文章目录

      • 背景
      • 输入点
      • 直接输入邻接矩阵

背景

网上倒是有一些关于使用sklearn进行谱聚类的教程，但是这些教程的输入都是一些点的集合，然后根据谱聚类的原理，其会每两个点计算一次亲密度（可以认为两个点距离越大，亲密度越小），假设一共有N个点，那么就是N*N个亲密度要计算，这特别像什么？图里面的邻接矩阵对不对。然后算法再根据这些亲密度进行聚类，即亲密度越大的点，他们应该聚在一起。

总结，这些教程都是输入点，没有说如何直接输入邻接矩阵,然后使用sklearn进行谱聚类。

输入点

下面的X就是输入的点的坐标，形状为(100,2)，我们是对这些点进行聚类，聚两类。然后affinity参数其实就是距离计算公式你选用哪个的意思，比如我们常常知道的欧式距离，曼哈顿距离，当然谱聚类里面不是这些。总之，实际使用中，哪个效果好用哪个，建议官方提供的距离你都可以试一试。

import numpy as npfrom sklearn import datasetsfrom sklearn.cluster import SpectralClusteringimport matplotlib.pyplot as pltX, _ = datasets.make_circles(n_samples=100, factor=0.5, noise=0.05)#X就是输入的点fig = plt.figure(figsize=(16,4))# 谱聚类默认聚类数为8model = SpectralClustering(n_clusters=2).fit(X)ax = fig.add_subplot(132)ax.scatter(X[:,0], X[:,1], c=model.labels_, marker='.')model = SpectralClustering(n_clusters=2, affinity="nearest_neighbors").fit(X)ax = fig.add_subplot(133)ax.scatter(X[:,0], X[:,1], c=model.labels_, marker='.')plt.show()

直接输入邻接矩阵

邻接矩阵表示各个点之间的亲密度，我们先准备好邻接矩阵如下，形状是N*N，注意邻接矩阵需要为正数，否则报错，所以我们下面用了指数。

adjacency_matrix=[[ 0.0470,0.0309,0.0269,0.0867,0.0548,0.0109,0.0771,0.0307,0.0276],[ 0.1033,0.0157,0.0012, -0.0097,0.0050,0.0059, -0.0179, -0.0133, -0.0074],[-0.0070,0.0795,0.0222, -0.0379, -0.0281, -0.0073, -0.0569, -0.0341, -0.0208],[ 0.0370,0.0165, -0.0008,0.0012, -0.0044, -0.0090,0.0311,0.0330,0.0124],[-0.0185, -0.0267, -0.0199,0.1049,0.0289, -0.0023, -0.0270, -0.0290, -0.0348],[-0.1064, -0.0719, -0.0368, -0.0589,0.0236, -0.0024, -0.0903, -0.0769, -0.0512],[ 0.0624,0.0479,0.0304,0.0762,0.0512,0.0178,0.0633,0.0288,0.0256],[-0.0258, -0.0148, -0.0024, -0.0092,0.0007, -0.0081,0.0819, -0.0039, -0.0092],[-0.0472, -0.0152, -0.0039, -0.0405, -0.0287, -0.0161, -0.0083,0.0608, -0.0053]]adjacency_matrix=np.exp(np.array(adjacency_matrix))
from sklearn.cluster import SpectralClusteringsc = SpectralClustering(3, affinity='precomputed', n_init=100,assign_labels='discretize')#precomputed就是说我们算好了的意思。sc.fit_predict(adjacency_matrix)

输出结果

array([1, 2, 2, 1, 0, 0, 1, 1, 0], dtype=int64)

这个就是我们9个点的聚类结果。

完结撒花