SpectralEmbedding (original) (raw)

class sklearn.manifold.SpectralEmbedding(n_components=2, *, affinity='nearest_neighbors', gamma=None, random_state=None, eigen_solver=None, eigen_tol='auto', n_neighbors=None, n_jobs=None)[source]#

Spectral embedding for non-linear dimensionality reduction.

Forms an affinity matrix given by the specified function and applies spectral decomposition to the corresponding graph laplacian. The resulting transformation is given by the value of the eigenvectors for each data point.

Note : Laplacian Eigenmaps is the actual algorithm implemented here.

Read more in the User Guide.

Parameters:

n_componentsint, default=2

The dimension of the projected subspace.

affinity{‘nearest_neighbors’, ‘rbf’, ‘precomputed’, ‘precomputed_nearest_neighbors’} or callable, default=’nearest_neighbors’

How to construct the affinity matrix.

‘nearest_neighbors’ : construct the affinity matrix by computing a graph of nearest neighbors.
‘rbf’ : construct the affinity matrix by computing 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 the n_neighbors nearest neighbors.
callable : use passed in function as affinity the function takes in data matrix (n_samples, n_features) and return affinity matrix (n_samples, n_samples).

gammafloat, default=None

Kernel coefficient for rbf kernel. If None, gamma will be set to 1/n_features.

random_stateint, RandomState instance or None, default=None

A pseudo random number generator used for the initialization of the lobpcg eigen vectors decomposition when eigen_solver == 'amg', and for the K-Means initialization. Use an int to make the results deterministic across calls (SeeGlossary).

Note

When using eigen_solver == 'amg', it is necessary to also fix the global numpy seed withnp.random.seed(int) to get deterministic results. Seepyamg/pyamg#139 for further information.

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. If None, then 'arpack' is used.

eigen_tolfloat, default=”auto”

Stopping criterion for eigendecomposition of the Laplacian matrix. If eigen_tol="auto" then the passed tolerance will depend on theeigen_solver:

If eigen_solver="arpack", then eigen_tol=0.0;
If eigen_solver="lobpcg" or eigen_solver="amg", theneigen_tol=None which configures the underlying lobpcg solver to automatically resolve the value according to their heuristics. See,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.

Added in version 1.2.

n_neighborsint, default=None

Number of nearest neighbors for nearest_neighbors graph building. If None, n_neighbors will be set to max(n_samples/10, 1).

n_jobsint, default=None

The number of parallel jobs to run.None means 1 unless in a joblib.parallel_backend context.-1 means using all processors. See Glossaryfor more details.

Attributes:

**embedding_**ndarray of shape (n_samples, n_components)

Spectral embedding of the training matrix.

**affinity_matrix_**ndarray of shape (n_samples, n_samples)

Affinity_matrix constructed from samples or precomputed.

**n_features_in_**int

Number of features seen during fit.

Added in version 0.24.

**feature_names_in_**ndarray of shape (n_features_in_,)

Names of features seen during fit. Defined only when Xhas feature names that are all strings.

Added in version 1.0.

**n_neighbors_**int

Number of nearest neighbors effectively used.

SpectralEmbedding (original) (raw)

Gallery examples#