"""Find the discrete partition closest to the eigenvector embedding.

This implementation was proposed in [1]_.

.. versionadded:: 1.1

Parameters

----------

vectors : array-like, shape: (n_samples, n_clusters)

The embedding space of the samples.

Returns

-------

labels : array of integers, shape: n_samples

The cluster labels of vectors.

References

----------

.. [1] :doi:`Simple, direct, and efficient multi-way spectral clustering, 2019

Anil Damle, Victor Minden, Lexing Ying

<10.1093/imaiai/iay008>`

"""

k = vectors.shape[1]

_, _, piv = qr(vectors.T, pivoting=True)

ut, _, v = svd(vectors[piv[:k], :].T)

vectors = abs(np.dot(vectors, np.dot(ut, v.conj())))

vectors, *, copy=True, max_svd_restarts=30, n_iter_max=20, random_state=None

):

"""Search for a partition matrix which is closest to the eigenvector embedding.

This implementation was proposed in [1]_.

Parameters

----------

vectors : array-like of shape (n_samples, n_clusters)

The embedding space of the samples.

copy : bool, default=True

Whether to copy vectors, or perform in-place normalization.

max_svd_restarts : int, default=30

Maximum number of attempts to restart SVD if convergence fails

n_iter_max : int, default=30

Maximum number of iterations to attempt in rotation and partition

matrix search if machine precision convergence is not reached

random_state : int, RandomState instance, default=None

Determines random number generation for rotation matrix initialization.

Use an int to make the randomness deterministic.

See :term:`Glossary <random_state>`.

Returns

-------

labels : array of integers, shape: n_samples

The labels of the clusters.

References

----------

.. [1] `Multiclass spectral clustering, 2003

Stella X. Yu, Jianbo Shi

<https://people.eecs.berkeley.edu/~jordan/courses/281B-spring04/readings/yu-shi.pdf>`_

Notes

-----

The eigenvector embedding is used to iteratively search for the

closest discrete partition. First, the eigenvector embedding is

normalized to the space of partition matrices. An optimal discrete

partition matrix closest to this normalized embedding multiplied by

an initial rotation is calculated. Fixing this discrete partition

matrix, an optimal rotation matrix is calculated. These two

calculations are performed until convergence. The discrete partition

matrix is returned as the clustering solution. Used in spectral

clustering, this method tends to be faster and more robust to random

initialization than k-means.

"""

random_state = check_random_state(random_state)

vectors = as_float_array(vectors, copy=copy)

eps = np.finfo(float).eps

n_samples, n_components = vectors.shape

# Normalize the eigenvectors to an equal length of a vector of ones.

# Reorient the eigenvectors to point in the negative direction with respect

# to the first element. This may have to do with constraining the

# eigenvectors to lie in a specific quadrant to make the discretization

# search easier.

norm_ones = np.sqrt(n_samples)

for i in range(vectors.shape[1]):

vectors[:, i] = (vectors[:, i] / np.linalg.norm(vectors[:, i])) * norm_ones

if vectors[0, i] != 0:

vectors[:, i] = -1 * vectors[:, i] * np.sign(vectors[0, i])

# Normalize the rows of the eigenvectors. Samples should lie on the unit

# hypersphere centered at the origin. This transforms the samples in the

# embedding space to the space of partition matrices.

vectors = vectors / np.sqrt((vectors**2).sum(axis=1))[:, np.newaxis]

svd_restarts = 0

has_converged = False

# If there is an exception we try to randomize and rerun SVD again

# do this max_svd_restarts times.

while (svd_restarts < max_svd_restarts) and not has_converged:

# Initialize first column of rotation matrix with a row of the

# eigenvectors

rotation = np.zeros((n_components, n_components))

rotation[:, 0] = vectors[random_state.randint(n_samples), :].T

# To initialize the rest of the rotation matrix, find the rows

# of the eigenvectors that are as orthogonal to each other as

# possible

c = np.zeros(n_samples)

for j in range(1, n_components):

