项目背景：通过微信文章的特征值来聚类分析。

将某微信文章的有利特征加总为第一特征值，将微信阅读量除以1000作为第二特征值。

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K-均值聚类算法

聚类是一种无监督的学习，它将相似的对象归到同一簇中，类似全自动分类。簇内的对象越相似，聚类的效果越好。K-均值聚类是每个类别簇都是采用簇中所含值的均值计算而成。聚类与分类的区别在于分类前目标已知，而聚类为无监督分类。

# kMeans.py
import kMeans# 加载数据
score_excel = pd.read_excel('WeChat20200923_np2.xlsx')
score_excel = score_excel.values
datMat = mat(score_excel)
datMat[:5]
#matrix([[5.   , 0.765],
#        [3.   , 0.515],
#        [3.   , 0.4  ],
#        [7.   , 2.284],
#        [4.   , 1.895]])# 运用kMeans算法
myCentroids, clustAssing = kMeans.kMeans(datMat,4)# 中心点
myCentroids
#matrix([[5.1       , 4.7074    ],
#        [7.6875    , 2.4608125 ],
#        [1.96938776, 0.49804082],
#        [4.72881356, 1.39588136]])# 聚类信息
clustAssing[:5]
#matrix([[3.        , 0.47155337],
#        [2.        , 1.06244921],
#        [2.        , 1.0717736 ],
#        [1.        , 0.50391891],
#        [3.        , 0.78028863]])# 绘制散点图
point_x = array(datMat[:,0])
point_y = array(datMat[:,1])
Centroid_x = array(myCentroids[:,0])  
Centroid_y = array(myCentroids[:,1]) 
fig, ax = plt.subplots(figsize=(10,5))
colors = array(clustAssing[:,0])
ax.scatter(point_x, point_y, s=30, c=colors, marker="o")
ax.scatter(Centroid_x,Centroid_y, s=300, c="b", marker="+", label="Centroid")
ax.legend()
ax.set_xlabel("factor1")
ax.set_ylabel("factor2")

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# 聚类数据与原特征数据整合
pd_myNewAssments = pd.DataFrame(clustAssing,columns=['聚类结果','SSE'])
score_excel = pd.read_excel('WeChat20200923_np2.xlsx')
my_data = score_excel.join(pd_myNewAssments)
my_data.to_excel('cluster_result.xlsx',index=False)
my_data

将聚类结果做枢纽分析可发现

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二分K-均值算法

二分K-均值类似后处理的切分思想，初始状态所有数据点属于一个大簇，之后每次选择一个簇切分成两个簇，这个切分满足使SSE值最大程度降低，直到簇数目达到k。另一种思路是每次选择SSE值最大的一个簇进行切分。

# 加载数据
score_excel = pd.read_excel('0803-np.xlsx')
score_excel = score_excel.values
datMat3 = mat(score_excel)
datMat3[:5]
#matrix([[5.   , 0.765],
#        [3.   , 0.515],
#        [3.   , 0.4  ],
#        [7.   , 2.284],
#        [4.   , 1.895]])# 运用二分K-均值算法
centList,myNewAssments = kMeans.biKmeans(datMat3,5)
#sseSplit, and notSplit:  425.0619055938215 0.0
#the bestCentToSplit is:  0
#the len of bestClustAss is:  183
#sseSplit, and notSplit:  72.36114612684459 255.93016197101448
#sseSplit, and notSplit:  159.85837841509434 169.131743622807
#the bestCentToSplit is:  0
#the len of bestClustAss is:  114
#sseSplit, and notSplit:  14.122875177845529 279.48989923632064
#sseSplit, and notSplit:  158.91046942649902 72.36114612684459
#sseSplit, and notSplit:  15.632300722727273 304.73157083255296
#the bestCentToSplit is:  1
#the len of bestClustAss is:  69# 中心点
centList
#matrix([[1.44615385, 0.4338    ],
#        [5.23404255, 1.55029787],
#        [3.28571429, 0.71612245],
#        [6.59090909, 3.70277273]])# 聚类信息
myNewAssments[:5]
#matrix([[1.        , 0.67146867],
#        [2.        , 0.12208289],
#        [2.        , 0.18156606],
#        [3.        , 2.18027142],
#        [1.        , 1.64168058]])# 绘制散点图
point_x = array(datMat3[:,0])
point_y = array(datMat3[:,1])
Centroid_x = array(centList[:,0])  
Centroid_y = array(centList[:,1]) 
fig, ax = plt.subplots(figsize=(10,5))
colors = array(myNewAssments[:,0])
ax.scatter(point_x, point_y, s=30, c=colors, marker="o")
ax.scatter(Centroid_x,Centroid_y, s=300, c="b", marker="+", label="Centroid")
ax.legend()
ax.set_xlabel("factor1")
ax.set_ylabel("factor2")

