创建正态分布的点并用k均值算法聚类
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一、要用python创建正态分布的点，你得安装相关安装包。
比如pip,numpy,scipy等:
pip是安装扩展名为.whl的python包用的工具。
1、下载地址：https://pypi.python.org/pypi/pip#downloads ，选择
目录的第二个，解压到一个目录下，比如D: 。
2、找到
python setup.py install指令。3、把C:/Python27/Scripts;添加到系统环境变量。
4、重启cmd，输入pip，显示pip的帮助信息，则安装成功。
numpy和scipy下载地址：
numpy：http://www.lfd.uci.edu/~gohlke/pythonlibs/#numpy
scipy： http://www.lfd.uci.edu/~gohlke/pythonlibs/#scipy
二、创建正态分布的随机点1、利用numpy包中的random.normal函数创建
例如：
import numpy#生成正态分布 x = numpy.round(numpy.random.normal(1.75, 0.5, 20),2) y = numpy.round(numpy.random.normal(100, 10, 20), 2)z = numpy.column_stack((x, y)) print(z) 输出：[[ 1.64 117.74] [ 1.7 103.37] [ 2.01 78.99] [ 2.07 96.34] [ 2.47 102.45] [ 1.48 98.99] [ 1.44 88.01] [ 1.55 105.95] [ 1.54 105.66] [ 1.57 113.98] [ 1.56 118.53] [ 1.62 102.22] [ 1.27 106.08] [ 1.84 111. ] [ 1.68 94.13] [ 2.19 86.87] [ 1.19 102.93] [ 1.13 115.38] [ 2.52 113.05] [ 2.31 88.71]]其中random.normal（a，b，c）函数的a为平均数，b为标准差，c为随机数的个数
2、把点在图表上表示出来
相关函数参考网址:http://blog.csdn.net/ywjun0919/article/details/8692018
例如：
import numpyimport matplotlib.pyplot as pltplt.figure(1)#生成正态分布 x = numpy.round(numpy.random.normal(1.75, 0.5, 200),2) y = numpy.round(numpy.random.normal(100, 10, 200), 2)plt.figure(1)plt.plot(x,y,'b*')plt.show()输出：
三、对上述方法得到的点用k均值算法聚类
k均值的介绍我放在了下一个博文中，如有不懂可查看我的下一个博文： k均值介绍
下面我采用的是k=3时的聚类，也就是分别创建了3组正态分布随机数
代码如下：
import numpyimport matplotlib.pyplot as pltimport randomplt.figure(1)plt.figure(2)plt.figure(3)#生成正态分布 x = numpy.round(numpy.random.normal(100, 10, 200),2) y = numpy.round(numpy.random.normal(100, 5, 200), 2) p = numpy.round(numpy.random.normal(125, 10, 200),2) q = numpy.round(numpy.random.normal(125, 8, 200), 2)j =numpy.round(numpy.random.normal(150, 10, 200), 2)k =numpy.round(numpy.random.normal(100, 6, 200), 2)a=[]b=[]for i in x: a.append(i)for i in p: a.append(i)for i in j: a.append(i)for i in y: b.append(i)for i in q: b.append(i)for i in k: b.append(i)def cal_distance(a, b): #计算两点的距离 return (a[0]- b[0]) ** 2 + (a[1] - b[1]) **2k1=[random.randint(100,150) for _ in range(2)]k2=[random.randint(100,150) for _ in range(2)]k3=[random.randint(100,150) for _ in range(2)]'''k1=[100,100]k2=[125,125]k3=[150,100]''' #若用上者的赋值，则容易出现一个聚类集合为空，用下者的话，不是很符合均值函数中的随机取值clu_k1 = [] #划分三个聚类clu_k2 = []clu_k3 = []while True: clu_k1 = [] clu_k2 = [] clu_k3 = [] for i in range(600): ab_distance1 = cal_distance(k1, [a[i], b[i]]) ab_distance2 = cal_distance(k2, [a[i], b[i]]) #计算每个样本到聚类中心的距离 ab_distance3 = cal_distance(k3, [a[i], b[i]]) if (ab_distance1 <= ab_distance2 and ab_distance1 <= ab_distance3): clu_k1.append(i) elif (ab_distance2 <= ab_distance1 and ab_distance2 <= ab_distance3): clu_k2.append(i) #每个样本归于更近的聚类中心 else: clu_k3.append(i) k1_x = sum([a[i] for i in clu_k1]) / len(clu_k1) #每类样本计算质心并使之成为新的聚类中心 k1_y = sum([b[i] for i in clu_k1]) / len(clu_k1) k2_x = sum([a[i] for i in clu_k2]) / len(clu_k2) k2_y = sum([b[i] for i in clu_k2]) / len(clu_k2) k3_x = sum([a[i] for i in clu_k3]) / len(clu_k3) k3_y = sum([b[i] for i in clu_k3]) / len(clu_k3) #原来质心和新质心的距离（也就是偏移量）与我们所给的标准进行比较 if cal_distance(k1, [k1_x, k1_y])>=0.1 or cal_distance(k2, [k2_x, k2_y])>=0.1 or cal_distance(k3, [k3_x, k3_y])>=0.1: k1 = [k1_x, k1_y] k2 = [k2_x, k2_y] k3 = [k3_x, k3_y] #若偏移量大于所给标准，则求出的质心取代原来的聚类中心 else: break #偏移量小于所给标准，则迭代终止kv1_x = [a[i] for i in clu_k1] #迭代终止后将同一类的点x,y分别以列表形式存放kv1_y = [b[i] for i in clu_k1]kv2_x = [a[i] for i in clu_k2]kv2_y = [b[i] for i in clu_k2]kv3_x = [a[i] for i in clu_k3]kv3_y = [b[i] for i in clu_k3]r = numpy.column_stack((a, b))s = numpy.column_stack((kv1_x, kv1_y))t = numpy.column_stack((kv2_x, kv2_y))o= numpy.column_stack((kv3_x, kv3_y))print '这些数为：',rprint '一类为：',sprint '第二类为',tprint '第三类为',oplt.figure(1)plt.plot(x,y,'r+')plt.plot(p,q,'gx')plt.plot(j,k,'c*')plt.figure(2)plt.plot(a,b,'b*')plt.figure(3)plt.plot(kv1_x,kv1_y ,'r+')plt.plot(kv2_x, kv2_y,'gx')plt.plot(kv3_x, kv3_y,'c*')plt.show()
输出：
这些数为： [[ 85.94 98.42] [ 104.67 100.14] [ 96.07 110.85] ..., [ 152.34 106.77] [ 156.34 97.74] [ 160.91 87.55]]一类为： [[ 117.08 111.11] [ 121.47 107.21] [ 122.64 106.21] [ 113.88 113.04] [ 110.61 115.01] [ 121.53 109.03] [ 140.98 118.19] [ 122.92 131.79] [ 136.95 120.17] [ 128.46 125.79] [ 130.69 124.46] [ 128.58 126.54] [ 134.97 134.14] [ 120.22 131.08] [ 128.08 122.5 ] [ 115.14 127.8 ] [ 135.58 111.11] [ 127.58 133.76] [ 134.96 115.2 ] [ 107.74 118.7 ] [ 110.78 127.36] [ 115.28 129. ] [ 131.63 120.76] [ 132.35 119.35] [ 134.2 134.82] [ 125.85 112.84] [ 123.5 113.75] [ 112.19 117.7 ] [ 116.82 126.86] [ 111.38 127.22] [ 132.31 118.51] [ 135.47 120.15] [ 115.99 120.46] [ 126.14 121.92] [ 136.24 122.32] [ 125.02 131.13] [ 107. 