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- 机器学习实战Chp10： K-均值聚类及改进的二分 K-均值算法
# -*- coding: utf-8 -*-
"""
Created on Wed Aug 01 09:48:28 2018
@author: muli
"""
from numpy import *
import matplotlib
import matplotlib.pyplot as plt
# 加载数据
def loadDataSet(fileName): #general function to parse tab -delimited floats
dataMat = [] #assume last column is target value
fr = open(fileName)
for line in fr.readlines():
curLine = line.strip().split('\t')
fltLine = map(float,curLine) #map all elements to float()
dataMat.append(fltLine)
return dataMat
# 向量间的欧式距离计算
def distEclud(vecA, vecB):
return sqrt(sum(power(vecA - vecB, 2))) #la.norm(vecA-vecB)
# k 个随机质心的集合，确保在每个特征值得最小值与最大值的范围内
def randCent(dataSet, k):
# 获取特征的个数
n = shape(dataSet)[1]
centroids = mat(zeros((k,n)))#create centroid mat
for j in range(n):#create random cluster centers, within bounds of each dimension
minJ = min(dataSet[:,j])
rangeJ = float(max(dataSet[:,j]) - minJ)
centroids[:,j] = mat(minJ + rangeJ * random.rand(k,1))
return centroids
# K-均值算法
def kMeans(dataSet, k, distMeas=distEclud, createCent=randCent):
m = shape(dataSet)[0]
# 0：簇索引号 1：误差
clusterAssment = mat(zeros((m,2)))#create mat to assign data points
#to a centroid, also holds SE of each point
# 该矩阵的每一行，为一个簇的初始“中心”
centroids = createCent(dataSet, k)
clusterChanged = True
num=0
while clusterChanged:
clusterChanged = False
for i in range(m):#for each data point assign it to the closest centroid
minDist = inf;
minIndex = -1
for j in range(k):
# 计算样本点到初始“中心”的距离
distJI = distMeas(centroids[j,:],dataSet[i,:])
# 距离判断，只留下距离最小的簇，即为该类的“中心”
if distJI < minDist:
minDist = distJI;
minIndex = j
if clusterAssment[i,0] != minIndex:
clusterChanged = True
clusterAssment[i,:] = minIndex,minDist**2
num +=1
print("第"+str(num)+"次更新")
print centroids
print("-----------")
# 更新“质心”的位置
for cent in range(k):#recalculate centroids
# nonzero(a):返回数组a中非零元素的索引值数组。
# ptsInClust:属于每个类的样本
# clusterAssment矩阵和dataSet是“等同”的
# 不断得跟新每个聚类的中心
ptsInClust = dataSet[nonzero(clusterAssment[:,0].A==cent)[0]]#get all the point in this cluster
# 对列进行计算
centroids[cent,:] = mean(ptsInClust, axis=0) #assign centroid to mean
return centroids, clusterAssment
# 二分 K-均值算法
def biKmeans(dataSet, k, distMeas=distEclud):
m = shape(dataSet)[0]
clusterAssment = mat(zeros((m,2)))
# 聚成一个类的簇中心
centroid0 = mean(dataSet, axis=0).tolist()[0]
# 将簇的质心 组成一个列表
centList =[centroid0] #create a list with one centroid
for j in range(m):#calc initial Error
clusterAssment[j,1] = distMeas(mat(centroid0), dataSet[j,:])**2
while (len(centList) < k):
lowestSSE = inf
for i in range(len(centList)):
# 取出每个类别的样本
ptsInCurrCluster = dataSet[nonzero(clusterAssment[:,0].A==i)[0],:]#get the data points currently in cluster i
# 对每个类别的样本进行再次K-均值聚类(k=2)
# splitClustAss:样本所属的类别、距离平方误差
centroidMat, splitClustAss = kMeans(ptsInCurrCluster, 2, distMeas)
sseSplit = sum(splitClustAss[:,1])#compare the SSE to the currrent minimum
# 剩余集的误差
sseNotSplit = sum(clusterAssment[nonzero(clusterAssment[:,0].A!=i)[0],1])
print "sseSplit, and notSplit: ",sseSplit,sseNotSplit
if (sseSplit + sseNotSplit) < lowestSSE:
# 会划分的簇
bestCentToSplit = i
# 簇的质心，一分为2
bestNewCents = centroidMat
# 样本的类别及距离误差平方
bestClustAss = splitClustAss.copy()
# 当前最小的SSE值
lowestSSE = sseSplit + sseNotSplit
# 执行簇的划分，更新簇的标号
bestClustAss[nonzero(bestClustAss[:,0].A == 1)[0],0] = len(centList) #change 1 to 3,4, or whatever
bestClustAss[nonzero(bestClustAss[:,0].A == 0)[0],0] = bestCentToSplit
print 'the bestCentToSplit is: ',bestCentToSplit
print 'the len of bestClustAss is: ', len(bestClustAss)
# 将新簇的质心，添加到列表
centList[bestCentToSplit] = bestNewCents[0,:].tolist()[0]#replace a centroid with two best centroids
centList.append(bestNewCents[1,:].tolist()[0])
# 将变动的样本，更新 类别及距离误差平方
clusterAssment[nonzero(clusterAssment[:,0].A == bestCentToSplit)[0],:]= bestClustAss#reassign new clusters, and SSE
# 返回值是 簇的质---样本的类别和误差平方和
return mat(centList), clusterAssment
# 测试模块
if __name__ == "__main__" :
# dataMat = mat(loadDataSet('testSet.txt'))
# print("第1列：")
# print(min(dataMat[:,0]))
# print(max(dataMat[:,0]))
# print("第2列：")
# print(min(dataMat[:,1]))
# print(max(dataMat[:,1]))
# print("-------------------------")
## m_result = randCent(dataMat,2)
## print(m_result)
# print("-------------------------")
# myCentroids,clusterAssing = kMeans(dataMat,4)
## print("最终的类中心：")
## print(myCentroids)
## print("类别------------误差：")
## print(clusterAssing)
## print(myCentroids,clusterAssing)
# print("K-均值聚类后，绘制图形如下所示：")
# point_x = dataMat[:,0].flatten().A[0]
# point_y = dataMat[:,1].flatten().A[0]
# cent_x = myCentroids[:,0].flatten().A[0]
# cent_y = myCentroids[:,1].flatten().A[0]
# 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")
print("------------------------------------------")
dataMat2 = mat(loadDataSet('testSet2.txt'))
centList, myNewAssments=biKmeans(dataMat2,3)
print("------------------------------------------")
print(centList)
print("------------------------------------------")
print("二分K-均值聚类后，绘制图形如下所示：")
point_x = dataMat2[:,0].flatten().A[0]
point_y = dataMat2[:,1].flatten().A[0]
cent_x = centList[:,0].flatten().A[0]
cent_y = centList[:,1].flatten().A[0]
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="x", label="centroids")
ax.legend()
ax.set_xlabel("factor1")
ax.set_ylabel("factor2")
- 绘图如下：
