1+ # -*- coding: utf-8 -*-
2+ """
3+ Created on Fri Aug 3 13:53:40 2018
4+
5+ @author: wzy
6+ """
7+ import matplotlib .pyplot as plt
8+ import numpy as np
9+
10+ """
11+ 函数说明：将文本文档中的数据读入到python中
12+
13+ Parameters:
14+ fileName - 文件名
15+
16+ Returns:
17+ dataMat - 数据矩阵
18+
19+ Modify:
20+ 2018-08-02
21+ """
22+ def loadDataSet (fileName ):
23+ dataMat = []
24+ fr = open (fileName )
25+ for line in fr .readlines ():
26+ curLine = line .strip ().split ('\t ' )
27+ fltLine = list (map (float , curLine ))
28+ dataMat .append (fltLine )
29+ return dataMat
30+
31+
32+ """
33+ 函数说明：数据向量计算欧式距离
34+
35+ Parameters:
36+ vecA - 数据向量A
37+ vecB - 数据向量B
38+
39+ Returns:
40+ 两个向量之间的欧几里德距离
41+
42+ Modify:
43+ 2018-08-02
44+ """
45+ def distEclud (vecA , vecB ):
46+ return np .sqrt (np .sum (np .power (vecA - vecB , 2 )))
47+
48+
49+ """
50+ 函数说明：随机初始化k个质心（质心满足数据边界之内）
51+
52+ Parameters:
53+ dataSet - 输入的数据集
54+ k - 选取k个质心
55+
56+ Returns:
57+ centroids - 返回初始化得到的k个质心向量
58+
59+ Modify:
60+ 2018-08-02
61+ """
62+ def randCent (dataSet , k ):
63+ # 得到数据样本的维度
64+ n = np .shape (dataSet )[1 ]
65+ # 初始化为一个(k,n)的全零矩阵
66+ centroids = np .mat (np .zeros ((k , n )))
67+ # 遍历数据集的每一个维度
68+ for j in range (n ):
69+ # 得到该列数据的最小值,最大值
70+ minJ = np .min (dataSet [:, j ])
71+ maxJ = np .max (dataSet [:, j ])
72+ # 得到该列数据的范围(最大值-最小值)
73+ rangeJ = float (maxJ - minJ )
74+ # k个质心向量的第j维数据值随机为位于(最小值，最大值)内的某一值
75+ # Create an array of the given shape and populate it with random samples from a uniform distribution over [0, 1).
76+ centroids [:, j ] = minJ + rangeJ * np .random .rand (k , 1 )
77+ # 返回初始化得到的k个质心向量
78+ return centroids
79+
80+
81+ """
82+ 函数说明：k-means聚类算法
83+
84+ Parameters:
85+ dataSet - 用于聚类的数据集
86+ k - 选取k个质心
87+ distMeas - 距离计算方法,默认欧氏距离distEclud()
88+ createCent - 获取k个质心的方法,默认随机获取randCent()
89+
90+ Returns:
91+ centroids - k个聚类的聚类结果
92+ clusterAssment - 聚类误差
93+
94+ Modify:
95+ 2018-08-02
96+ """
97+ def kMeans (dataSet , k , distMeas = distEclud , createCent = randCent ):
98+ # 获取数据集样本数
99+ m = np .shape (dataSet )[0 ]
100+ # 初始化一个（m,2）全零矩阵
101+ clusterAssment = np .mat (np .zeros ((m , 2 )))
102+ # 创建初始的k个质心向量
103+ centroids = createCent (dataSet , k )
104+ # 聚类结果是否发生变化的布尔类型
105+ clusterChanged = True
106+ # 只要聚类结果一直发生变化，就一直执行聚类算法，直至所有数据点聚类结果不发生变化
107+ while clusterChanged :
108+ # 聚类结果变化布尔类型置为False
109+ clusterChanged = False
110+ # 遍历数据集每一个样本向量
111+ for i in range (m ):
112+ # 初始化最小距离为正无穷，最小距离对应的索引为-1
113+ minDist = float ('inf' )
114+ minIndex = - 1
115+ # 循环k个类的质心
116+ for j in range (k ):
117+ # 计算数据点到质心的欧氏距离
118+ distJI = distMeas (centroids [j , :], dataSet [i , :])
119+ # 如果距离小于当前最小距离
120+ if distJI < minDist :