125.96] [ 124.05 116.46] [ 126.9 128.11] [ 116.47 120.48] [ 144.51 132.16] [ 127.85 122.97] [ 128.22 142.98] [ 116.81 125.1 ] [ 113.67 136.17] [ 133.76 120.26] [ 121.84 129. ] [ 132.75 110.94] [ 120.41 117.21] [ 129.81 133.96] [ 120.68 130.02] [ 136.23 128.13] [ 118.04 113.01] [ 138.17 137.38] [ 108.74 117.03] [ 125.56 131.15] [ 135.09 126.98] [ 129.13 114.04] [ 129.78 125.32] [ 115.42 128.88] [ 115.83 126.32] [ 146.63 137.55] [ 146.59 125.28] [ 110.07 133.52] [ 122.91 137.7 ] [ 133.78 127.74] [ 115.83 134.04] [ 131.22 120.95] [ 134.69 129.15] [ 119.62 113.19] [ 122.44 116.64] [ 124.48 116.24] [ 132.64 135.51] [ 106.91 133.5 ] [ 134.41 118.75] [ 126.19 122.9 ] [ 120.95 124.54] [ 140.78 117.69] [ 125.24 134.05] [ 113.44 124.26] [ 116.16 118.94] [ 130.39 133.65] [ 125.03 120.55] [ 126.43 118.81] [ 116.41 135.06] [ 114.1 136.29] [ 125.01 131.88] [ 123.86 139.1 ] [ 127.59 127.12] [ 130.04 127.25] [ 117.69 124.44] [ 130.93 123.8 ] [ 129.73 138.21] [ 115.97 112.83] [ 125.98 130.39] [ 121.69 115.37] [ 126.61 136.99] [ 118.24 123.29] [ 126.46 113.5 ] [ 128.99 128.78] [ 122.22 112.55] [ 122.98 121.08] [ 118.27 125.11] [ 119.56 127.51] [ 130.38 131.22] [ 128.63 116.32] [ 114.43 115.93] [ 114.99 138.32] [ 126.03 126.67] [ 133.54 128.57] [ 125.24 128.95] [ 120.54 118.91] [ 121.13 127.35] [ 112.52 115.22] [ 125.38 122.02] [ 130.35 117.77] [ 122.06 129.59] [ 118.78 120.62] [ 110.21 124.38] [ 107.48 120.17] [ 127.55 116.25] [ 133.23 125.54] [ 141.03 125. ] [ 118.81 122.75] [ 110.42 121.52] [ 121.58 115.07] [ 122.19 121.11] [ 131.58 133.09] [ 136.7 125.87] [ 113.1 131.95] [ 122.72 140.4 ] [ 142.88 126.34] [ 128.15 120.3 ] [ 135.99 136.01] [ 120.98 131.72] [ 114.63 120.99] [ 108.25 127.23] [ 114.11 130.01] [ 121.29 121.7 ] [ 113.51 132.91] [ 118.63 135.44] [ 118.37 127.7 ] [ 131.56 121.23] [ 130.07 115.02] [ 135.67 125.13] [ 114.33 133.69] [ 125.85 112.15] [ 110.54 130.47] [ 127.17 123.51] [ 121.2 121.05] [ 141.71 128.24] [ 128.67 116.3 ] [ 134.6 133.75] [ 125.17 124.42] [ 130.29 128.19] [ 121.64 128.79] [ 132.1 121.2 ] [ 132.77 117.34] [ 132.82 127.24] [ 131.42 129.05] [ 136.77 135.73] [ 130.28 133.91] [ 119.77 132.7 ] [ 122.37 106.25] [ 123.01 133.01] [ 125.45 128.39] [ 127.67 131.19] [ 123.17 133.13] [ 129.82 133.66] [ 129.82 124.02] [ 120.41 125.03] [ 131.81 136.02] [ 131.73 123.62] [ 132.79 119.01] [ 127.09 125.82] [ 126.03 127.94] [ 141.63 121.94] [ 130.32 138.81] [ 120.55 126.12] [ 120.64 129.58] [ 136.87 136.63] [ 127.12 113.78] [ 128.05 121.69] [ 107.79 134.64] [ 95.35 139.67] [ 127. 