机器学习实战-10k-means聚类

一句话总结，即将数据集分为k个类别。原理：1、首先选取k个初始点作为中心；然后遍历所有的点，对于每一个点，计算k个中心中到这个点距离最小的中心，然后将这个点划分到这个中心；3、当所有的点划分完毕，重新计算类别的计算中心（将均值作为中心），直到中心点不再变化。但是这种方式可能陷入局部最小解，为了克服这个缺陷，提出了二分k-means算法，这种方式类似于二分法。即先划分两类，然后，再将其中一类划分为两类，这样就扩展到三类，一次类推。对于到底选取哪一类进行扩张，衡量刻度是到质心的总距离，选取最小的那一个。

一、应用场景

这是一种无监督的学习，一般用来划分，实际生活中常常遇到，比如村落的划分，经常是把村落聚集的一个划分为一个村落。同样比如美国的大选，对于某一些地区的选民，很显然有一部分选民很大程度上是一致的态度，如果能找到他们这一个群里，汇集起来，就可以专门针对，来进行宣传。同样，对于推荐系统等，找到某一类共同特制的人群，也可以进行定点推销。

二、聚类算法

由于原理简单，只是动手做了原理部分，没有亲自实现案列部分。





代码：kMeans.py

"""
@author: zoutai
@file: kMeans.py
@time: 2017/11/20
@description: K-均值聚类
"""

from numpy import *

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 = list(map(float,curLine)) #map all elements to float()
dataMat.append(fltLine)
return dataMat

# 距离计算函数：欧氏距离
def distEclud(vecA,vecB):
return sqrt(sum(power(vecA-vecB,2)))

def randCent(dataSet,k):
n = shape(dataSet)[1]
centroids = mat(zeros((k,n)))
for j in range(n):
minJ = min(dataSet[:,j])
rangJ = float(max(dataSet[:,j])-minJ)
centroids[:,j] = minJ + rangJ * random.rand(k,1) # 随机数范围0-1，矩阵为k*1
return centroids

#
def kMeans(dataSet,k,distMeas=distEclud,createCent=randCent):
m = shape(dataSet)[0]
clusterAssment = mat(zeros((m,2)))
centroids = createCent(dataSet,k)
clusterChanged = True
while clusterChanged:
clusterChanged = False
for i in range(m):
minDist = inf;minIndex = -1
for j in range(k):
distJI = distEclud(centroids[j,:],dataSet[i,:])
if distJI < minDist:
minDist = distJI
minIndex = j
# 是否更新质心，重新扫描。（即如果全部的点最后都不改变了，则停止学习）
if clusterAssment[i,0] != minIndex:
clusterChanged = True
clusterAssment[i,:] = minIndex,minDist**2 # 记录点所属的簇
print(centroids)
# 更新质心
for cent in range(k):
ptsInClust = dataSet[nonzero(clusterAssment[:,0]==cent)[0]] # 第cent簇的点集合
centroids[cent,:] = mean(ptsInClust,axis=0) #取均值作为质心
return centroids,clusterAssment

def biKmeans(dataSet,k,disMeas=distEclud):
m = shape(dataSet)[0]
clusterAssment = mat(zeros((m,2)))
# 1，先求出所有点的质心
centroid0 = mean(dataSet,axis=0).tolist()[0]
centList = [centroid0] # 保存所有的质心

# 遍历，求出每个点到质心的距离^2
for j in range(m):
clusterAssment[j,1] = distEclud(mat(centroid0),dataSet[j,:])**2 # ^2是错误的

while len(centList) < k:
lowestSSE = inf

# 2,接下来，对已经划分完成的，尝试将每一个k类二次划分，找出最好的，就相当于增加了一个类
for i in range(len(centList)):
ptsInCurrCluster = dataSet[nonzero(clusterAssment[:,0].A==i)[0],:] # 生成所有第i类的数据集datasetI
# 不知道哪里逻辑错了，这里需要判断空
if len(ptsInCurrCluster)==0:
continue
centroidIMat,splitClustAss = kMeans(ptsInCurrCluster,2,disMeas) # 求出新的子划分

# 计算新的总误差大小：sum = 1第I个新的子划分+2（原始的划分-第I个划分）
# 1.第I个新的子划分误差
firstSplit = sum(splitClustAss[:,1])
secondSplit = sum(clusterAssment[nonzero(clusterAssment[:,0].A != i)[0],1])
print("firstSplit is :",firstSplit,"secondSplit is ；",secondSplit)

# 如果小于原始误差，则划分保存
if firstSplit + secondSplit < lowestSSE:
bestCentToSplit = i
bestNewCents = centroidIMat
bestClustAss = splitClustAss.copy()
lowestSSE = firstSplit+secondSplit

# 更新分配结果，将上面得到的最好结果保存:
# 将新划分的两类划分给原始集合：第一类划分下标为被分解的簇bestCentToSplit，第二类，为新的簇，即len(centList)
bestClustAss[nonzero(bestClustAss[:,0].A == 0)[0],0] = bestCentToSplit
bestClustAss[nonzero(bestClustAss[:,0].A == 1)[0],0] = len(centList)

print("the bestCentToSplit is",bestCentToSplit)