121+ # 当前距离为最小距离，最小距离对应索引应为j(第j个类)
122+ minDist = distJI
123+ minIndex = j
124+ # 当前聚类结果中第i个样本的聚类结果发生变化：布尔值置为True，继续聚类算法
125+ if clusterAssment [i , 0 ] != minIndex :
126+ clusterChanged = True
127+ # 更新当前变化样本的聚类结果和平方误差
128+ clusterAssment [i , :] = minIndex , minDist ** 2
129+ # 打印k-means聚类的质心
130+ # print(centroids)
131+ # 遍历每一个质心
132+ for cent in range (k ):
133+ # 将数据集中所有属于当前质心类的样本通过条件过滤筛选出来
134+ ptsInClust = dataSet [np .nonzero (clusterAssment [:, 0 ].A == cent )[0 ]]
135+ # 计算这些数据的均值(axis=0:求列均值)，作为该类质心向量
136+ centroids [cent , :] = np .mean (ptsInClust , axis = 0 )
137+ # 返回k个聚类，聚类结果及误差
138+ return centroids , clusterAssment
139+
140+
141+ """
142+ 函数说明：二分k-means聚类算法
143+
144+ Parameters:
145+ dataSet - 用于聚类的数据集
146+ k - 选取k个质心
147+ distMeas - 距离计算方法,默认欧氏距离distEclud()
148+
149+ Returns:
150+ centList - k个聚类的聚类结果
151+ clusterAssment - 聚类误差
152+
153+ Modify:
154+ 2018-08-03
155+ """
156+ def biKmeans (dataSet , k , distMeas = distEclud ):
157+ # 获取数据集的样本数
158+ m = np .shape (dataSet )[0 ]
159+ # 初始化一个元素均值0的(m, 2)矩阵
160+ clusterAssment = np .mat (np .zeros ((m , 2 )))
161+ # 获取数据集每一列数据的均值，组成一个列表
162+ centroid0 = np .mean (dataSet , axis = 0 ).tolist ()[0 ]
163+ # 当前聚类列表为将数据集聚为一类
164+ centList = [centroid0 ]
165+ # 遍历每个数据集样本
166+ for j in range (m ):
167+ # 计算当前聚为一类时各个数据点距离质心的平方距离
168+ clusterAssment [j , 1 ] = distMeas (np .mat (centroid0 ), dataSet [j , :])** 2
169+ # 循环，直至二分k-Means值达到k类为止
170+ while (len (centList ) < k ):
171+ # 将当前最小平方误差置为正无穷
172+ lowerSSE = float ('inf' )
173+ # 遍历当前每个聚类
174+ for i in range (len (centList )):
175+ # 通过数组过滤筛选出属于第i类的数据集合
176+ ptsInCurrCluster = dataSet [np .nonzero (clusterAssment [:, 0 ].A == i )[0 ], :]
177+ # 对该类利用二分k-means算法进行划分，返回划分后的结果以及误差
178+ centroidMat , splitClustAss = kMeans (ptsInCurrCluster , 2 , distMeas )
179+ # 计算该类划分后两个类的误差平方和
180+ sseSplit = np .sum (splitClustAss [:, 1 ])
181+ # 计算数据集中不属于该类的数据的误差平方和
182+ sseNotSplit = np .sum (clusterAssment [np .nonzero (clusterAssment [:, 0 ].A != i )[0 ], 1 ])
183+ # 打印这两项误差值
184+ print ('sseSplit = %f, and notSplit = %f' % (sseSplit , sseNotSplit ))
185+ # 划分第i类后总误差小于当前最小总误差
186+ if (sseSplit + sseNotSplit ) < lowerSSE :
187+ # 第i类作为本次划分类
188+ bestCentToSplit = i
189+ # 第i类划分后得到的两个质心向量
190+ bestNewCents = centroidMat
191+ # 复制第i类中数据点的聚类结果即误差值
192+ bestClustAss = splitClustAss .copy ()
193+ # 将划分第i类后的总误差作为当前最小误差
194+ lowerSSE = sseSplit + sseNotSplit
195+ # 数组过滤选出本次2-means聚类划分后类编号为1数据点，将这些数据点类编号变为
196+ # 当前类个数+1， 作为新的一个聚类
197+ bestClustAss [np .nonzero (bestClustAss [:, 0 ].A == 1 )[0 ], 0 ] = len (centList )
198+ # 同理，将划分数据中类编号为0的数据点的类编号仍置为被划分的类编号，使类编号
199+ # 连续不出现空缺
200+ bestClustAss [np .nonzero (bestClustAss [:, 0 ].A == 0 )[0 ], 0 ] = bestCentToSplit