137.27] [ 136.58 136.18] [ 132.77 120.15] [ 119.21 114.64] [ 115. 122.49] [ 110.04 120.82] [ 134.93 137.31] [ 123.08 106.97]]第二类为 [[ 85.94 98.42] [ 104.67 100.14] [ 96.07 110.85] [ 97.14 90.87] [ 104.5 103.29] [ 107.28 105.57] [ 92.69 111.78] [ 82.03 98.47] [ 102.64 103.9 ] [ 107.01 97.89] [ 110.17 94.62] [ 98.72 91.91] [ 85.47 99.38] [ 100.61 98.24] [ 107.11 93.61] [ 82.44 101.42] [ 111.77 108.28] [ 109.39 97.56] [ 100.27 99.97] [ 106.47 108.75] [ 98.54 107.64] [ 103.39 96.33] [ 92.78 97.27] [ 99.55 93.84] [ 90.69 100.79] [ 96.41 105.07] [ 117.98 94.37] [ 97.1 97.87] [ 99.01 93.17] [ 115.48 97.11] [ 110.49 98.66] [ 110.7 106.9 ] [ 106.26 97. ] [ 107.27 106.58] [ 70.16 98.68] [ 101.42 105.1 ] [ 102.81 102.88] [ 96.86 92.76] [ 102.71 114.37] [ 113.23 94.97] [ 103.45 95.69] [ 104.2 104.2 ] [ 95.34 98.38] [ 107.51 106.93] [ 99.92 101.5 ] [ 96.51 105.15] [ 103.75 99.07] [ 94.64 94.3 ] [ 99.17 100.34] [ 101.49 97.35] [ 90.49 99.07] [ 106.51 100.84] [ 84.3 93.33] [ 104.59 104.71] [ 100.08 103.65] [ 97.56 105.2 ] [ 81.7 104.04] [ 103.19 99.19] [ 91.21 93.94] [ 107.03 95.11] [ 116. 97.57] [ 84.79 98.99] [ 98.75 92.25] [ 100.46 106.45] [ 111.36 107.92] [ 105.86 93.73] [ 92.15 101.89] [ 84.59 101.17] [ 110.73 102.56] [ 95. 100.32] [ 74.73 101.95] [ 105.67 104.96] [ 87.6 97.67] [ 94.49 105.52] [ 103.92 97.27] [ 98.53 104.61] [ 102.07 102.04] [ 78.75 93.58] [ 97.7 98.76] [ 89.67 92.57] [ 110.06 103.42] [ 114.09 98.98] [ 113.36 92.11] [ 92.66 95.43] [ 107.16 97.19] [ 107.26 88.18] [ 98.57 98.01] [ 99.04 100.53] [ 93.87 105.02] [ 91.62 102.17] [ 110.93 98.81] [ 102.56 96.88] [ 105.72 100.65] [ 108.16 100.89] [ 108.58 99.34] [ 109.37 99.38] [ 94.71 99.59] [ 89.94 106.1 ] [ 112.24 101.64] [ 82.86 94.53] [ 103.5 101.06] [ 103.06 101.95] [ 106.04 107.56] [ 99.96 108.03] [ 95.98 90.36] [ 118.23 97.22] [ 111.92 98.94] [ 90.16 100.53] [ 103.03 99.87] [ 100.62 95.92] [ 100.79 96.87] [ 114. 99.36] [ 106.23 105.05] [ 93. 99.92] [ 92.27 93.08] [ 95.31 103.68] [ 101.03 96.02] [ 97.31 104.47] [ 99.37 91.35] [ 100.93 102.39] [ 110.32 100.67] [ 78.26 96.78] [ 102.27 106.81] [ 90.53 102.33] [ 99.81 99.23] [ 104.63 117.48] [ 86.48 106.39] [ 90.5 98.98] [ 96.4 100.16] [ 100.51 107.16] [ 84.44 99.57] [ 102.05 94.76] [ 98.69 107.32] [ 91.82 90.08] [ 87.95 105.95] [ 108.88 89.58] [ 81.32 100.93] [ 103.97 98.03] [ 108.86 100.43] [ 108.7 98.99] [ 94.59 101.57] [ 96.58 105.37] [ 93.01 94.2 ] [ 93.4 101.47] [ 98.32 90.39] [ 98.3 100.36] [ 108.27 94.91] [ 97.78 98.28] [ 93.79 102.6 ] [ 101.35 112.03] [ 110.4 106.31] [ 92.39 101.15] [ 87.44 104.65] [ 101.15 102.91] [ 103.95 98. ] [ 101.46 108.39] [ 91.1 96.25] [ 101.85 106.58] [ 88.95 97.83] [ 91.68 107.33] [ 89.7 101.55] [ 108.26 100.37] [ 114.75 92.22] [ 99.22 111.48] [ 111. 