# 聚类数据与原特征数据整合
pd_myNewAssments = pd.DataFrame(myNewAssments,columns=['聚类结果','SSE'])
score_excel = pd.read_excel('WeChat20200923_np2.xlsx')
my_data = score_excel.join(pd_myNewAssments)
my_data.to_excel('cluster_result2.xlsx',index=False)
my_data

将聚类结果做枢纽分析可发现

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kMeans.py

from numpy import *
import numpy as npdef loadDataSet(fileName):      #general function to parse tab -delimited floatsdataMat = []                #assume last column is target valuefr = 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 dataMatdef distEclud(vecA, vecB):return sqrt(sum(power(vecA - vecB, 2))) #la.norm(vecA-vecB)#def randCent(data_set, k):
#    n = data_set.shape[1]    
#    centroids = np.zeros((k, n))
#    for j in range(n):
#        min_j = float(min(data_set[:,j]))
#        range_j = float(max(data_set[:,j])) - min_j
#        centroids[:,j] = (min_j + range_j * np.random.rand(k, 1))[:,0]
#    return centroidsdef randCent(dataSet, k):n = shape(dataSet)[1]centroids = mat(zeros((k,n)))#create centroid matfor j in range(n):#create random cluster centers, within bounds of each dimension#minJ = min(dataSet[:,j]) #rangeJ = float(max(dataSet[:,j]) - minJ)minJ = float(min(dataSet[:,j]))rangeJ = float(max(dataSet[:,j]))- minJcentroids[:,j] = mat(minJ + rangeJ * random.rand(k,1))return centroidsdef 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 pointcentroids = createCent(dataSet, k)clusterChanged = Truewhile clusterChanged:clusterChanged = Falsefor i in range(m):#for each data point assign it to the closest centroidminDist = inf; minIndex = -1for j in range(k):distJI = distMeas(centroids[j,:],dataSet[i,:])if distJI < minDist:minDist = distJI; minIndex = jif clusterAssment[i,0] != minIndex: clusterChanged = TrueclusterAssment[i,:] = minIndex,minDist**2#print (centroids)for cent in range(k):#recalculate centroidsptsInClust = dataSet[nonzero(clusterAssment[:,0].A==cent)[0]]#get all the point in this clustercentroids[cent,:] = mean(ptsInClust, axis=0) #assign centroid to mean return centroids, clusterAssmentdef 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 centroidfor j in range(m):#calc initial ErrorclusterAssment[j,1] = distMeas(mat(centroid0), dataSet[j,:])**2while (len(centList) < k):lowestSSE = inffor i in range(len(centList)):ptsInCurrCluster = dataSet[nonzero(clusterAssment[:,0].A==i)[0],:]#get the data points currently in cluster icentroidMat, splitClustAss = kMeans(ptsInCurrCluster, 2, distMeas)sseSplit = sum(splitClustAss[:,1])#compare the SSE to the currrent minimumsseNotSplit = sum(clusterAssment[nonzero(clusterAssment[:,0].A!=i)[0],1])print ("sseSplit, and notSplit: ",sseSplit,sseNotSplit)if (sseSplit + sseNotSplit) < lowestSSE:bestCentToSplit = ibestNewCents = centroidMatbestClustAss = splitClustAss.copy()lowestSSE = sseSplit + sseNotSplitbestClustAss[nonzero(bestClustAss[:,0].A == 1)[0],0] = len(centList) #change 1 to 3,4, or whateverbestClustAss[nonzero(bestClustAss[:,0].A == 0)[0],0] = bestCentToSplitprint ('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 SSEreturn mat(centList), clusterAssment