k-均值聚类是非监督学习的一种，输入必须指定聚簇中心个数k。k均值是基于相似度的聚类，为没有标签的一簇实例分为一类。
一 经典的k-均值聚类
思路：
1 随机创建k个质心（k必须指定，二维的很容易确定，可视化数据分布，直观确定即可）；
2 遍历数据集的每个实例，计算其到每个质心的相似度，这里也就是欧氏距离；把每个实例都分配到距离最近的质心的那一类，用一个二维数组数据结构保存，第一列是最近质心序号，第二列是距离；
3 根据二维数组保存的数据，重新计算每个聚簇新的质心；
4 迭代2 和 3，直到收敛，即质心不再变化；
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 = map(float,curLine) #map all elements to float()
dataMat.append(fltLine)
return dataMat
def distEclud(vecA, vecB):
return sqrt(sum(power(vecA - vecB, 2))) #la.norm(vecA-vecB)
def randCent(dataSet, k):
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
def kMeans(dataSet, k, distMeas=distEclud, createCent=randCent):
m = shape(dataSet)[0]
clusterAssment = mat(zeros((m,2)))#create mat to assign data points
#to a centroid, also holds SE of each point
centroids = createCent(dataSet, k)
clusterChanged = True
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):
distJI = distMeas(centroids[j,:],dataSet[i,:])
if distJI < minDist:
minDist = distJI; minIndex = j
if clusterAssment[i,0] != minIndex: clusterChanged = True
clusterAssment[i,:] = minIndex,minDist**2
print centroids
for cent in range(k):#recalculate centroids
ptsInClust = dataSet[nonzero(clusterAssment[:,0].A==cent)[0]]#get all the point in this cluster
centroids[cent,:] = mean(ptsInClust, axis=0) #assign centroid to mean
return centroids, clusterAssment
经典的k均值聚类有很大的缺点就是很容易收敛到局部最优，为了避免这种局部最优，我们引入了二分k-均值算法。
二 二分k-均值聚类算法
二分k-均值聚类算法是基于经典k-均值算法实现的；里面调用经典k-均值（k=2），把一个聚簇分成两个，迭代到分成k个停止；
具体思路：
1 把整个数据集看成一个聚簇，计算质心；并用同样的数据结构二维数组保存每个实例到质心的距离；
2 对每一个聚簇进行2-均值聚类划分；
3 计算划分后的误差，选择所有被划分的聚簇中总误差最小的划分保存；
4 迭代2 和 3 直到聚簇数目达到k停止；
def biKmeans(dataSet, k, distMeas=distEclud):
m = shape(dataSet)[0]
clusterAssment = mat(zeros((m,2)))
centroid0 = mean(dataSet, axis=0).tolist()[0]
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)):
ptsInCurrCluster = dataSet[nonzero(clusterAssment[:,0].A==i)[0],:]#get the data points currently in cluster i
centroidMat, splitClustAss = kMeans(ptsInCurrCluster, 2, distMeas)
sseSplit = sum(splitClustAss[:,1])#compare the SSE to the currrent minimum
sseNotSplit = sum(clusterAssment[nonzero(clusterAssment[:,0].A!=i)[0],1])
print "sseSplit, and notSplit: ",sseSplit,‘--‘,sseNotSplit
if (sseSplit + sseNotSplit) < lowestSSE:
bestCentToSplit = i
bestNewCents = centroidMat
bestClustAss = splitClustAss.copy()
lowestSSE = sseSplit + sseNotSplit
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)
centList[bestCentToSplit] = bestNewCents[0,:].tolist()[0]#replace a centroid with two best centroids
centList.append(bestNewCents[1,:].tolist()[0])
clusterAssment[nonzero(clusterAssment[:,0].A == bestCentToSplit)[0],:]= bestClustAss#reassign new clusters, and SSE
return mat(centList), clusterAssment
三 地理位置聚簇实例
地理位置的经纬度正好是二维的，可以可视化出来，所以很适合聚类算法确定质心个数k值；值得注意的是，球面计算距离，不能简单的用欧式距离，而需要用球面距离公式，见函数distSLC；
代码的含义给定n个俱乐部地址名称，然后使用urllib包，调用yahoo地图的API返回经纬度，调用我们上面实现的k均值聚类算法，找到聚簇的中心，最后利用matplotlib工具可视化出来；
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 "%s\t%f\t%f" % (lineArr[0], lat, lng)
fw.write(‘%s\t%f\t%f\n‘ % (line, lat, lng))
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):
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, distMeas=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)
ax1.scatter(myCentroids[:,0].flatten().A[0], myCentroids[:,1].flatten().A[0], marker=‘+‘, s=300)
plt.show()
四 总结
优点：易实现；
缺点：可能收敛到局部最小值，在大数据集上收敛较慢；
适用数据类型：数值型；
时间： 2024-10-22 23:44:24