[機器學習10.1-2] K-均值聚類算法對未標註數據分組

• 容易實現
• 可能收斂局部最小值(局部最優解),大數據集上收斂慢
• 適用於數值類型數據
• 用戶給定分組數量

隨機選擇K個起點做爲質心
	計算每一個數據點到每一個質心的距離
		將數據點分配到最近的簇
		對每一個簇計算簇中數據點的均值做爲新的質心,直到每一個數據點所在的簇不發生變化

python代碼

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

datas = mat(loadDataSet('testSet.txt'))
centroids,clusterAssment = kMeans(datas, 2)

經過SSE(偏差平方和)來評判結果

• clusterAssment第一列的之和
• 對偏差取平方表明更重視遠離的點

方法:

• 增長k值(不符合初衷)
• 合併靠近的簇而後從新計算k爲2的質心
• 二分K-均值(見10.3章)