201+ # 打印本次执行2-means聚类算法的类
202+ print ('the bestCentToSplit is %d' % bestCentToSplit )
203+ # 打印被划分的类的数据个数
204+ print ('the len of bestClustAss is %d' % len (bestClustAss ))
205+ # 更新质心列表中变化后的质心向量
206+ centList [bestCentToSplit ] = bestNewCents [0 , :]
207+ # 添加新的类的质心向量
208+ centList .append (bestNewCents [1 , :])
209+ # 更新clusterAssment列表中参与2-means聚类数据点变化后的分类编号，及数据该类的误差平方
210+ clusterAssment [np .nonzero (clusterAssment [:, 0 ].A == bestCentToSplit )[0 ], :] = bestClustAss
211+ # 返回聚类结果
212+ return centList , clusterAssment
213+
214+
215+ """
216+ 函数说明：绘制数据集
217+
218+ Parameters:
219+ fileName - 文件名
220+ k - 选取k个质心
221+
222+ Returns:
223+ None
224+
225+ Modify:
226+ 2018-08-01
227+ """
228+ def plotDataSet (filename , k ):
229+ # 导入数据
230+ datMat = np .mat (loadDataSet (filename ))
231+ # 进行k-means算法其中k为4
232+ centList , clusterAssment = biKmeans (datMat , k )
233+ clusterAssment = clusterAssment .tolist ()
234+ xcord = [[], [], []]
235+ ycord = [[], [], []]
236+ datMat = datMat .tolist ()
237+ m = len (clusterAssment )
238+ for i in range (m ):
239+ if int (clusterAssment [i ][0 ]) == 0 :
240+ xcord [0 ].append (datMat [i ][0 ])
241+ ycord [0 ].append (datMat [i ][1 ])
242+ elif int (clusterAssment [i ][0 ]) == 1 :
243+ xcord [1 ].append (datMat [i ][0 ])
244+ ycord [1 ].append (datMat [i ][1 ])
245+ elif int (clusterAssment [i ][0 ]) == 2 :
246+ xcord [2 ].append (datMat [i ][0 ])
247+ ycord [2 ].append (datMat [i ][1 ])
248+ fig = plt .figure ()
249+ ax = fig .add_subplot (111 )
250+ # 绘制样本点
251+ ax .scatter (xcord [0 ], ycord [0 ], s = 20 , c = 'b' , marker = '*' , alpha = .5 )
252+ ax .scatter (xcord [1 ], ycord [1 ], s = 20 , c = 'r' , marker = 'D' , alpha = .5 )
253+ ax .scatter (xcord [2 ], ycord [2 ], s = 20 , c = 'c' , marker = '>' , alpha = .5 )
254+ # 绘制质心
255+ for i in range (k ):
256+ ax .scatter (centList [i ].tolist ()[0 ][0 ], centList [i ].tolist ()[0 ][1 ], s = 100 , c = 'k' , marker = '+' , alpha = .5 )
257+ # ax.scatter(centList[0].tolist()[0][0], centList[0].tolist()[0][1], s=100, c='k', marker='+', alpha=.5)
258+ # ax.scatter(centList[1].tolist()[0][0], centList[1].tolist()[0][1], s=100, c='k', marker='+', alpha=.5)
259+ # ax.scatter(centList[2].tolist()[0][0], centList[2].tolist()[0][1], s=100, c='k', marker='+', alpha=.5)
260+ plt .title ('DataSet' )
261+ plt .xlabel ('X' )
262+ plt .show ()
263+
264+
265+ if __name__ == '__main__' :
266+ datMat = np .mat (loadDataSet ('testSet2.txt' ))
267+ centList , myNewAssments = biKmeans (datMat , 3 )
268+ plotDataSet ('testSet2.txt' , 3 )
269+
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