密度加权Nyström谱聚类代码

以下是Python中使用密度加权Nyström谱聚类的示例代码：

import numpy as np
from scipy.sparse import diags, csr_matrix
from sklearn.cluster import KMeans
from sklearn.metrics.pairwise import rbf_kernel

class DensityWeightedNystromSpectralClustering:
    def __init__(self, n_clusters, n_components=None, gamma=None, random_state=None):
        self.n_clusters = n_clusters
        self.n_components = n_components
        self.gamma = gamma
        self.random_state = random_state
        self.eigenvecs_ = None
        self.kmeans_ = None

    def fit(self, X):
        n_samples, n_features = X.shape

        # 1. Compute pairwise distances
        distances = np.zeros((n_samples, n_samples))
        for i in range(n_samples):
            for j in range(i+1, n_samples):
                distances[i, j] = np.linalg.norm(X[i] - X[j])
                distances[j, i] = distances[i, j]

        # 2. Compute density weights
        sigma = np.mean(distances) / 2
        densities = np.zeros(n_samples)
        for i in range(n_samples):
            densities[i] = np.sum(np.exp(-distances[i] ** 2 / (2 * sigma ** 2)))
        D = diags(densities, format='csr')
        W = csr_matrix(np.exp(-distances ** 2 / (2 * sigma ** 2)))

        # 3. Random subset of the data
        if self.n_components is None:
            self.n_components = n_samples // 2
        if self.random_state is not None:
            random_state = np.random.RandomState(self.random_state)
        else:
            random_state = np.random
        idx = random_state.permutation(n_samples)[:self.n_components]

        # 4. Compute kernel matrix
        if self.gamma is None:
            self.gamma = 1.0 / n_features
        K = rbf_kernel(X[idx], gamma=self.gamma)

        # 5. Compute approximate eigenvalues and eigenvectors of W^(-1/2) K W^(-1/2)
        D_inv_sqrt = diags(1.0 / np.sqrt(densities), format='csr')
        M = D_inv_sqrt.dot(W.dot(D_inv_sqrt.dot(K)))
        eigenvalues, eigenvectors = np.linalg.eigh(M)
        self.eigenvecs_ = D_inv_sqrt.dot(eigenvectors[:, ::-1])

        # 6. Cluster rows of eigenvectors with k-means
        self.kmeans_ = KMeans(n_clusters=self.n_clusters, random_state=self.random_state)
        self.kmeans_.fit(self.eigenvecs_)

    def predict(self, X):
        distances = np.zeros((X.shape[0], self.eigenvecs_.shape[0]))
        for i in range(X.shape[0]):
            for j in range(self.eigenvecs_.shape[0]):
                distances[i, j] = np.linalg.norm(X[i] - X[j])
        W = np.exp(-distances ** 2 / (2 * sigma ** 2))
        D_inv_sqrt = diags(1.0 / np.sqrt(np.sum(W, axis=1)), format='csr')
        K = rbf_kernel(X, self.eigenvecs_, gamma=self.gamma)
        M = D_inv_sqrt.dot(W.dot(D_inv_sqrt.dot(K)))
        return self.kmeans_.predict(M.dot(self.eigenvecs_))

使用示例：

from sklearn.datasets import make_moons
import matplotlib.pyplot as plt

X, y = make_moons(n_samples=1000, noise=0.05, random_state=42)
model = DensityWeightedNystromSpectralClustering(n_clusters=2, n_components=50, gamma=10.0, random_state=42)
model.fit(X)
y_pred = model.predict(X)

plt.scatter(X[:, 0], X[:, 1], c=y_pred)
plt.show()

在这个例子中，我们生成了一个二维月亮形数据集，并使用密度加权Nyström谱聚类将其分成两个簇。