《機器學習實戰》學習筆記———利用K-均值聚類演算法對未標註資料分組
阿新 • • 發佈：2019-02-02
引言
K-均值演算法試圖將一系列樣本分割成K個不同的類簇（其中K是模型的輸入引數），其形式化的目標函式稱為類簇內的方差和（within cluster sum of squared errors，WCSS）。K-均值聚類的目的是最小化所有類簇中的方差之和。標準的K-均值演算法初始化K個類中心（為每個類簇中所有樣本的平均向量）
原理
k-均值聚類演算法
建立個點作為起始質點（經常是隨機選擇）
進行迭代
將每個資料點分配到離他距離最近的質點的簇。
全部分配後，用各個簇中的資料點的位置均值來更新質點的位置
直到達到迭代次數，或者所有的資料點所在的簇不發生改變
這意味著需要某種距離運算。資料集上k-均值演算法的效能會受到所選距離計算方法的影響。我們可列出k-均值聚類支援函式:
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() 第一個函式的功能是進行資料匯入，第二個函式的功能是計算兩個向量的歐氏距離，最後一個函式是為給定資料集構建一個包含個隨機之心的集合。
然後便是k-均值聚類演算法：
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例項分析
可以對它進行一些測試，測試集採用如下測試集
一個書中自帶的測試集
輸入如下命令：
datMat=mat(loadDataSet('testSet.txt'))
myCentroids,clustAssing=kMeans(datMat,4)得到如下結果，進行了四次迭代後演算法收斂
二分k-均值演算法
將所有點看成一個簇
當簇數目小於k時
對於每一個簇：
計算總誤差
在給定的簇上面進行K-均值聚類
計算將該簇一分為二後的總誤差
選擇使得誤差最小的那個簇進行劃分操作
程式碼如下
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例項分析
在上述測試集中進行測試
輸入
datMat=mat(loadDataSet('testSet.txt'))
CentList,MyNewAssments=biKmeans(datMat,4)
print(CentList)得到聚類結果
也可用一個較難的資料集
一個書中自帶的測試集
輸入
datMat=mat(loadDataSet('testSet2.txt'))
CentList,MyNewAssments=biKmeans(datMat,3)
print(CentList)得到聚類結果
例項
運用經典的iris資料集進行分類
使用經典的k-均值演算法進行分類
datMat=mat(loadDataSet('iris.txt'))
CentList,MyNewAssments=kMeans(datMat,3)可得到迭代結果
經過10次迭代，演算法收斂最後的聚類中心
以及最後的聚類集
部分聚類集
程式碼
from numpy import *
import matplotlib.pyplot as plt
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
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
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參考文獻
《機器學習實戰》