94.33] [ 90.31 98.04] [ 108.6 95. ] [ 78.58 100.99] [ 100.73 98.51] [ 91.79 104.08] [ 100.01 97.01] [ 113.51 93.62] [ 108.12 100.31] [ 96.63 101.95] [ 81.69 95.06] [ 99.58 95.83] [ 101.77 100.68] [ 87.12 99.15] [ 80.84 98.46] [ 102.06 98.26] [ 92.38 89.01] [ 99.54 95.1 ] [ 95.65 95.09] [ 95.54 106.35] [ 108.57 99.14] [ 105.22 97.37] [ 90.48 107.22] [ 94.91 106.98] [ 103.12 97.47] [ 89.14 93.38] [ 104.15 89.53] [ 87.44 105.46] [ 108.15 103.46] [ 96.91 102.67] [ 94.8 94.87] [ 114.39 106.93] [ 115.33 107.57] [ 103.54 120.73] [ 112.4 110.67] [ 114.57 104.11] [ 124.05 95.5 ] [ 124.37 97.43] [ 120.98 103.96] [ 124.71 99.59]]第三类为 [[ 140.22 113.22] [ 145.09 111.17] [ 140.4 113.12] [ 137.95 110.67] [ 144.58 119.59] [ 138.9 111.16] [ 148.78 123.14] [ 154.16 127.13] [ 161.42 100.84] [ 145.19 95.56] [ 170.73 97.93] [ 160.22 106.44] [ 142.26 106.71] [ 176.96 92.9 ] [ 139.42 91.28] [ 149.74 99.03] [ 153.46 109.42] [ 138.67 97.41] [ 155.09 96.9 ] [ 152.88 99.27] [ 153.83 92.88] [ 153.97 102.97] [ 134.24 89.21] [ 147.48 93.85] [ 129.19 99.21] [ 141.13 94.51] [ 142.05 108.65] [ 156.1 93.23] [ 154.15 83.91] [ 157.36 108.43] [ 157.88 107.4 ] [ 169.16 101.57] [ 150.15 96.11] [ 137.05 109.06] [ 160.61 104.39] [ 143.14 99.95] [ 135.94 94.58] [ 161.08 95.15] [ 154.01 105.74] [ 148.56 89.02] [ 145.88 101.15] [ 164.54 100.36] [ 152.5 109.39] [ 136.17 98.47] [ 153.52 100.93] [ 134.34 98.59] [ 162.44 109.99] [ 144.84 100.99] [ 166.12 103.65] [ 155.08 95.23] [ 165.29 99.48] [ 141.86 101.51] [ 142.43 99.33] [ 143.75 111.87] [ 127.13 99.37] [ 141.67 106.6 ] [ 132.92 101.7 ] [ 173.51 85.79] [ 140.04 97.97] [ 166.98 98.86] [ 151.12 94.18] [ 170.41 92.78] [ 156.52 94.77] [ 138.61 99.24] [ 142.49 105.61] [ 140.71 107.89] [ 147.17 93.45] [ 164.42 106.34] [ 156.61 91.57] [ 146.55 98.77] [ 137.27 98.88] [ 136.17 101.28] [ 164.52 88.44] [ 159.22 96.07] [ 132.19 93.62] [ 145.76 94.03] [ 159.41 95.08] [ 134.48 102.17] [ 168.69 100.78] [ 153.7 108.77] [ 161.62 109.73] [ 159.07 108.53] [ 154.43 100.74] [ 157.27 101.07] [ 153.47 96.14] [ 