聚类是一种无监督的学习，将相似的对象放到同一簇中，有点像是全自动分类，簇内的对象越相似，簇间的对象差别越大，则聚类效果越好。
1、k均值聚类算法
k均值聚类将数据分为k个簇，每个簇通过其质心，即簇中所有点的中心来描述。首先随机确定k个初始点作为质心，然后将数据集分配到距离最近的簇中。然后将每个簇的质心更新为所有数据集的平均值。然后再进行第二次划分数据集，直到聚类结果不再变化为止。
伪代码为
随机创建k个簇质心
当任意一个点的簇分配发生改变时：
对数据集中的每个数据点：
对每个质心：
计算数据集到质心的距离
将数据集分配到最近距离质心对应的簇
对每一个簇，计算簇中所有点的均值并将均值作为质心
python实现
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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 center 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均值算法
K均值算法可能会收敛到局部最小值，而非全局最小。一种用于度量聚类效果的指标为误差平方和（SSE）。因为取了平方，更加重视原理中心的点。为了克服k均值算法可能会收敛到局部最小值的问题，有人提出来二分k均值算法。
首先将所有点作为一个簇，然后将该簇一分为二，然后选择所有簇中对其划分能够最大程度减低SSE的值的簇，直到满足指定簇数为止。
伪代码
将所有点看成一个簇
计算SSE
while 当簇数目小于k时：
for 每一个簇：
计算总误差
在给定的簇上进行k均值聚类(k=2)
计算将该簇一分为二的总误差
选择使得误差最小的那个簇进行划分操作
python实现
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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) |
代码及数据集下载：K-means
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原文链接：http://blog.csdn.net/weixin_37895339/article/details/78634144
