Implementation:Scikit learn Scikit learn SpectralClustering

Knowledge Sources	Scikit_learn Scikit-learn Docs
Domains	Clustering, Graph-Based Clustering
Last Updated	2026-02-08 15:00 GMT

Overview

Concrete tool for performing spectral clustering via projection of the normalized Laplacian provided by scikit-learn.

Description

SpectralClustering applies clustering to a projection of the normalized graph Laplacian. It constructs an affinity matrix (using a kernel function such as RBF or k-nearest neighbors connectivity), computes a spectral embedding from the graph Laplacian, and then applies K-Means or discretization to the embedding to find clusters. It is particularly effective when the cluster structure is highly non-convex, such as nested circles or complex manifold shapes, where centroid-based methods fail.

Usage

Use SpectralClustering when clusters have non-convex shapes, when data lies on complex manifolds, or when working with graph-structured data where you want to find normalized graph cuts. It is also useful when you have a precomputed affinity or adjacency matrix. Note that it does not scale well to very large datasets.

Code Reference

Source Location

• Repository: scikit-learn
• File: sklearn/cluster/_spectral.py

Signature

class SpectralClustering(ClusterMixin, BaseEstimator):
    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,
    ):

Import

from sklearn.cluster import SpectralClustering

I/O Contract

Inputs

Name	Type	Required	Description
n_clusters	int	No	Dimension of projection subspace (number of clusters). Default is 8.
eigen_solver	str or None	No	Eigenvalue solver: "arpack", "lobpcg", or "amg". Default is None.
n_components	int or None	No	Number of eigenvectors for spectral embedding. Default is None (uses n_clusters).
random_state	int or RandomState	No	Random state for K-Means initialization and eigenvector computation. Default is None.
n_init	int	No	Number of K-Means initializations for label assignment. Default is 10.
gamma	float	No	Kernel coefficient for rbf, poly, sigmoid, laplacian, and chi2 kernels. Default is 1.0.
affinity	str or callable	No	Affinity construction method: "rbf", "nearest_neighbors", "precomputed", or a kernel name. Default is "rbf".
n_neighbors	int	No	Number of neighbors for nearest_neighbors affinity. Default is 10.
eigen_tol	float or "auto"	No	Stopping criterion for eigenvalue decomposition. Default is "auto".
assign_labels	str	No	Strategy for assigning labels: "kmeans", "discretize", or "cluster_qr". Default is "kmeans".
degree	float	No	Degree of the polynomial kernel. Default is 3.
coef0	float	No	Zero coefficient for polynomial and sigmoid kernels. Default is 1.
kernel_params	dict or None	No	Parameters for custom kernel functions. Default is None.
n_jobs	int or None	No	Number of parallel jobs for nearest neighbors. Default is None.
verbose	bool	No	Verbosity mode. Default is False.

Outputs

Name	Type	Description
affinity_matrix_	ndarray of shape (n_samples, n_samples)	Affinity matrix used for clustering.
labels_	ndarray of shape (n_samples,)	Cluster labels for each sample.
n_features_in_	int	Number of features seen during fit.

Usage Examples

Basic Usage

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)
print(clustering.labels_)

Related Pages

• Principle:Scikit_learn_Scikit_learn_Clustering