176.55 101.37] [ 166.57 92.83] [ 128.1 99.42] [ 125.46 97.47] [ 151.29 98.63] [ 157.32 103.41] [ 141.39 103.78] [ 145.94 111.27] [ 140.07 110.24] [ 129.89 90.19] [ 147.32 90.43] [ 171.42 108.46] [ 161.11 102.88] [ 140.86 104.19] [ 153.79 90.24] [ 144.06 101.68] [ 157.89 100.08] [ 141.19 94.75] [ 148.95 101.38] [ 164.12 89.32] [ 146.78 90.48] [ 147.1 89.21] [ 136.71 95.82] [ 163.09 92.78] [ 165.03 98.33] [ 147.3 92.59] [ 134.33 98.48] [ 160.82 100.99] [ 152.7 93.09] [ 143. 90.57] [ 158.23 95.32] [ 155.4 106.84] [ 140.83 90.63] [ 135.44 98.71] [ 136.81 109.46] [ 141.36 101.03] [ 147.3 90.44] [ 142.59 109.69] [ 159.99 97.44] [ 150.64 97.3 ] [ 144.57 106.3 ] [ 145.98 92.15] [ 146.37 102.35] [ 142.57 89.99] [ 152.87 106.97] [ 154.44 98.33] [ 161.81 93.26] [ 145.53 94.39] [ 152.15 107.16] [ 143.96 106.32] [ 149.2 98.84] [ 153.71 100.52] [ 159.73 110.09] [ 130.68 101.46] [ 163.25 96.68] [ 164.91 99.8 ] [ 136.45 102.94] [ 129.72 103.31] [ 150.47 105.76] [ 161.78 102.04] [ 153.16 97.61] [ 149.5 105.62] [ 146.55 101.11] [ 139.91 102.71] [ 140.57 99.44] [ 145.02 102.73] [ 151.41 101.53] [ 141.24 85.42] [ 147.58 103.44] [ 153.03 102.85] [ 136.19 102.22] [ 139.8 106.6 ] [ 174.63 108.34] [ 141.53 92.38] [ 138.82 97.27] [ 163.37 91.86] [ 164.82 107.82] [ 148.52 90.85] [ 150.08 108.38] [ 147.47 99.07] [ 155.28 88.86] [ 137.69 108.6 ] [ 146.37 93.46] [ 168.86 104.28] [ 170.26 111.08] [ 155.75 93.26] [ 137.99 95.27] [ 148.7 98.92] [ 154.64 97.04] [ 156.74 97.11] [ 137.03 94.26] [ 143.12 101.26] [ 140.46 105.23] [ 142.47 102.32] [ 139.57 100.14] [ 152.88 98.73] [ 159.45 88.95] [ 150.17 104.48] [ 138.02 97.35] [ 143.38 94.66] [ 156.91 88.23] [ 147.37 92.18] [ 146.25 99.9 ] [ 146.63 106.08] [ 149.78 106.48] [ 136.01 102.04] [ 133.15 99.86] [ 137.34 97.34] [ 137.17 93.68] [ 151.14 104.75] [ 154.13 96.9 ] [ 160.01 87.6 ] [ 142.98 104.83] [ 147.54 94.89] [ 157.04 98.87] [ 152.34 106.77] [ 156.34 97.74] [ 160.91 87.55]]
注：在上述代码中随机数的产生random.normal（a，b，c），a，b的变化可能会导致计算过程出现某个集合为空，导致出现错误，如：
Traceback (most recent call last): File "C:\Python27\Daima\k均值算法\正态分布k=3.py", line 61, in <module> k2_x = sum([a[i] for i in clu_k2]) / len(clu_k2)ZeroDivisionError: integer division or modulo by zero#当出现这样的错误时，不用担心，这是由于取初始质心时，这个点离数据太远，导致这个相应的聚类集合为空，你可以试着多试几次或者调节random.normal（a，b，c）函数中a，b的值，当然更有效的方法是自己定义初始的质心，初始质心选的好，就不会出现刚才所述的问题了。 阅读全文
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