人以类聚,物以群分,k-means聚类算法就是体现。数学公式不要,直接用白话描述的步骤就是:
- 1.随机选取k个质心(k值取决于你想聚成几类)
- 2.计算样本到质心的距离,距离质心距离近的归为一类,分为k类
- 3.求出分类后的每类的新质心
- 4.判断新旧质心是否相同,如果相同就代表已经聚类成功,如果没有就循环2-3直到相同
用程序的语言描述就是:
- 1.输入样本
- 2.随机去k个质心
- 3.重复下面过程知道算法收敛:
计算样本到质心距离(欧几里得距离)
样本距离哪个质心近,就记为那一类
- 计算每个类别的新质心(平均值)
import numpy
import random
import codecs
import copy
import re
import matplotlib.pyplot as plt
def calcuDistance(vec1, vec2):
# 计算向量vec1和向量vec2之间的欧氏距离
return numpy.sqrt(numpy.sum(numpy.square(vec1 - vec2)))
def loadDataSet(inFile):
# 载入数据测试数据集
# 数据由文本保存,为二维坐标
inDate = codecs.open(inFile, 'r', 'utf-8').readlines()
dataSet = list()
for line in inDate:
line = line.strip()
strList = re.split('[ ]+', line) # 去除多余的空格
# print strList[0], strList[1]
numList = list()
for item in strList:
num = float(item)
numList.append(num)
# print numList
dataSet.append(numList)
return dataSet # dataSet = [[], [], [], ...]
def initCentroids(dataSet, k):
# 初始化k个质心,随机获取
return random.sample(dataSet, k) # 从dataSet中随机获取k个数据项返回
def minDistance(dataSet, centroidList):
# 对每个属于dataSet的item,计算item与centroidList中k个质心的欧式距离,找出距离最小的,
# 并将item加入相应的簇类中
clusterDict = dict() # 用dict来保存簇类结果
for item in dataSet:
vec1 = numpy.array(item) # 转换成array形式
flag = 0 # 簇分类标记,记录与相应簇距离最近的那个簇
minDis = float("inf") # 初始化为最大值
for i in range(len(centroidList)):
vec2 = numpy.array(centroidList[i])
distance = calcuDistance(vec1, vec2) # 计算相应的欧式距离
if distance < minDis:
minDis = distance
flag = i # 循环结束时,flag保存的是与当前item距离最近的那个簇标记
if flag not in clusterDict.keys(): # 簇标记不存在,进行初始化
clusterDict[flag] = list()
# print flag, item
clusterDict[flag].append(item) # 加入相应的类别中
return clusterDict # 返回新的聚类结果
def getCentroids(clusterDict):
# 得到k个质心
centroidList = list()
for key in clusterDict.keys():
centroid = numpy.mean(numpy.array(clusterDict[key]), axis=0) # 计算每列的均值,即找到质心
# print key, centroid
centroidList.append(centroid)
return numpy.array(centroidList).tolist()
def getVar(clusterDict, centroidList):
# 计算簇集合间的均方误差
# 将簇类中各个向量与质心的距离进行累加求和
sum = 0.0
for key in clusterDict.keys():
vec1 = numpy.array(centroidList[key])
distance = 0.0
for item in clusterDict[key]:
vec2 = numpy.array(item)
distance += calcuDistance(vec1, vec2)
sum += distance
return sum
def showCluster(centroidList, clusterDict):
# 展示聚类结果
colorMark = ['or', 'ob', 'og', 'ok', 'oy', 'ow'] # 不同簇类的标记 'or' --> 'o'代表圆,'r'代表red,'b':blue
centroidMark = ['dr', 'db', 'dg', 'dk', 'dy', 'dw'] # 质心标记 同上'd'代表棱形
for key in clusterDict.keys():
plt.plot(centroidList[key][0], centroidList[key][1], centroidMark[key], markersize=12) # 画质心点
for item in clusterDict[key]:
plt.plot(item[0], item[1], colorMark[key]) # 画簇类下的点
plt.show()
if __name__ == '__main__':
inFile = "C:\\Users\\zuo\\Desktop\\test.txt" # 数据集文件
dataSet = loadDataSet(inFile) # 载入数据集
centroidList = initCentroids(dataSet, 4) # 初始化质心,设置k=4
clusterDict = minDistance(dataSet, centroidList) # 第一次聚类迭代
newVar = getVar(clusterDict, centroidList) # 获得均方误差值,通过新旧均方误差来获得迭代终止条件
oldVar = -0.0001 # 旧均方误差值初始化为-1
print
'***** 第1次迭代 *****'
print
print
'簇类'
for key in clusterDict.keys():
print
(key, ' --> ', clusterDict[key])
print
('k个均值向量: ', centroidList)
print
('平均均方误差: ', newVar)
print()
showCluster(centroidList, clusterDict) # 展示聚类结果
k = 2
while abs(newVar - oldVar) >= 0.0001: # 当连续两次聚类结果小于0.0001时,迭代结束
centroidList = getCentroids(clusterDict) # 获得新的质心
clusterDict = minDistance(dataSet, centroidList) # 新的聚类结果
oldVar = newVar
newVar = getVar(clusterDict, centroidList)
print
'***** 第%d次迭代 *****' % k
print
print
'簇类'
for key in clusterDict.keys():
print
(key, ' --> ', clusterDict[key])
print
('k个均值向量: ', centroidList)
print
('平均均方误差: ', newVar)
print()
showCluster(centroidList, clusterDict) # 展示聚类结果
k += 1
-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