机器学习 | K-均值聚类

聚类效果

数据集

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

代码

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\t进行分割
        cur_line = line.strip().split("\t")
        #['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])