Spectral clustering谱聚类算法的实现代码

#导入需要的包
import numpy as np
from sklearn.cluster import KMeans
from sklearn.datasets import make_moons#生成数据集，形成两个弯月。
from sklearn.datasets import make_circles#生成数据集，形成一个二维的大圆，包含一个小圆
from sklearn.datasets import make_blobs#为聚类生成符合正态分布的数据集，产生一个数据集和相应的标签
import matplotlib.pyplot as plt

def get_eigen(L, num_clusters):#获取特征
    eigenvalues, eigenvectors = np.linalg.eigh(L)#获取特征值  特征向量
    best_eigenvalues = np.argsort(eigenvalues)[0:num_clusters]#argsort函数返回的是数组值从小到大的索引值
    U = np.zeros((L.shape[0], num_clusters))
    U = eigenvectors[:, best_eigenvalues]#将这些特征取出 构成新矩阵
    return U

#K-Means聚类
def cluster(data, num_clusters):
    data = np.array(data)
    W = affinity_matrix(data)
    D = getD(W)
    L = getL(D, W)
    eigenvectors = get_eigen(L, num_clusters)
    clf = KMeans(n_clusters=num_clusters)
    s = clf.fit(eigenvectors)  # 聚类
    label = s.labels_
    return label

#导入需要的包
import numpy as np
from sklearn.cluster import KMeans
from sklearn.datasets import make_moons#生成数据集，形成两个弯月。
from sklearn.datasets import make_circles#生成数据集，形成一个二维的大圆，包含一个小圆
from sklearn.datasets import make_blobs#为聚类生成符合正态分布的数据集，产生一个数据集和相应的标签
import matplotlib.pyplot as plt

#定义高斯核函数
def kernel(x1, x2, sigma_sq=0.05):
    return np.exp(-(np.linalg.norm(x1 - x2) ** 2) / (2 * sigma_sq ** 2))

#定义相似度矩阵
def affinity_matrix(X):
    A = np.zeros((len(X), len(X)))#零矩阵
    for i in range(len(X) - 1):#长度为len(x) 但是从0开始
        for j in range(i   1, len(X)):#从1开始，到len(x) 是方阵 为啥下角标取值的初始值不同？？？
            A[i, j] = A[j, i] = kernel(X[i], X[j])
    return A#通过高斯核的计算 给矩阵赋予新值    10*10

# 计算度矩阵
def getD(A):
    D = np.zeros(A.shape)
    for i in range(A.shape[0]):
        D[i, i] = np.sum(A[i, :])
    return D

#计算拉普拉斯矩阵
def getL(D, A):
    L = D - A
    return L


def get_eigen(L, num_clusters):#获取特征
    eigenvalues, eigenvectors = np.linalg.eigh(L)#获取特征值  特征向量
    best_eigenvalues = np.argsort(eigenvalues)[0:num_clusters]#argsort函数返回的是数组值从小到大的索引值
    U = np.zeros((L.shape[0], num_clusters))
    U = eigenvectors[:, best_eigenvalues]#将这些特征取出 构成新矩阵
    return U

#K-Means聚类
def cluster(data, num_clusters):
    data = np.array(data)
    W = affinity_matrix(data)
    D = getD(W)
    L = getL(D, W)
    eigenvectors = get_eigen(L, num_clusters)
    clf = KMeans(n_clusters=num_clusters)
    s = clf.fit(eigenvectors)  # 聚类
    label = s.labels_
    return label


def plotRes(data, clusterResult, clusterNum):
    """
    结果可似化
    : data:  样本集
    : clusterResult: 聚类结果
    : clusterNum: 聚类个数
    :return:
    n = len(data)
    scatterColors = ['black', 'blue', 'red', 'yellow', 'green', 'purple', 'orange']
    for i in range(clusterNum):
        color = scatterColors[i % len(scatterColors)]
        x1 = []
        y1 = []
        for j in range(n):
            if clusterResult[j] == i:
                x1.append(data[j, 0])
                y1.append(data[j, 1])
        plt.scatter(x1, y1, c=color, marker=' ')


if __name__ == '__main__':
# # #月牙形数据集,sigma=0.1
# #     # cluster_num = 2
# #     # data, target = make_moons()
# #     # label = cluster(data, cluster_num)
# #     # print(label)
# #     # plotRes(data, label, cluster_num)
# #
#     # 圆形数据集,sigma=0.05
    cluster_num = 2
    data, target = make_circles(n_samples=1000, shuffle=True, noise=0.05, factor=0.5)
    label = cluster(data, cluster_num)
    print(label)
    plotRes(data, label, cluster_num)
# #    #  # 正态数据集
# #    # # n_samples是待生成的样本的总数。
# #    #  # n_features是每个样本的特征数。
# #    #  # centers表示类别数。
# #    #  # cluster_std表示每个类别的方差，例如我们希望生成2类数据，其中一类比另一类具有更大的方差，可以将cluster_std设置为[1.0, 3.0]。
# #    #  cluster_num = 2
# #    #  data, target = make_blobs(n_samples=1500, n_features=2, centers=4, random_state=24)
# #    #  label = cluster(data, cluster_num)
# #    #  print(label)
# #    #  plt.subplot(121)
# #    #  plotRes(data, target, cluster_num)
# #    #  plt.subplot(122)
# #    #  plotRes(data, label, cluster_num)
plt.show()