# 将第bestCentToSplit个修改；增加另外一个
centList[bestCentToSplit] = bestNewCents[0,:]
centList.append(bestNewCents[1,:])
# 赋均值
clusterAssment[nonzero(clusterAssment[:,0].A == bestCentToSplit)[0],:] = bestClustAss
return centList,clusterAssment

import urllib
import json

def geoGrab(stAddress, city):
apiStem = 'http://where.yahooapis.com/geocode?'  # create a dict and constants for the goecoder
params = {}
params['flags'] = 'J'  # JSON return type
params['appid'] = 'aaa0VN6k'
params['location'] = '%s %s' % (stAddress, city)
url_params = urllib.urlencode(params)
yahooApi = apiStem + url_params  # print url_params
print(yahooApi)
c = urllib.urlopen(yahooApi)
return json.loads(c.read())

from time import sleep

def massPlaceFind(fileName):
fw = open('places.txt', 'w')
for line in open(fileName).readlines():
line = line.strip()
lineArr = line.split('\t')
retDict = geoGrab(lineArr[1], lineArr[2])
if retDict['ResultSet']['Error'] == 0:
lat = float(retDict['ResultSet']['Results'][0]['latitude'])
lng = float(retDict['ResultSet']['Results'][0]['longitude'])
print(lineArr[0], lat, lng)
fw.write(line,'\t', lat,'\t', lng,'\n')
else:
print("error fetching")
sleep(1)
fw.close()

def distSLC(vecA, vecB):  # Spherical Law of Cosines
a = sin(vecA[0, 1] * pi / 180) * sin(vecB[0, 1] * pi / 180)
b = cos(vecA[0, 1] * pi / 180) * cos(vecB[0, 1] * pi / 180) * \
cos(pi * (vecB[0, 0] - vecA[0, 0]) / 180)
return arccos(a + b) * 6371.0  # pi is imported with numpy

import matplotlib
import matplotlib.pyplot as plt

def clusterClubs(numClust=5):
numClust = numClust+1 # 不知道哪里逻辑错了，必须+1，最后会有一个空集
datList = []
for line in open('places.txt').readlines():
lineArr = line.split('\t')
datList.append([float(lineArr[4]), float(lineArr[3])])
datMat = mat(datList)
myCentroids, clustAssing = biKmeans(datMat, numClust, disMeas=distSLC)
fig = plt.figure()
rect = [0.1, 0.1, 0.8, 0.8]
scatterMarkers = ['s', 'o', '^', '8', 'p', \
'd', 'v', 'h', '>', '<']
axprops = dict(xticks=[], yticks=[])
ax0 = fig.add_axes(rect, label='ax0', **axprops)
imgP = plt.imread('Portland.png')
ax0.imshow(imgP)
ax1 = fig.add_axes(rect, label='ax1', frameon=False)
for i in range(numClust):
ptsInCurrCluster = datMat[nonzero(clustAssing[:, 0].A == i)[0], :]
markerStyle = scatterMarkers[i % len(scatterMarkers)]
ax1.scatter(ptsInCurrCluster[:, 0].flatten().A[0], ptsInCurrCluster[:, 1].flatten().A[0], marker=markerStyle,
s=90)

newDataSet = zeros((len(myCentroids),2))
newDataSet = [list(array(myCentroids[i])[0]) for i in range(len(myCentroids))]
ax1.scatter(mat(newDataSet)[:, 0].flatten().A[0], mat(newDataSet)[:, 1].flatten().A[0], marker='+', s=300)
plt.show()

画图代码：plotTest.py

"""
@author: zoutai
@file: plotTest.py
@time: 2017/11/22
@description:
"""

# 画这个图费了好长时间，主要的问题还是在于各种数据类型的转换和匹配，真是想说python真是个垃圾语言，对初学者很难适应

import matplotlib.pyplot as plt
from numpy import *
def plotGraph(dataSet,centList):
fig = plt.figure()
ax = fig.add_subplot(111)

newDataSet = zeros((len(centList),2))
newDataSet = [list(array(centList[i])[0]) for i in range(len(centList))]
# for i in range(len(centList)):
#     newDataSet.(array(centList[i])[0])
newMat = mat(newDataSet)
print(newMat)
# ax.plot(dataSet[:,0],dataSet[:,1],marker = 'x')
# ax.plot(centList[:,0],centList[:,1],marker = '+',color='r')
ax.scatter(dataSet[:,0].flatten().A[0],dataSet[:,1].flatten().A[0],marker='^',s=90)
ax.scatter(newMat[:,0].flatten().A[0],newMat[:,1].flatten().A[0],marker='o',s=90)
plt.show()

测试代码：test.py

"""
@author: zoutai
@file: test.py
@time: 2017/11/21
@description:
"""
from unit10.kMeans import *
from unit10.plotTest import *
from numpy import *

# test1
dataMat = mat(loadDataSet('testSet.txt'))
myCentroids,clustAssing = kMeans(dataMat,4)
print(myCentroids)

# test2
# dataMat3 = mat(loadDataSet('testSet2.txt'))
# centList,newAssment = biKmeans(dataMat3,3)
# print(centList)
# plotGraph(dataMat3,centList)
# # dataLast = row_stack(dataMat3,mat(centList))
# print(centList)

# test3
clusterClubs(5)