python實現kMeans演算法的詳解

聚類是一種無監督的學習，將相似的對象放到同一簇中，有點像是全自動分類，簇內的對象越相似，簇間的對象差別越大，則聚類效果越好。本文主要為大家詳細介紹了python實現kMeans演算法，具有一定的參考價值，感興趣的小夥伴們可以參考一下，希望能協助到大家。

1、k均值聚類演算法

k均值聚類將資料分為k個簇，每個簇通過其質心，即簇中所有點的中心來描述。首先隨機確定k個初始點作為質心，然後將資料集分配到距離最近的簇中。然後將每個簇的質心更新為所有資料集的平均值。然後再進行第二次劃分資料集，直到聚類結果不再變化為止。

虛擬碼為

隨機建立k個簇質心
當任意一個點的簇分配發生改變時：
對資料集中的每個資料點：
對每個質心：
計算資料集到質心的距離
將資料集分配到最近距離質心對應的簇
對每一個簇，計算簇中所有點的均值並將均值作為質心

python實現

import numpy as npimport matplotlib.pyplot as pltdef loadDataSet(fileName):  dataMat = []  with open(fileName) as f:  for line in f.readlines():   line = line.strip().split('\t')   dataMat.append(line) dataMat = np.array(dataMat).astype(np.float32) return dataMatdef distEclud(vecA,vecB): return np.sqrt(np.sum(np.power((vecA-vecB),2)))def randCent(dataSet,k): m = np.shape(dataSet)[1] center = np.mat(np.ones((k,m))) for i in range(m):  centmin = min(dataSet[:,i])  centmax = max(dataSet[:,i])  center[:,i] = centmin + (centmax - centmin) * np.random.rand(k,1) return centerdef kMeans(dataSet,k,distMeans = distEclud,createCent = randCent): m = np.shape(dataSet)[0] clusterAssment = np.mat(np.zeros((m,2))) centroids = createCent(dataSet,k) clusterChanged = True while clusterChanged:  clusterChanged = False  for i in range(m):   minDist = np.inf   minIndex = -1   for j in range(k):    distJI = distMeans(dataSet[i,:],centroids[j,:])    if distJI < minDist:     minDist = distJI     minIndex = j   if clusterAssment[i,0] != minIndex:    clusterChanged = True   clusterAssment[i,:] = minIndex,minDist**2  for cent in range(k):   ptsInClust = dataSet[np.nonzero(clusterAssment[:,0].A == cent)[0]]   centroids[cent,:] = np.mean(ptsInClust,axis = 0) return centroids,clusterAssmentdata = loadDataSet('testSet.txt')muCentroids, clusterAssing = kMeans(data,4)fig = plt.figure(0)ax = fig.add_subplot(111)ax.scatter(data[:,0],data[:,1],c = clusterAssing[:,0].A)plt.show()print(clusterAssing)

2、二分k均值演算法

K均值演算法可能會收斂到局部最小值，而非全域最小。一種用於度量聚類效果的指標為誤差平方和（SSE）。因為取了平方，更加重視原理中心的點。為了克服k均值演算法可能會收斂到局部最小值的問題，有人提出來二分k均值演算法。
首先將所有點作為一個簇，然後將該簇一分為二，然後選擇所有簇中對其劃分能夠最大程度減低SSE的值的簇，直到滿足指定簇數為止。

虛擬碼

將所有點看成一個簇
計算SSE
while 當簇數目小於k時：
for 每一個簇：
計算總誤差
在給定的簇上進行k均值聚類(k=2)
計算將該簇一分為二的總誤差
選擇使得誤差最小的那個簇進行劃分操作

python實現

import numpy as npimport matplotlib.pyplot as pltdef loadDataSet(fileName):  dataMat = []  with open(fileName) as f:  for line in f.readlines():   line = line.strip().split('\t')   dataMat.append(line) dataMat = np.array(dataMat).astype(np.float32) return dataMatdef distEclud(vecA,vecB): return np.sqrt(np.sum(np.power((vecA-vecB),2)))def randCent(dataSet,k): m = np.shape(dataSet)[1] center = np.mat(np.ones((k,m))) for i in range(m):  centmin = min(dataSet[:,i])  centmax = max(dataSet[:,i])  center[:,i] = centmin + (centmax - centmin) * np.random.rand(k,1) return centerdef kMeans(dataSet,k,distMeans = distEclud,createCent = randCent): m = np.shape(dataSet)[0] clusterAssment = np.mat(np.zeros((m,2))) centroids = createCent(dataSet,k) clusterChanged = True while clusterChanged:  clusterChanged = False  for i in range(m):   minDist = np.inf   minIndex = -1   for j in range(k):    distJI = distMeans(dataSet[i,:],centroids[j,:])    if distJI < minDist:     minDist = distJI     minIndex = j   if clusterAssment[i,0] != minIndex:    clusterChanged = True   clusterAssment[i,:] = minIndex,minDist**2  for cent in range(k):   ptsInClust = dataSet[np.nonzero(clusterAssment[:,0].A == cent)[0]]   centroids[cent,:] = np.mean(ptsInClust,axis = 0) return centroids,clusterAssmentdef biKmeans(dataSet,k,distMeans = distEclud): m = np.shape(dataSet)[0] clusterAssment = np.mat(np.zeros((m,2))) centroid0 = np.mean(dataSet,axis=0).tolist() centList = [centroid0] for j in range(m):  clusterAssment[j,1] = distMeans(dataSet[j,:],np.mat(centroid0))**2 while (len(centList)<k):  lowestSSE = np.inf  for i in range(len(centList)):   ptsInCurrCluster = dataSet[np.nonzero(clusterAssment[:,0].A == i)[0],:]   centroidMat,splitClustAss = kMeans(ptsInCurrCluster,2,distMeans)   sseSplit = np.sum(splitClustAss[:,1])   sseNotSplit = np.sum(clusterAssment[np.nonzero(clusterAssment[:,0].A != i)[0],1])   if (sseSplit + sseNotSplit) < lowestSSE:    bestCentToSplit = i    bestNewCents = centroidMat.copy()    bestClustAss = splitClustAss.copy()    lowestSSE = sseSplit + sseNotSplit  print('the best cent to split is ',bestCentToSplit)#  print('the len of the bestClust')  bestClustAss[np.nonzero(bestClustAss[:,0].A == 1)[0],0] = len(centList)  bestClustAss[np.nonzero(bestClustAss[:,0].A == 0)[0],0] = bestCentToSplit  clusterAssment[np.nonzero(clusterAssment[:,0].A == bestCentToSplit)[0],:] = bestClustAss.copy()  centList[bestCentToSplit] = bestNewCents[0,:].tolist()[0]  centList.append(bestNewCents[1,:].tolist()[0]) return np.mat(centList),clusterAssmentdata = loadDataSet('testSet2.txt')muCentroids, clusterAssing = biKmeans(data,3)fig = plt.figure(0)ax = fig.add_subplot(111)ax.scatter(data[:,0],data[:,1],c = clusterAssing[:,0].A,cmap=plt.cm.Paired)ax.scatter(muCentroids[:,0],muCentroids[:,1])plt.show()print(clusterAssing)print(muCentroids)

代碼及資料集下載：K-means