[机器学习10.1-2] K-均值聚类算法对未标注数据分组

• 容易实现
• 可能收敛局部最小值(局部最优解),大数据集上收敛慢
• 适用于数值类型数据
• 用户给定分组数量

随机选择K个起点做为质心
	计算每一个数据点到每一个质心的距离
		将数据点分配到最近的簇
		对每一个簇计算簇中数据点的均值做为新的质心,直到每一个数据点所在的簇不发生变化

python代码

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)

经过SSE(偏差平方和)来评判结果

• clusterAssment第一列的之和
• 对偏差取平方表明更重视远离的点

方法:

• 增长k值(不符合初衷)
• 合并靠近的簇而后从新计算k为2的质心
• 二分K-均值(见10.3章)