# Accumulate c to ensure row is as orthogonal as possible to

# previous picks as well as current one

c += np.abs(np.dot(vectors, rotation[:, j - 1]))

rotation[:, j] = vectors[c.argmin(), :].T

last_objective_value = 0.0

n_iter = 0

while not has_converged:

n_iter += 1

t_discrete = np.dot(vectors, rotation)

labels = t_discrete.argmax(axis=1)

vectors_discrete = csc_matrix(

(np.ones(len(labels)), (np.arange(0, n_samples), labels)),

shape=(n_samples, n_components),

)

t_svd = vectors_discrete.T * vectors

try:

U, S, Vh = np.linalg.svd(t_svd)

except LinAlgError:

svd_restarts += 1

print("SVD did not converge, randomizing and trying again")

break

ncut_value = 2.0 * (n_samples - S.sum())

if (abs(ncut_value - last_objective_value) < eps) or (n_iter > n_iter_max):

has_converged = True

else:

# otherwise calculate rotation and continue

last_objective_value = ncut_value

rotation = np.dot(Vh.T, U.T)

if not has_converged:

raise LinAlgError("SVD did not converge")

affinity,

*,

n_clusters=8,

n_components=None,

eigen_solver=None,

random_state=None,

n_init=10,

eigen_tol="auto",

assign_labels="kmeans",

verbose=False,

):

"""Apply clustering to a projection of the normalized Laplacian.

In practice Spectral Clustering is very useful when the structure of

the individual clusters is highly non-convex or more generally when

a measure of the center and spread of the cluster is not a suitable

description of the complete cluster. For instance, when clusters are

nested circles on the 2D plane.

If affinity is the adjacency matrix of a graph, this method can be

used to find normalized graph cuts [1]_, [2]_.

Read more in the :ref:`User Guide <spectral_clustering>`.

Parameters

----------

affinity : {array-like, sparse matrix} of shape (n_samples, n_samples)

The affinity matrix describing the relationship of the samples to

embed. **Must be symmetric**.

Possible examples:

- adjacency matrix of a graph,

- heat kernel of the pairwise distance matrix of the samples,

- symmetric k-nearest neighbours connectivity matrix of the samples.

n_clusters : int, default=None

Number of clusters to extract.

n_components : int, default=n_clusters

Number of eigenvectors to use for the spectral embedding.

eigen_solver : {None, 'arpack', 'lobpcg', or 'amg'}

The eigenvalue decomposition method. If None then ``'arpack'`` is used.

See [4]_ for more details regarding ``'lobpcg'``.

Eigensolver ``'amg'`` runs ``'lobpcg'`` with optional

Algebraic MultiGrid preconditioning and requires pyamg to be installed.

It can be faster on very large sparse problems [6]_ and [7]_.

random_state : int, RandomState instance, default=None

A pseudo random number generator used for the initialization

of the lobpcg eigenvectors decomposition when `eigen_solver ==

'amg'`, and for the K-Means initialization. Use an int to make

the results deterministic across calls (See

:term:`Glossary <random_state>`).

.. note::

When using `eigen_solver == 'amg'`,

it is necessary to also fix the global numpy seed with

`np.random.seed(int)` to get deterministic results. See

https://github.com/pyamg/pyamg/issues/139 for further

information.

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. Only used if

``assign_labels='kmeans'``.

eigen_tol : float, default="auto"

Stopping criterion for eigendecomposition of the Laplacian matrix.

If `eigen_tol="auto"` then the passed tolerance will depend on the

`eigen_solver`:

- If `eigen_solver="arpack"`, then `eigen_tol=0.0`;

- If `eigen_solver="lobpcg"` or `eigen_solver="amg"`, then

`eigen_tol=None` which configures the underlying `lobpcg` solver to

automatically resolve the value according to their heuristics. See,

:func:`scipy.sparse.linalg.lobpcg` for details.

Note that when using `eigen_solver="lobpcg"` or `eigen_solver="amg"`

values of `tol<1e-5` may lead to convergence issues and should be

avoided.

.. versionadded:: 1.2

Added 'auto' option.

assign_labels : {'kmeans', 'discretize', 'cluster_qr'}, default='kmeans'

The strategy to use to assign labels in the embedding

space. There are three ways to assign labels after the Laplacian

embedding. k-means can be applied and is a popular choice. But it can

also be sensitive to initialization. Discretization is another

approach which is less sensitive to random initialization [3]_.

