated “auto” and “full”. Changed “auto” to use “lloyd” instead of “elkan”.

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, weighted by the sample weights if provided.

n_iter_ int

Number of iterations run.

n_features_in_ int

Number of features seen during fit .

New in version 0.24.

feature_names_in_ ndarray of shape (


     
      n_features_in_

Names of features seen during fit . Defined only when X has feature names that are all strings.

New in version 1.0.

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), where 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. Refer to “How slow is the k-means method?” D. Arthur and S. Vassilvitskii - SoCG2006. for more details.

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

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, n_init="auto").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.]])
Methods
fit(X[, y, sample_weight])
Compute k-means 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 cluster-distance space.
get_feature_names_out([input_features])
Get output feature names for transformation.
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 K-means objective.
set_output(*[, transform])
Set output container.
set_params(**params)
Set the parameters of this estimator.
transform(X)
Transform X to a cluster-distance space.
Parameters:
X{array-like, sparse matrix} of 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 C-contiguous.
If a sparse matrix is passed, a copy will be made if it’s not in
CSR format.
yIgnored
Not used, present here for API consistency by convention.
sample_weightarray-like of shape (n_samples,), default=None
The weights for each observation in X. If None, all observations
are assigned equal weight.
New in version 0.20.
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{array-like, sparse matrix} of shape (n_samples, n_features)
New data to transform.
yIgnored
Not used, present here for API consistency by convention.
sample_weightarray-like of shape (n_samples,), default=None
The weights for each observation in X. If None, all observations
are assigned equal weight.
Returns:
labelsndarray of 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 cluster-distance space.
Equivalent to fit(X).transform(X), but more efficiently implemented.
Parameters:
X{array-like, sparse matrix} of shape (n_samples, n_features)
New data to transform.
yIgnored
Not used, present here for API consistency by convention.
sample_weightarray-like of shape (n_samples,), default=None
The weights for each observation in X. If None, all observations
are assigned equal weight.
Returns:
X_newndarray of shape (n_samples, n_clusters)
X transformed in the new space.
get_feature_names_out(input_features=None)[source]¶
Get output feature names for transformation.
The feature names out will prefixed by the lowercased class name. For
example, if the transformer outputs 3 features, then the feature names
out are: ["class_name0", "class_name1", "class_name2"].
Parameters:
input_featuresarray-like of str or None, default=None
Only used to validate feature names with the names seen in fit.
Returns:
feature_names_outndarray of str objects
Transformed feature names.
Parameters:
deepbool, default=True
If True, will return the parameters for this estimator and
contained subobjects that are estimators.
Returns:
paramsdict
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{array-like, sparse matrix} of shape (n_samples, n_features)
New data to predict.
sample_weightarray-like of shape (n_samples,), default=None
The weights for each observation in X. If None, all observations
are assigned equal weight.
Returns:
labelsndarray of 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 K-means objective.
Parameters:
X{array-like, sparse matrix} of shape (n_samples, n_features)
New data.
yIgnored
Not used, present here for API consistency by convention.
sample_weightarray-like of shape (n_samples,), default=None
The weights for each observation in X. If None, all observations
are assigned equal weight.
Returns:
scorefloat
Opposite of the value of X on the K-means objective.
set_output(*, transform=None)[source]¶
Set output container.
See Introducing the set_output API
for an example on how to use the API.
Parameters:
transform{“default”, “pandas”}, default=None
Configure output of transform and fit_transform.
"default": Default output format of a transformer
"pandas": DataFrame output
None: Transform configuration is unchanged
set_params(**params)[source]¶
Set the parameters of this estimator.
The method works on simple estimators as well as on nested objects
(such as Pipeline). The latter have
parameters of the form <component>__<parameter> so that it’s
possible to update each component of a nested object.
Parameters:
**paramsdict
Estimator parameters.
Returns:
selfestimator instance
Estimator instance.
transform(X)[source]¶
Transform X to a cluster-distance 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{array-like, sparse matrix} of shape (n_samples, n_features)
New data to transform.
Returns:
X_newndarray of shape (n_samples, n_clusters)
X transformed in the new space.
  Release Highlights for scikit-learn 0.23




    

A demo of K-Means clustering on the handwritten digits data
  A demo of K-Means clustering on the handwritten digits data
Bisecting K-Means and Regular K-Means Performance Comparison
  Bisecting K-Means and Regular K-Means Performance Comparison
Color Quantization using K-Means
  Color Quantization using K-Means
Comparison of the K-Means and MiniBatchKMeans clustering algorithms
  Comparison of the K-Means and MiniBatchKMeans clustering algorithms
Demonstration of k-means assumptions
  Demonstration of k-means assumptions
Empirical evaluation of the impact of k-means initialization
  Empirical evaluation of the impact of k-means initialization
K-means Clustering
  K-means Clustering
Selecting the number of clusters with silhouette analysis on KMeans clustering
  Selecting the number of clusters with silhouette analysis on KMeans clustering
Clustering text documents using k-means
  Clustering text documents using k-means