sklearn.cluster
.SpectralClustering¶

class
sklearn.cluster.
SpectralClustering
(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=0.0, assign_labels='kmeans', degree=3, coef0=1, kernel_params=None, n_jobs=None, verbose=False)[source]¶ 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 nonconvex, 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.
When calling
fit
, an affinity matrix is constructed using either a kernel function such the Gaussian (aka RBF) kernel with Euclidean distanced(X, X)
:np.exp(gamma * d(X,X) ** 2)
or a knearest neighbors connectivity matrix.
Alternatively, a userprovided affinity matrix can be specified by setting
affinity='precomputed'
.Read more in the User Guide.
 Parameters
 n_clustersint, 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. n_componentsint, default=n_clusters
Number of eigenvectors to use for the spectral embedding
 random_stateint, RandomState instance, default=None
A pseudo random number generator used for the initialization of the lobpcg eigenvectors decomposition when
eigen_solver='amg'
and by the KMeans initialization. Use an int to make the randomness deterministic. See Glossary. n_initint, 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. Only used if
assign_labels='kmeans'
. gammafloat, default=1.0
Kernel coefficient for rbf, poly, sigmoid, laplacian and chi2 kernels. Ignored for
affinity='nearest_neighbors'
. affinitystr 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 then_neighbors
nearest neighbors of each instance.one of the kernels supported by
pairwise_kernels
.
Only kernels that produce similarity scores (nonnegative values that increase with similarity) should be used. This property is not checked by the clustering algorithm.
 n_neighborsint, default=10
Number of neighbors to use when constructing the affinity matrix using the nearest neighbors method. Ignored for
affinity='rbf'
. eigen_tolfloat, default=0.0
Stopping criterion for eigendecomposition of the Laplacian matrix when
eigen_solver='arpack'
. assign_labels{‘kmeans’, ‘discretize’}, default=’kmeans’
The strategy for assigning labels in the embedding space. There are two ways to assign labels after the Laplacian embedding. kmeans is a popular choice, but it can be sensitive to initialization. Discretization is another approach which is less sensitive to random initialization.
 degreefloat, default=3
Degree of the polynomial kernel. Ignored by other kernels.
 coef0float, default=1
Zero coefficient for polynomial and sigmoid kernels. Ignored by other kernels.
 kernel_paramsdict of str to any, default=None
Parameters (keyword arguments) and values for kernel passed as callable object. Ignored by other kernels.
 n_jobsint, default=None
The number of parallel jobs to run when
affinity='nearest_neighbors'
oraffinity='precomputed_nearest_neighbors'
. The neighbors search will be done in parallel.None
means 1 unless in ajoblib.parallel_backend
context.1
means using all processors. See Glossary for more details. verbosebool, default=False
Verbosity mode.
New in version 0.24.
 Attributes
 affinity_matrix_arraylike 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
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 wellsuited 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 knearest neighbors connectivity matrix of the points.
If the pyamg package is installed, it is used: this greatly speeds up computation.
References
Normalized cuts and image segmentation, 2000 Jianbo Shi, Jitendra Malik http://citeseer.ist.psu.edu/viewdoc/summary?doi=10.1.1.160.2324
A Tutorial on Spectral Clustering, 2007 Ulrike von Luxburg http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.165.9323
Multiclass spectral clustering, 2003 Stella X. Yu, Jianbo Shi https://www1.icsi.berkeley.edu/~stellayu/publication/doc/2003kwayICCV.pdf
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)
Methods
fit
(X[, y])Perform spectral clustering from features, or affinity matrix.
fit_predict
(X[, y])Perform spectral clustering from features, or affinity matrix, and return cluster labels.
get_params
([deep])Get parameters for this estimator.
set_params
(**params)Set the parameters of this estimator.

fit
(X, y=None)[source]¶ Perform spectral clustering from features, or affinity matrix.
 Parameters
 X{arraylike, 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 ifaffinity='precomputed_nearest_neighbors
. If a sparse matrix is provided in a format other thancsr_matrix
,csc_matrix
, orcoo_matrix
, it will be converted into a sparsecsr_matrix
. yIgnored
Not used, present here for API consistency by convention.
 Returns
 self

fit_predict
(X, y=None)[source]¶ Perform spectral clustering from features, or affinity matrix, and return cluster labels.
 Parameters
 X{arraylike, 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 ifaffinity='precomputed_nearest_neighbors
. If a sparse matrix is provided in a format other thancsr_matrix
,csc_matrix
, orcoo_matrix
, it will be converted into a sparsecsr_matrix
. yIgnored
Not used, present here for API consistency by convention.
 Returns
 labelsndarray of shape (n_samples,)
Cluster labels.

get_params
(deep=True)[source]¶ Get parameters for this estimator.
 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.

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.