The cluster_qr method [5]_ directly extracts clusters from eigenvectors

in spectral clustering. In contrast to k-means and discretization, cluster_qr

has no tuning parameters and is not an iterative method, yet may outperform

k-means and discretization in terms of both quality and speed.

.. versionchanged:: 1.1

Added new labeling method 'cluster_qr'.

verbose : bool, default=False

Verbosity mode.

.. versionadded:: 0.24

Returns

-------

labels : array of integers, shape: n_samples

The labels of the clusters.

Notes

-----

The graph should contain only one connected component, elsewhere

the results make little sense.

This algorithm solves the normalized cut for `k=2`: it is a

normalized spectral clustering.

References

----------

.. [1] :doi:`Normalized cuts and image segmentation, 2000

Jianbo Shi, Jitendra Malik

<10.1109/34.868688>`

.. [2] :doi:`A Tutorial on Spectral Clustering, 2007

Ulrike von Luxburg

<10.1007/s11222-007-9033-z>`

.. [3] `Multiclass spectral clustering, 2003

Stella X. Yu, Jianbo Shi

<https://people.eecs.berkeley.edu/~jordan/courses/281B-spring04/readings/yu-shi.pdf>`_

.. [4] :doi:`Toward the Optimal Preconditioned Eigensolver:

Locally Optimal Block Preconditioned Conjugate Gradient Method, 2001

A. V. Knyazev

SIAM Journal on Scientific Computing 23, no. 2, pp. 517-541.

<10.1137/S1064827500366124>`

.. [5] :doi:`Simple, direct, and efficient multi-way spectral clustering, 2019

Anil Damle, Victor Minden, Lexing Ying

<10.1093/imaiai/iay008>`

.. [6] :doi:`Multiscale Spectral Image Segmentation Multiscale preconditioning

for computing eigenvalues of graph Laplacians in image segmentation, 2006

Andrew Knyazev

<10.13140/RG.2.2.35280.02565>`

.. [7] :doi:`Preconditioned spectral clustering for stochastic block partition

streaming graph challenge (Preliminary version at arXiv.)

David Zhuzhunashvili, Andrew Knyazev

<10.1109/HPEC.2017.8091045>`

Examples

--------

>>> import numpy as np

>>> from sklearn.metrics.pairwise import pairwise_kernels

>>> from sklearn.cluster import spectral_clustering

>>> X = np.array([[1, 1], [2, 1], [1, 0],

... [4, 7], [3, 5], [3, 6]])

>>> affinity = pairwise_kernels(X, metric='rbf')

>>> spectral_clustering(

... affinity=affinity, n_clusters=2, assign_labels="discretize", random_state=0

... )

array([1, 1, 1, 0, 0, 0])

"""

clusterer = SpectralClustering(

n_clusters=n_clusters,

n_components=n_components,

eigen_solver=eigen_solver,

random_state=random_state,

n_init=n_init,

affinity="precomputed",

eigen_tol=eigen_tol,

assign_labels=assign_labels,

verbose=verbose,

).fit(affinity)

"""Apply clustering to a projection of the normalized Laplacian.

In practice Spectral Clustering is very useful when the structure of

the individual clusters is highly non-convex, or more generally when

a measure of the center and spread of the cluster is not a suitable

description of the complete cluster, such as when clusters are

nested circles on the 2D plane.

If the affinity matrix is the adjacency matrix of a graph, this method

can be used to find normalized graph cuts [1]_, [2]_.

When calling ``fit``, an affinity matrix is constructed using either

a kernel function such the Gaussian (aka RBF) kernel with Euclidean

distance ``d(X, X)``::

np.exp(-gamma * d(X,X) ** 2)

or a k-nearest neighbors connectivity matrix.

Alternatively, a user-provided affinity matrix can be specified by

setting ``affinity='precomputed'``.

Read more in the :ref:`User Guide <spectral_clustering>`.

Parameters

----------

n_clusters : int, default=8

The dimension of the projection subspace.

eigen_solver : {'arpack', 'lobpcg', 'amg'}, default=None

The eigenvalue decomposition strategy to use. AMG requires pyamg

to be installed. It can be faster on very large, sparse problems,

but may also lead to instabilities. If None, then ``'arpack'`` is

used. See [4]_ for more details regarding `'lobpcg'`.

n_components : int, default=None

Number of eigenvectors to use for the spectral embedding. If None,

defaults to `n_clusters`.

random_state : int, RandomState instance, default=None

A pseudo random number generator used for the initialization

of the lobpcg eigenvectors decomposition when `eigen_solver ==

'amg'`, and for the K-Means initialization. Use an int to make

the results deterministic across calls (See

:term:`Glossary <random_state>`).

