机器学习 | K-均值聚类

摘要：聚类效果数据集代码从文件中加载数据一次性读取文件中的所有数据遍历数据中的每一行对

1.658985    4.285136
-3.453687    3.424321
4.838138    -1.151539
-5.379713    -3.362104
0.972564    2.924086
-3.567919    1.531611
0.450614    -3.302219
-3.487105    -1.724432
2.668759    1.594842
-3.156485    3.191137
3.165506    -3.999838
-2.786837    -3.099354
4.208187    2.984927
-2.123337    2.943366
0.704199    -0.479481
-0.392370    -3.963704
2.831667    1.574018
-0.790153    3.343144
2.943496    -3.357075
-3.195883    -2.283926
2.336445    2.875106
-1.786345    2.554248
2.190101    -1.906020
-3.403367    -2.778288
1.778124    3.880832
-1.688346    2.230267
2.592976    -2.054368
-4.007257    -3.207066
2.257734    3.387564
-2.679011    0.785119
0.939512    -4.023563
-3.674424    -2.261084
2.046259    2.735279
-3.189470    1.780269
4.372646    -0.822248
-2.579316    -3.497576
1.889034    5.190400
-0.798747    2.185588
2.836520    -2.658556
-3.837877    -3.253815
2.096701    3.886007
-2.709034    2.923887
3.367037    -3.184789
-2.121479    -4.232586
2.329546    3.179764
-3.284816    3.273099
3.091414    -3.815232
-3.762093    -2.432191
3.542056    2.778832
-1.736822    4.241041
2.127073    -2.983680
-4.323818    -3.938116
3.792121    5.135768
-4.786473    3.358547
2.624081    -3.260715
-4.009299    -2.978115
2.493525    1.963710
-2.513661    2.642162
1.864375    -3.176309
-3.171184    -3.572452
2.894220    2.489128
-2.562539    2.884438
3.491078    -3.947487
-2.565729    -2.012114
3.332948    3.983102
-1.616805    3.573188
2.280615    -2.559444
-2.651229    -3.103198
2.321395    3.154987
-1.685703    2.939697
3.031012    -3.620252
-4.599622    -2.185829
4.196223    1.126677
-2.133863    3.093686
4.668892    -2.562705
-2.793241    -2.149706
2.884105    3.043438
-2.967647    2.848696
4.479332    -1.764772
-4.905566    -2.911070

import numpy as np
import math
import matplotlib.pyplot as plt

#从文件中加载数据
def loadDataSet(file_name):
    data_mat = []
    with open(file_name) as fr:
        #一次性读取文件中的所有数据
        lines = fr.readlines()
        #print(lines)
    #遍历数据中的每一行
    for line in lines:
        #对每一行以	进行分割
        cur_line = line.strip().split("	")
        #["1.658985", "4.285136"]
        #print(cur_line)
        #将每一行的内容由字符串转换成float
        flt_line = list(map(lambda x:float(x), cur_line))
        #[-4.905566, -2.91107]
        #print(flt_line)
        #将转换后的内容append到data_mat中
        data_mat.append(flt_line)
    #返回一个array类型
    return np.array(data_mat)


#计算两个向量的欧式距离
#传入vecA=(x1,y1);vecB=(x2,y2)
#计算的是sqrt((x1-x2)^2+(y1-y2)^2)
def dist_eclud(vecA,vecB):
    vec_square = []
    for element in vecA - vecB:
        element = element ** 2
        vec_square.append(element)
    return sum(vec_square) ** 0.5


#构建k个随机质心
def rand_cent(dataSet,k):
    #n表示dataSet的列数
    n = data_set.shape[1] 
    #print(np.shape(dataSet))
    #构造一个k*n的0矩阵
    centroids = np.zeros((k, n))
    #填充矩阵的每一列
    for j in range(n):
        #得到dataSet中第j列的最小值s
        min_j = float(min(data_set[:,j]))
        #获得第j列的最小值与最大值的差
        range_j = float(max(data_set[:,j])) - min_j
        #minJ+最小值与最大值的差*一个(0-1)之间的随机数
        centroids[:,j] = (min_j + range_j * np.random.rand(k, 1))[:,0]
    return centroids


#K-均值聚类算法
def Kmeans(data_set, k):  
    #m为dataSet的行数  
    m = data_set.shape[0]  
    #初始化一个m*2的0矩阵 
    #每一行表示每一个点，[0]存放该点对应的质心的行;[1]为到质心的距离
    cluster_assment = np.zeros((m, 2))  
    #构建k个随机质心
    centroids = rand_cent(data_set, k)  
    cluster_changed = True   
    #当任意一点所属的类别发生了变化的时候     
    while cluster_changed:       
        cluster_changed = False  
        #遍历每个点（每一行） 
        for i in range(m):      
            #初始化  
            min_dist = np.inf; min_index = -1   
            #遍历每一个质心
            for j in range(k):
                #计算当前这一点与质心的dis
                dist_ji = dist_eclud(centroids[j,:], data_set[i,:])
                #更新最小的dis与对应的质心所在的行j
                if dist_ji < min_dist:              
                    min_dist = dist_ji; min_index = j 
            #该点的质心所在的行发生了变换——该点所属的类别发生了变化
            if cluster_assment[i,0] != min_index:    
                cluster_changed = True      
            #更新类别与该点到质心的距离
            cluster_assment[i,:] = min_index, min_dist**2   
        #更新质心
        for cent in range(k):   
            pts_inclust = data_set[np.nonzero(list(map(lambda x:x==cent, cluster_assment[:,0])))]
            centroids[cent,:] = np.mean(pts_inclust, axis=0)
    #返回质心，一个m*2的矩阵，[0]存放该点对应的质心的行(类别);[1]为到质心的距离
    return centroids, cluster_assment      


#绘制散点图
def drawFigure(dataMat):
    #第一列（特征1）为横坐标
    pointX=dataMat[:,0]
    pointY=dataMat[:,1]
    fig, ax = plt.subplots(figsize=(10,5))
    ax.scatter(pointX, pointY, s=30, c="r", marker="o", label="sample point")
    ax.legend()
    ax.set_xlabel("factor1")
    ax.set_ylabel("factor2")
    plt.show()


#绘制聚类后的散点图
def drawFigure2(data_set,my_centroids):
    point_x = data_set[:,0]
    point_y = data_set[:,1]  
    cent_x = my_centroids[:,0]
    cent_y = my_centroids[:,1]
    fig, ax = plt.subplots(figsize=(10,5))
    ax.scatter(point_x, point_y, s=30, c="r", marker="o", label="sample point")
    ax.scatter(cent_x, cent_y, s=100, c="black", marker="v", label="centroids")
    ax.legend()
    ax.set_xlabel("factor1")
    ax.set_ylabel("factor2")
    plt.show()


if __name__=="__main__":
    #将文本内容转换成矩阵
    data_set=loadDataSet("testSet.txt")
    my_centroids, my_cluster_assment = Kmeans(data_set, 4)
    drawFigure2(data_set,my_centroids)
    #print(my_centroids)
    # print(my_cluster_assment)
    #画图
    #drawFigure(dataMat)
    #计算第一行与第二行的距离
    #dist=distEclud(dataMat[0],dataMat[1])
    #print(dist)
    #mm=randCent(dataMat,2)
    #print(mm)
    #print(dataMat)
    #第一列
    #print(dataMat[:,0])
    #第一行
    #print(dataMat[0])