sklearn.cluster
.SpectralClustering¶

class
sklearn.cluster.
SpectralClustering
(n_clusters=8, eigen_solver=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=1)[source]¶ Apply clustering to a projection to 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 plan.
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_clusters : integer, 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
random_state : int, RandomState instance or None, optional, 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. If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by np.random.
n_init : int, 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.
gamma : float, default=1.0
Kernel coefficient for rbf, poly, sigmoid, laplacian and chi2 kernels. Ignored for
affinity='nearest_neighbors'
.affinity : string, arraylike or callable, default ‘rbf’
If a string, this may be one of ‘nearest_neighbors’, ‘precomputed’, ‘rbf’ or one of the kernels supported by sklearn.metrics.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_neighbors : integer
Number of neighbors to use when constructing the affinity matrix using the nearest neighbors method. Ignored for
affinity='rbf'
.eigen_tol : float, optional, default: 0.0
Stopping criterion for eigendecomposition of the Laplacian matrix when using arpack eigen_solver.
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.
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 : dictionary of string to any, optional
Parameters (keyword arguments) and values for kernel passed as callable object. Ignored by other kernels.
n_jobs : int, optional (default = 1)
The number of parallel jobs to run. If
1
, then the number of jobs is set to the number of CPU cores.Attributes
affinity_matrix_ (arraylike, shape (n_samples, n_samples)) Affinity matrix used for clustering. Available only if after calling fit
.labels_ : 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 http://www1.icsi.berkeley.edu/~stellayu/publication/doc/2003kwayICCV.pdf
Methods
fit
(X[, y])Creates an affinity matrix for X using the selected affinity, then applies spectral clustering to this affinity matrix. fit_predict
(X[, y])Performs clustering on X and returns 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, 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=1)[source]¶

fit
(X, y=None)[source]¶ Creates an affinity matrix for X using the selected affinity, then applies spectral clustering to this affinity matrix.
Parameters: X : arraylike or sparse matrix, shape (n_samples, n_features)
OR, if affinity==`precomputed`, a precomputed affinity matrix of shape (n_samples, n_samples)

fit_predict
(X, y=None)[source]¶ Performs clustering on X and returns cluster labels.
Parameters: X : ndarray, shape (n_samples, n_features)
Input data.
Returns: y : ndarray, shape (n_samples,)
cluster labels