nystrom谱聚类代码

以下是Python中使用Nystrom谱聚类的示例代码：

import numpy as np
from sklearn.cluster import KMeans
from sklearn.metrics.pairwise import rbf_kernel

class NystromSpectralClustering:
    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. 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]

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

        # 3. Compute approximate eigenvalues and eigenvectors of K
        eigenvalues, eigenvectors = np.linalg.eigh(K)
        self.eigenvecs_ = eigenvectors[:, ::-1]

        # 4. 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):
        K = rbf_kernel(X, self.eigenvecs_, gamma=self.gamma)
        return self.kmeans_.predict(K)

使用示例：

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

X, y = make_circles(n_samples=1000, noise=0.05, factor=0.5, random_state=42)
model = NystromSpectralClustering(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环形数据集，并使用Nystrom谱聚类将其分成两个簇。