.. note::

When using `eigen_solver == 'amg'`,

it is necessary to also fix the global numpy seed with

`np.random.seed(int)` to get deterministic results. See

https://github.com/pyamg/pyamg/issues/139 for further

information.

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. Only used if

``assign_labels='kmeans'``.

gamma : float, default=1.0

Kernel coefficient for rbf, poly, sigmoid, laplacian and chi2 kernels.

Ignored for ``affinity='nearest_neighbors'``, ``affinity='precomputed'``

or ``affinity='precomputed_nearest_neighbors'``.

affinity : str or callable, default='rbf'

How to construct the affinity matrix.

- 'nearest_neighbors': construct the affinity matrix by computing a

graph of nearest neighbors.

- 'rbf': construct the affinity matrix using a radial basis function

(RBF) kernel.

- 'precomputed': interpret ``X`` as a precomputed affinity matrix,

where larger values indicate greater similarity between instances.

- 'precomputed_nearest_neighbors': interpret ``X`` as a sparse graph

of precomputed distances, and construct a binary affinity matrix

from the ``n_neighbors`` nearest neighbors of each instance.

- one of the kernels supported by

:func:`~sklearn.metrics.pairwise.pairwise_kernels`.

Only kernels that produce similarity scores (non-negative values that

increase with similarity) should be used. This property is not checked

by the clustering algorithm.

n_neighbors : int, default=10

Number of neighbors to use when constructing the affinity matrix using

the nearest neighbors method. Ignored for ``affinity='rbf'``.

eigen_tol : float, default="auto"

Stopping criterion for eigen decomposition of the Laplacian matrix.

If `eigen_tol="auto"` then the passed tolerance will depend on the

`eigen_solver`:

- If `eigen_solver="arpack"`, then `eigen_tol=0.0`;

- If `eigen_solver="lobpcg"` or `eigen_solver="amg"`, then

`eigen_tol=None` which configures the underlying `lobpcg` solver to

automatically resolve the value according to their heuristics. See,

:func:`scipy.sparse.linalg.lobpcg` for details.

Note that when using `eigen_solver="lobpcg"` or `eigen_solver="amg"`

values of `tol<1e-5` may lead to convergence issues and should be

avoided.

.. versionadded:: 1.2

Added 'auto' option.

assign_labels : {'kmeans', 'discretize', 'cluster_qr'}, default='kmeans'

The strategy for assigning labels in the embedding space. There are two

ways to assign labels after the Laplacian embedding. k-means is a

popular choice, but it can be sensitive to initialization.

Discretization is another approach which is less sensitive to random

initialization [3]_.

The cluster_qr method [5]_ directly extract clusters from eigenvectors

in spectral clustering. In contrast to k-means and discretization, cluster_qr

has no tuning parameters and runs no iterations, yet may outperform

k-means and discretization in terms of both quality and speed.

.. versionchanged:: 1.1

Added new labeling method 'cluster_qr'.

degree : float, default=3

Degree of the polynomial kernel. Ignored by other kernels.

coef0 : float, default=1

Zero coefficient for polynomial and sigmoid kernels.

Ignored by other kernels.

kernel_params : dict of str to any, default=None

Parameters (keyword arguments) and values for kernel passed as

callable object. Ignored by other kernels.

n_jobs : int, default=None

The number of parallel jobs to run when `affinity='nearest_neighbors'`

or `affinity='precomputed_nearest_neighbors'`. The neighbors search

will be done 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.

verbose : bool, default=False

Verbosity mode.

.. versionadded:: 0.24

Attributes

----------

affinity_matrix_ : array-like of shape (n_samples, n_samples)

Affinity matrix used for clustering. Available only after calling

``fit``.

labels_ : ndarray of shape (n_samples,)

Labels of each point

n_features_in_ : int

Number of features seen during :term:`fit`.

