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# `sklearn.cluster`.KMeans

class sklearn.cluster.KMeans(n_clusters=8, *, init='k-means++', n_init='warn', max_iter=300, tol=0.0001, verbose=0, random_state=None, copy_x=True, algorithm='lloyd')

  K-Means clustering.

  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.

      For an example of how to use the different `init` strategy, see the example entitled A demo of K-Means clustering on the handwritten digits data.

    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'` or `init` is a callable; 1 if using `init='k-means++'` or `init` is an array-like.

      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.

  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), 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 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, 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_metadata_routing`() | Get metadata routing of this object.
  `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_fit_request`(*[, sample_weight]) | Request metadata passed to the `fit` method.
  `set_output`(*[, transform]) | Set output container.
  `set_params`(**params) | Set the parameters of this estimator.
  `set_predict_request`(*[, sample_weight]) | Request metadata passed to the `predict` method.
  `set_score_request`(*[, sample_weight]) | Request metadata passed to the `score` method.
  `transform`(X) | Transform X to a cluster-distance space.

  fit(X, y=None, sample_weight=None)

    Compute k-means clustering.

    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.

      y Ignored

        Not used, present here for API consistency by convention.

      sample_weight array-like of shape (n_samples,), default=None

        The weights for each observation in X. If None, all observations are assigned equal weight. `sample_weight` is not used during initialization if `init` is a callable or a user provided array.

        New in version 0.20.

    Returns:
      self object

        Fitted estimator.

  fit_predict(X, y=None, sample_weight=None)

    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.

      y Ignored

        Not used, present here for API consistency by convention.

      sample_weight array-like of shape (n_samples,), default=None

        The weights for each observation in X. If None, all observations are assigned equal weight.

    Returns:
      labels ndarray of shape (n_samples,)

        Index of the cluster each sample belongs to.

  fit_transform(X, y=None, sample_weight=None)

    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.

      y Ignored

        Not used, present here for API consistency by convention.

      sample_weight array-like of shape (n_samples,), default=None

        The weights for each observation in X. If None, all observations are assigned equal weight.

    Returns:
      X_new ndarray of shape (n_samples, n_clusters)

        X transformed in the new space.

  get_feature_names_out(input_features=None)

    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_features array-like of str or None, default=None

        Only used to validate feature names with the names seen in `fit`.

    Returns:
      feature_names_out ndarray of str objects

        Transformed feature names.

  get_metadata_routing()

    Get metadata routing of this object.

    Please check User Guide on how the routing mechanism works.

    Returns:
      routing MetadataRequest

        A `MetadataRequest` encapsulating routing information.

  get_params(deep=True)

    Get parameters for this estimator.

    Parameters:
      deep bool, default=True

        If True, will return the parameters for this estimator and contained subobjects that are estimators.

    Returns:
      params dict

        Parameter names mapped to their values.

  predict(X, sample_weight='deprecated')

    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_weight array-like of shape (n_samples,), default=None

        The weights for each observation in X. If None, all observations are assigned equal weight.

        Deprecated since version 1.3: The parameter `sample_weight` is deprecated in version 1.3 and will be removed in 1.5.

    Returns:
      labels ndarray of shape (n_samples,)

        Index of the cluster each sample belongs to.

  score(X, y=None, sample_weight=None)

    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.

      y Ignored

        Not used, present here for API consistency by convention.

      sample_weight array-like of shape (n_samples,), default=None

        The weights for each observation in X. If None, all observations are assigned equal weight.

    Returns:
      score float

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

  set_fit_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → KMeans

    Request metadata passed to the `fit` method.

    Note that this method is only relevant if `enable_metadata_routing=True` (see `sklearn.set_config`). Please see User Guide on how the routing mechanism works.

    The options for each parameter are:

    - `True`: metadata is requested, and passed to `fit` if provided. The request is ignored if metadata is not provided.

    - `False`: metadata is not requested and the meta-estimator will not pass it to `fit`.

    - `None`: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

    - `str`: metadata should be passed to the meta-estimator with this given alias instead of the original name.

    The default (`sklearn.utils.metadata_routing.UNCHANGED`) retains the existing request. This allows you to change the request for some parameters and not others.

    New in version 1.3.

    Note

    This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a `Pipeline`. Otherwise it has no effect.

    Parameters:
      sample_weight str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

        Metadata routing for `sample_weight` parameter in `fit`.

    Returns:
      self object

        The updated object.

  set_output(*, transform=None)

    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

    Returns:
      self estimator instance

        Estimator instance.

  set_params(**params)

    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:
      **params dict

        Estimator parameters.

    Returns:
      self estimator instance

        Estimator instance.

  set_predict_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → KMeans

    Request metadata passed to the `predict` method.

    Note that this method is only relevant if `enable_metadata_routing=True` (see `sklearn.set_config`). Please see User Guide on how the routing mechanism works.

    The options for each parameter are:

    - `True`: metadata is requested, and passed to `predict` if provided. The request is ignored if metadata is not provided.

    - `False`: metadata is not requested and the meta-estimator will not pass it to `predict`.

    - `None`: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

    - `str`: metadata should be passed to the meta-estimator with this given alias instead of the original name.

    The default (`sklearn.utils.metadata_routing.UNCHANGED`) retains the existing request. This allows you to change the request for some parameters and not others.

    New in version 1.3.

    Note

    This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a `Pipeline`. Otherwise it has no effect.

    Parameters:
      sample_weight str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

        Metadata routing for `sample_weight` parameter in `predict`.

    Returns:
      self object

        The updated object.

  set_score_request(*, sample_weight: bool | None | str = '$UNCHANGED$') → KMeans

    Request metadata passed to the `score` method.

    Note that this method is only relevant if `enable_metadata_routing=True` (see `sklearn.set_config`). Please see User Guide on how the routing mechanism works.

    The options for each parameter are:

    - `True`: metadata is requested, and passed to `score` if provided. The request is ignored if metadata is not provided.

    - `False`: metadata is not requested and the meta-estimator will not pass it to `score`.

    - `None`: metadata is not requested, and the meta-estimator will raise an error if the user provides it.

    - `str`: metadata should be passed to the meta-estimator with this given alias instead of the original name.

    The default (`sklearn.utils.metadata_routing.UNCHANGED`) retains the existing request. This allows you to change the request for some parameters and not others.

    New in version 1.3.

    Note

    This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a `Pipeline`. Otherwise it has no effect.

    Parameters:
      sample_weight str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

        Metadata routing for `sample_weight` parameter in `score`.

    Returns:
      self object

        The updated object.

  transform(X)

    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_new ndarray of shape (n_samples, n_clusters)

        X transformed in the new space.

## Examples using `sklearn.cluster.KMeans`

Release Highlights for scikit-learn 1.1

Release Highlights for scikit-learn 1.1

Release Highlights for scikit-learn 0.23

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