谱聚类算法python代码

以下是谱聚类算法的Python代码：

import numpy as np
from sklearn.cluster import KMeans
from sklearn.neighbors import kneighbors_graph
from scipy.sparse.linalg import eigsh

def spectral_clustering(X, n_clusters=8, n_neighbors=10, gamma=1.0):
    """
    Implementation of spectral clustering algorithm 
    using KMeans and nearest neighbor graphs with RBF kernel.

    Parameters
    ----------
    X : array-like or sparse matrix, shape (n_samples, n_features)
        Input data.

    n_clusters : int, optional, default: 8
        The dimension of the projection subspace.

    n_neighbors : int, optional, default: 10
        The number of nearest neighbors to include in the 
        constructed k-NN matrix.

    gamma : float, optional, default: 1.0
        Parameter for RBF kernel.

    Returns
    -------
    y_pred : array-like, shape (n_samples,)
        Predicted cluster labels.
    """
    
    # Construct k-nearest neighbor graph with RBF kernel
    knn_graph = kneighbors_graph(X, n_neighbors=n_neighbors, mode='connectivity', metric='euclidean')
    affinity_matrix = np.exp(-gamma * np.square(knn_graph))

    # Get Laplacian matrix
    degree_matrix = np.diag(np.sum(affinity_matrix, axis=1))
    laplacian_matrix = degree_matrix - affinity_matrix

    # Compute eigenvectors of Laplacian matrix
    _, eigenvectors = eigsh(laplacian_matrix, k=n_clusters, which='SM')

    # Normalize eigenvectors row-wise and use KMeans to get labels
    row_norm = np.linalg.norm(eigenvectors, axis=1, ord=2)
    normalized_eigenvectors = eigenvectors / row_norm[:, np.newaxis]
    kmeans = KMeans(n_clusters=n_clusters)
    y_pred = kmeans.fit_predict(normalized_eigenvectors)

    return y_pred

这个实现使用欧几里得距离来构建k-NN矩阵，并使用RBF内核将其转换为相似性矩阵。它还使用Laplacian矩阵表示图形，并计算Laplacian矩阵的前$n\_clusters$个最小特征向量。这些特征向量被归一化，用于聚类标签预测，由KMeans算法执行。