.. versionadded:: 0.24

feature_names_in_ : ndarray of shape (`n_features_in_`,)

Names of features seen during :term:`fit`. Defined only when `X`

has feature names that are all strings.

.. versionadded:: 1.0

See Also

--------

sklearn.cluster.KMeans : K-Means clustering.

sklearn.cluster.DBSCAN : Density-Based Spatial Clustering of

Applications with Noise.

Notes

-----

A distance matrix for which 0 indicates identical elements and high values

indicate very dissimilar elements can be transformed into an affinity /

similarity matrix that is well-suited for the algorithm by

applying the Gaussian (aka RBF, heat) kernel::

np.exp(- dist_matrix ** 2 / (2. * delta ** 2))

where ``delta`` is a free parameter representing the width of the Gaussian

kernel.

An alternative is to take a symmetric version of the k-nearest neighbors

connectivity matrix of the points.

If the pyamg package is installed, it is used: this greatly

speeds up computation.

References

----------

.. [1] :doi:`Normalized cuts and image segmentation, 2000

Jianbo Shi, Jitendra Malik

<10.1109/34.868688>`

.. [2] :doi:`A Tutorial on Spectral Clustering, 2007

Ulrike von Luxburg

<10.1007/s11222-007-9033-z>`

.. [3] `Multiclass spectral clustering, 2003

Stella X. Yu, Jianbo Shi

<https://people.eecs.berkeley.edu/~jordan/courses/281B-spring04/readings/yu-shi.pdf>`_

.. [4] :doi:`Toward the Optimal Preconditioned Eigensolver:

Locally Optimal Block Preconditioned Conjugate Gradient Method, 2001

A. V. Knyazev

SIAM Journal on Scientific Computing 23, no. 2, pp. 517-541.

<10.1137/S1064827500366124>`

.. [5] :doi:`Simple, direct, and efficient multi-way spectral clustering, 2019

Anil Damle, Victor Minden, Lexing Ying

<10.1093/imaiai/iay008>`

Examples

--------

>>> from sklearn.cluster import SpectralClustering

>>> import numpy as np

>>> X = np.array([[1, 1], [2, 1], [1, 0],

... [4, 7], [3, 5], [3, 6]])

>>> clustering = SpectralClustering(n_clusters=2,

... assign_labels='discretize',

... random_state=0).fit(X)

>>> clustering.labels_

array([1, 1, 1, 0, 0, 0])

>>> clustering

SpectralClustering(assign_labels='discretize', n_clusters=2,

random_state=0)

"""

_parameter_constraints: dict = {

"n_clusters": [Interval(Integral, 1, None, closed="left")],

"eigen_solver": [StrOptions({"arpack", "lobpcg", "amg"}), None],

"n_components": [Interval(Integral, 1, None, closed="left"), None],

"random_state": ["random_state"],

"n_init": [Interval(Integral, 1, None, closed="left")],

"gamma": [Interval(Real, 0, None, closed="left")],

"affinity": [

callable,

StrOptions(

set(KERNEL_PARAMS)

| {"nearest_neighbors", "precomputed", "precomputed_nearest_neighbors"}

),

],

"n_neighbors": [Interval(Integral, 1, None, closed="left")],

"eigen_tol": [

Interval(Real, 0.0, None, closed="left"),

StrOptions({"auto"}),

],

"assign_labels": [StrOptions({"kmeans", "discretize", "cluster_qr"})],

"degree": [Interval(Real, 0, None, closed="left")],

"coef0": [Interval(Real, None, None, closed="neither")],

"kernel_params": [dict, None],

"n_jobs": [Integral, None],

"verbose": ["verbose"],

}

def __init__(

self,

n_clusters=8,

*,

eigen_solver=None,

n_components=None,

random_state=None,

n_init=10,

gamma=1.0,

affinity="rbf",

n_neighbors=10,

eigen_tol="auto",

assign_labels="kmeans",

degree=3,

coef0=1,

kernel_params=None,

n_jobs=None,

verbose=False,

):

self.n_clusters = n_clusters

self.eigen_solver = eigen_solver

self.n_components = n_components

self.random_state = random_state

self.n_init = n_init

self.gamma = gamma

self.affinity = affinity

self.n_neighbors = n_neighbors

self.eigen_tol = eigen_tol

self.assign_labels = assign_labels

self.degree = degree

self.coef0 = coef0

self.kernel_params = kernel_params

self.n_jobs = n_jobs

self.verbose = verbose

@_fit_context(prefer_skip_nested_validation=True)

def fit(self, X, y=None):

"""Perform spectral clustering from features, or affinity matrix.

