三维点云课程—Special Clustering代码

from sklearn import datasets
import numpy as np
from sklearn.cluster import KMeans
from matplotlib import pyplot as plt
from itertools import cycle, islice


# 计算两个坐标之间的欧氏距离
def distance(x1, x2):
   res = np.sqrt(np.sum((x1 - x2) ** 2))
   return res


# 计算数据之间的距离矩阵,分别计算一个坐标与其他坐标间的距离
def distanceMatrix(X):
   M = np.array(X)
   Z = np.zeros((len(M), len(M)))
   for i in range(len(M)):
       for j in range(i + 1, len(M)):
           Z[i][j] = 1.0 * distance(X[i], X[j])
           Z[j][i] = Z[i][j]
   return Z


# 计算相似矩阵,采用KNN法+高斯核函数，Z距离矩阵，k聚类数
def adjacencyMatrix(Z, k, sigma=1.0):
   N = len(Z)
   A = np.zeros((N, N))
   for i in range(N):
       """
        >>>a = [1,2,3]
        >>> b = [4,5,6]
        >>> c = [4,5,6,7,8]
        >>> zipped = zip(a,b)     # 打包为元组的列表
        [(1, 4), (2, 5), (3, 6)]
        >>> zip(a,c)              # 元素个数与最短的列表一致
        [(1, 4), (2, 5), (3, 6)]
        >>> zip(*zipped)          # 与 zip 相反，*zipped 可理解为解压，返回二维矩阵式
        [(1, 2, 3), (4, 5, 6)]
       """
       dist = zip(Z[i], range(N))  # 将Z矩阵的一行内的元素进行逐个标识下标(下标从0-range(N))
       dist_index = sorted(dist, key=lambda x: x[0])  # 根据X[0]=dist[i][0]的元素进行从小到大排序
       neibours_id = [dist_index[m][1] for m in range(k + 1)]  # 挑出排序前K的元素的下标索引
       sigma=np.var(Z)/4
       for index in neibours_id:
           A[i][index] = np.exp(-(Z[i][index]**2) / (2 * sigma * sigma))
           A[index][i] = A[i][index]
   return A


# 计算拉普拉斯矩阵及其特征矩阵,A相似矩阵，k聚类数
def laplacianMatrix(A,k):
   # 计算对角矩阵D
   D = np.sum(A, axis=1)
   # 计算普通的拉普拉斯矩阵
   L = np.diag(D) - A
   # 计算标准化之后的拉普拉斯矩阵
   squareD = np.diag(1.0 / (D ** (0.5)))
   #Lsym=I-D^(-1/2)*W*D^(-1/2)=D^(-1/2)*L*D^(-1/2)
   standardization_L = np.dot(np.dot(squareD, L), squareD)
   # 计算标准化拉普拉斯矩阵的特征值和特征向量
   x, V = np.linalg.eig(standardization_L)
   V=V.astype(float)

   # y=np.copy(x)
   # z=np.partition(y,list(range(len(y))))
   # n_cluster=0;
   # diff_value=abs(abs(z[1])-abs(z[0]))
   # for i in range(1,len(z)):
   #     if abs(abs(z[i-1])-abs(z[i]))>diff_value*2 and abs(z[i-1])*3<abs(z[i]):
   #         n_cluster=i+1
   #         break
   #     diff_value=abs(abs(z[i-1])-abs(z[i]))
   # print (n_cluster)

   # 将特征值进行排序
   idx_k_smallest = np.where(x < np.partition(x, k)[k])
   H = np.hstack([V[:, i] for i in idx_k_smallest])

   return H


def read_txt(path):
    filename = path  # txt文件和当前脚本在同一目录下，所以不用写具体路径
    pos = []
    Efield = []
    with open(filename, 'r') as file_to_read:
        while True:
            lines = file_to_read.readline()  # 整行读取数据
            if not lines:
                break
                pass
            p_tmp, E_tmp = [float(i) for i in lines.split(",")]  # 将整行数据分割处理，如果分割符是空格，括号里就不用传入参数，如果是逗号， 则传入‘，'字符。
            pos.append(p_tmp)  # 添加新读取的数据
            Efield.append(E_tmp)
            pass
    pos = np.array(pos)  # 将数据从list类型转换为array类型。
    Efield = np.array(Efield)
    x=np.vstack(pos)
    y=np.vstack(Efield)
    X=np.concatenate((x,y),axis=1)
    return X

fig, ax = plt.subplots(4, 2)
def show_result(x,i,j,n_labels):
    ax[i][j].scatter(x[:, 0], x[:, 1], s=20, c="b", marker='o')
    ax[i][j].set_xlabel('x')
    ax[i][j].set_ylabel('y')

    list_max = max(n_labels)

    if list_max == 1:
        for idx, value in enumerate(n_labels):
            if value == 0:
                ax[i][j+1].scatter(x[idx, 0], x[idx, 1], s=20, c="r", marker='*')
            elif value == 1:
                ax[i][j+1].scatter(x[idx, 0], x[idx, 1], s=20, c="g", marker='+')
    elif list_max == 2:
        for idx, value in enumerate(n_labels):
            if value == 0:
                ax[i][j+1].scatter(x[idx, 0], x[idx, 1], s=20, c="r", marker='*')
            elif value == 1:
                ax[i][j+1].scatter(x[idx, 0], x[idx, 1], s=20, c="g", marker='+')
            elif value == 2:
                ax[i][j+1].scatter(x[idx, 0], x[idx, 1], s=20, c="y", marker='^')
    ax[i][j+1].set_xlabel('x')
    ax[i][j+1].set_ylabel('y')

if __name__ == '__main__':
   data_circle=read_txt("circle.txt")
   Z_circle = distanceMatrix(data_circle)
   M_cicle = adjacencyMatrix(Z_circle, 5)
   H_cicle = laplacianMatrix(M_cicle,2)
   sp_circle = KMeans(n_clusters=2).fit(H_cicle)
   show_result(data_circle,0,0,sp_circle.labels_)
   print("the first cluster successful")

   data_moons = read_txt("moons.txt")
   Z_moons = distanceMatrix(data_moons)
   M_moons = adjacencyMatrix(Z_moons, 6)
   H_moons = laplacianMatrix(M_moons,2)
   sp_moons = KMeans(n_clusters=2).fit(H_moons)
   show_result(data_moons, 1, 0, sp_moons.labels_)
   print("the second cluster successful")

   data_varied = read_txt("varied.txt")
   Z_varied = distanceMatrix(data_varied)
   M_varied = adjacencyMatrix(Z_varied, 30)
   H_varied = laplacianMatrix(M_varied,3)
   sp_varied = KMeans(init='k-means++',n_clusters=3,tol=1e-6).fit(H_varied)
   show_result(data_varied, 2, 0, sp_varied.labels_)
   print("the third cluster successful")

   data_aniso = read_txt("aniso.txt")
   Z_aniso = distanceMatrix(data_aniso)
   M_aniso = adjacencyMatrix(Z_aniso, 20)
   H_aniso = laplacianMatrix(M_aniso,3)
   sp_aniso = KMeans(init="k-means++",n_clusters=3,tol=1e-6).fit(H_aniso)
   show_result(data_aniso, 3, 0, sp_aniso.labels_)
   print("the fourth cluster successful")

   plt.show()