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)[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. 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.
When calling
fit
, an affinity matrix is constructed using either kernel function such the Gaussian (aka RBF) kernel of the euclidean distancedd(X, X)
:np.exp(gamma * d(X,X) ** 2)
or a knearest neighbors connectivity matrix.
Alternatively, using
precomputed
, a userprovided affinity matrix can be used.Read more in the User Guide.
 Parameters
 n_clustersinteger, optional
The dimension of the projection subspace.
 eigen_solver{None, ‘arpack’, ‘lobpcg’, or ‘amg’}
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.
 n_componentsinteger, optional, default=n_clusters
Number of eigen vectors to use for the spectral embedding
 random_stateint, RandomState instance, default=None
A pseudo random number generator used for the initialization of the lobpcg eigen vectors decomposition when
eigen_solver='amg'
and by the KMeans initialization. Use an int to make the randomness deterministic. See Glossary. n_initint, optional, 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.
 gammafloat, default=1.0
Kernel coefficient for rbf, poly, sigmoid, laplacian and chi2 kernels. Ignored for
affinity='nearest_neighbors'
. affinitystring 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.‘precomputed_nearest_neighbors’ : interpret
X
as a sparse graph of precomputed nearest neighbors, and constructs the affinity matrix by selecting then_neighbors
nearest neighbors.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_neighborsinteger
Number of neighbors to use when constructing the affinity matrix using the nearest neighbors method. Ignored for
affinity='rbf'
. eigen_tolfloat, optional, default: 0.0
Stopping criterion for eigendecomposition of the Laplacian matrix when
eigen_solver='arpack'
. assign_labels{‘kmeans’, ‘discretize’}, default: ‘kmeans’
The strategy to use to assign labels in the embedding space. There are two ways to assign labels after the laplacian embedding. kmeans 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.
 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_paramsdictionary of string to any, optional
Parameters (keyword arguments) and values for kernel passed as callable object. Ignored by other kernels.
 n_jobsint or None, optional (default=None)
The number of parallel jobs to run.
None
means 1 unless in ajoblib.parallel_backend
context.1
means using all processors. See Glossary for more details.
 Attributes
 affinity_matrix_arraylike, shape (n_samples, n_samples)
Affinity matrix used for clustering. Available only if after calling
fit
. labels_array, shape (n_samples,)
Labels of each point
Notes
If you have an affinity matrix, such as a distance matrix, for which 0 means identical elements, and high values means very dissimilar elements, it can be transformed in a similarity matrix that is well suited for the algorithm by applying the Gaussian (RBF, heat) kernel:
np.exp( dist_matrix ** 2 / (2. * delta ** 2))
Where
delta
is a free parameter representing the width of the Gaussian kernel.Another 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
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.

__init__
(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)[source]¶ Initialize self. See help(type(self)) for accurate signature.

fit
(X, y=None)[source]¶ Perform spectral clustering from features, or affinity matrix.
 Parameters
 Xarraylike or sparse matrix, shape (n_samples, n_features), or arraylike, shape (n_samples, n_samples)
Training instances to cluster, or similarities / affinities between instances if
affinity='precomputed'
. 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
 Xarraylike or sparse matrix, shape (n_samples, n_features), or arraylike, shape (n_samples, n_samples)
Training instances to cluster, or similarities / affinities between instances if
affinity='precomputed'
. 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, 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
 paramsmapping of string to any
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 pipelines). 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
 selfobject
Estimator instance.