Parameters

----------

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

(n_samples, n_samples)

Training instances to cluster, similarities / affinities between

instances if ``affinity='precomputed'``, or distances between

instances if ``affinity='precomputed_nearest_neighbors``. If a

sparse matrix is provided in a format other than ``csr_matrix``,

``csc_matrix``, or ``coo_matrix``, it will be converted into a

sparse ``csr_matrix``.

y : Ignored

Not used, present here for API consistency by convention.

Returns

-------

self : object

A fitted instance of the estimator.

"""

X = self._validate_data(

X,

accept_sparse=["csr", "csc", "coo"],

dtype=np.float64,

ensure_min_samples=2,

)

allow_squared = self.affinity in [

"precomputed",

"precomputed_nearest_neighbors",

]

if X.shape[0] == X.shape[1] and not allow_squared:

warnings.warn(

"The spectral clustering API has changed. ``fit``"

"now constructs an affinity matrix from data. To use"

" a custom affinity matrix, "

"set ``affinity=precomputed``."

)

if self.affinity == "nearest_neighbors":

connectivity = kneighbors_graph(

X, n_neighbors=self.n_neighbors, include_self=True, n_jobs=self.n_jobs

)

self.affinity_matrix_ = 0.5 * (connectivity + connectivity.T)

elif self.affinity == "precomputed_nearest_neighbors":

estimator = NearestNeighbors(

n_neighbors=self.n_neighbors, n_jobs=self.n_jobs, metric="precomputed"

).fit(X)

connectivity = estimator.kneighbors_graph(X=X, mode="connectivity")

self.affinity_matrix_ = 0.5 * (connectivity + connectivity.T)

elif self.affinity == "precomputed":

self.affinity_matrix_ = X

else:

params = self.kernel_params

if params is None:

params = {}

if not callable(self.affinity):

params["gamma"] = self.gamma

params["degree"] = self.degree

params["coef0"] = self.coef0

self.affinity_matrix_ = pairwise_kernels(

X, metric=self.affinity, filter_params=True, **params

)

random_state = check_random_state(self.random_state)

n_components = (

self.n_clusters if self.n_components is None else self.n_components

)

# We now obtain the real valued solution matrix to the

# relaxed Ncut problem, solving the eigenvalue problem

# L_sym x = lambda x and recovering u = D^-1/2 x.

# The first eigenvector is constant only for fully connected graphs

# and should be kept for spectral clustering (drop_first = False)

# See spectral_embedding documentation.

maps = _spectral_embedding(

self.affinity_matrix_,

n_components=n_components,

eigen_solver=self.eigen_solver,

random_state=random_state,

eigen_tol=self.eigen_tol,

drop_first=False,

)

if self.verbose:

print(f"Computing label assignment using {self.assign_labels}")

if self.assign_labels == "kmeans":

_, self.labels_, _ = k_means(

maps,

self.n_clusters,

random_state=random_state,

n_init=self.n_init,

verbose=self.verbose,

)

elif self.assign_labels == "cluster_qr":

self.labels_ = cluster_qr(maps)

else:

self.labels_ = discretize(maps, random_state=random_state)

return self

def fit_predict(self, X, y=None):

"""Perform spectral clustering on `X` and return cluster labels.

Parameters

----------

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

(n_samples, n_samples)

Training instances to cluster, similarities / affinities between

instances if ``affinity='precomputed'``, or distances between

instances if ``affinity='precomputed_nearest_neighbors``. If a

sparse matrix is provided in a format other than ``csr_matrix``,

``csc_matrix``, or ``coo_matrix``, it will be converted into a

sparse ``csr_matrix``.

y : Ignored

Not used, present here for API consistency by convention.

Returns

-------

labels : ndarray of shape (n_samples,)

Cluster labels.

"""

return super().fit_predict(X, y)

def _more_tags(self):

return {

"pairwise": self.affinity

in [

"precomputed",

"precomputed_nearest_neighbors",

]