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# `sklearn.cluster`.BisectingKMeans

class sklearn.cluster.BisectingKMeans(n_clusters=8, *, init='random', n_init=1, random_state=None, max_iter=300, verbose=0, tol=0.0001, copy_x=True, algorithm='lloyd', bisecting_strategy='biggest_inertia')

  Bisecting K-Means clustering.

  Read more in the User Guide.

  New in version 1.1.

  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 callable, default=’random’

      Method for initialization:

      ‘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 `n_clusters` observations (rows) at random from data for the initial centroids.

      If a callable is passed, it should take arguments X, n_clusters and a random state and return an initialization.

    n_init int, default=1

      Number of time the inner k-means algorithm will be run with different centroid seeds in each bisection. That will result producing for each bisection best output of n_init consecutive runs in terms of inertia.

    random_state int, RandomState instance or None, default=None

      Determines random number generation for centroid initialization in inner K-Means. Use an int to make the randomness deterministic. See Glossary.

    max_iter int, default=300

      Maximum number of iterations of the inner k-means algorithm at each bisection.

    verbose int, default=0

      Verbosity mode.

    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. Used in inner k-means algorithm at each bisection to pick best possible clusters.

    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”}, default=”lloyd”

      Inner K-means algorithm used in bisection. 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)`.

    bisecting_strategy{“biggest_inertia”, “largest_cluster”}, default=”biggest_inertia”

      Defines how bisection should be performed:

      > - “biggest_inertia” means that BisectingKMeans will always check

      >     all calculated cluster for cluster with biggest SSE (Sum of squared errors) and bisect it. This approach concentrates on precision, but may be costly in terms of execution time (especially for larger amount of data points).

      > - “largest_cluster” - BisectingKMeans will always split cluster with

      >     largest amount of points assigned to it from all clusters previously calculated. That should work faster than picking by SSE (‘biggest_inertia’) and may produce similar results in most cases.

  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_features_in_int

      Number of features seen during fit.

    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.

  See also

  `KMeans`

    Original implementation of K-Means algorithm.

  Notes

  It might be inefficient when n_cluster is less than 3, due to unnecessary calculations for that case.

  Examples

      >>> from sklearn.cluster import BisectingKMeans
      >>> import numpy as np
      >>> X = np.array([[1, 1], [10, 1], [3, 1],
      ...               [10, 0], [2, 1], [10, 2],
      ...               [10, 8], [10, 9], [10, 10]])
      >>> bisect_means = BisectingKMeans(n_clusters=3, random_state=0).fit(X)
      >>> bisect_means.labels_
      array([0, 2, 0, 2, 0, 2, 1, 1, 1], dtype=int32)
      >>> bisect_means.predict([[0, 0], [12, 3]])
      array([0, 2], dtype=int32)
      >>> bisect_means.cluster_centers_
      array([[ 2., 1.],
             [10., 9.],
             [10., 1.]])

  Methods

  `fit`(X[, y, sample_weight]) | Compute bisecting 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) | Predict which 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 bisecting k-means clustering.

    Parameters:
      X{array-like, sparse matrix} of shape (n_samples, n_features)

        Training instances to cluster.

        Note

        The data will be converted to C ordering, which will cause a memory copy if the given data is not C-contiguous.

      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.

    Returns:
      self

        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)

    Predict which cluster each sample in X belongs to.

    Prediction is made by going down the hierarchical tree in searching of closest leaf cluster.

    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.

    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 = '$UNCHANGED$') → BisectingKMeans

    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 = '$UNCHANGED$') → BisectingKMeans

    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 = '$UNCHANGED$') → BisectingKMeans

    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.BisectingKMeans`

Release Highlights for scikit-learn 1.1

Release Highlights for scikit-learn 1.1

Bisecting K-Means and Regular K-Means Performance Comparison

Bisecting K-Means and Regular K-Means Performance Comparison