用于光谱聚类的密度加权Nyström方法代码

以下是用于光谱聚类的密度加权Nyström方法的Python代码：

import numpy as np
from scipy import sparse
from sklearn.cluster import KMeans
from sklearn.metrics.pairwise import rbf_kernel
from sklearn.utils import check_random_state


class DensityWeightedNystromSpectralClustering:
    def __init__(self, n_clusters=8, n_components=100, gamma=1.0, random_state=None):
        self.n_clusters = n_clusters
        self.n_components = n_components
        self.gamma = gamma
        self.random_state = random_state

    def fit(self, X):
        rng = check_random_state(self.random_state)
        n_samples = X.shape[0]
        W = rbf_kernel(X, gamma=self.gamma)
        D = np.diag(np.sum(W, axis=1))
        L = D - W
        s = np.sum(L, axis=1) / np.trace(L)
        S = sparse.diags(s, format='csr')
        M = S.dot(L).dot(S)
        U, sigma, _ = sparse.linalg.svds(M, k=self.n_components, tol=1e-3, random_state=rng)
        V = U.dot(np.diag(np.sqrt(sigma)))
        kmeans = KMeans(n_clusters=self.n_clusters, random_state=rng).fit(V)
        self.labels_ = kmeans.labels_

    def predict(self, X):
        rng = check_random_state(self.random_state)
        W = rbf_kernel(X, self.X_, gamma=self.gamma)
        D = np.diag(np.sum(W, axis=1))
        L = D - W
        s = np.sum(L, axis=1) / np.trace(L)
        S = sparse.diags(s, format='csr')
        M = S.dot(L).dot(S)
        U, sigma, _ = sparse.linalg.svds(M, k=self.n_components, tol=1e-3, random_state=rng)
        V = U.dot(np.diag(np.sqrt(sigma)))
        return KMeans(n_clusters=self.n_clusters, random_state=rng).fit_predict(V)

该代码与前面的代码非常相似，唯一的区别在于我们使用了稀疏矩阵SVD的方法sparse.linalg.svds来计算前n_components个特征向量。这种方法可以更有效地处理大型数据集，因为它可以在内存中处理稀疏矩阵，并且只计算最重要的特征向量。