聚类算法——python实现层次聚类（AGNES）

算法思想

层次聚类是在不同层次上对数据进行划分，从而形成树状的聚类结构。
AGNES算法是自底向上的层次聚类算法。开始时将数据集中的每个样本初始化为一个簇，然后找到距离最近的两个簇，将他们合并，不断重复这个过程，直达到到预设的聚类数目为止。
计算距离的三个公式：



AGNES算法根据上面个三个不同的公式，相应的被称为均链接，单链接和全链接。
算法步骤如下：

1. 将数据集中的每个样本初始化为一个簇，并放入集合C中。计算任意两个集合之间的距离，并存到M中。
2. 设置当前聚类数目q = m。
3. 当q大于k时执行如下步骤：
   3.1找到距离最近的两个集合Ci和Cj, 将Ci和Cj合并。并赋值给Ci。
   3.2在集合C中将Cj删除，更新Cj+1到Cq的下标。
   3.3删除M的第j行和第j列。更新M的第i行和第i列。
   3.4q = q-1
4. 返回聚类集合C

python实现算法

 #-*- coding:utf-8 -*-import mathimport pylab as pl#数据集：每三个是一组分别是西瓜的编号，密度，含糖量data = """1,0.697,0.46,2,0.774,0.376,3,0.634,0.264,4,0.608,0.318,5,0.556,0.215,6,0.403,0.237,7,0.481,0.149,8,0.437,0.211,9,0.666,0.091,10,0.243,0.267,11,0.245,0.057,12,0.343,0.099,13,0.639,0.161,14,0.657,0.198,15,0.36,0.37,16,0.593,0.042,17,0.719,0.103,18,0.359,0.188,19,0.339,0.241,20,0.282,0.257,21,0.748,0.232,22,0.714,0.346,23,0.483,0.312,24,0.478,0.437,25,0.525,0.369,26,0.751,0.489,27,0.532,0.472,28,0.473,0.376,29,0.725,0.445,30,0.446,0.459"""#数据处理 dataset是30个样本（密度，含糖量）的列表a = data.split(',')dataset = [(float(a[i]), float(a[i+1])) for i in range(1, len(a)-1, 3)]#计算欧几里得距离,a,b分别为两个元组def dist(a, b):    return math.sqrt(math.pow(a[0]-b[0], 2)+math.pow(a[1]-b[1], 2))#dist_mindef dist_min(Ci, Cj):    return min(dist(i, j) for i in Ci for j in Cj)#dist_maxdef dist_max(Ci, Cj):    return max(dist(i, j) for i in Ci for j in Cj)#dist_avgdef dist_avg(Ci, Cj):    return sum(dist(i, j) for i in Ci for j in Cj)/(len(Ci)*len(Cj))#找到距离最小的下标def find_Min(M):    min = 1000    x = 0; y = 0    for i in range(len(M)):        for j in range(len(M[i])):            if i != j and M[i][j] < min:                min = M[i][j];x = i; y = j    return (x, y, min)#算法模型：def AGNES(dataset, dist, k):    #初始化C和M    C = [];M = []    for i in dataset:        Ci = []        Ci.append(i)        C.append(Ci)    for i in C:        Mi = []        for j in C:            Mi.append(dist(i, j))        M.append(Mi)    q = len(dataset)    #合并更新    while q > k:        x, y, min = find_Min(M)        C[x].extend(C[y])        C.remove(C[y])        M = []        for i in C:            Mi = []            for j in C:                Mi.append(dist(i, j))            M.append(Mi)        q -= 1    return C#画图def draw(C):    colValue = ['r', 'y', 'g', 'b', 'c', 'k', 'm']    for i in range(len(C)):        coo_X = []    #x坐标列表        coo_Y = []    #y坐标列表        for j in range(len(C[i])):            coo_X.append(C[i][j][0])            coo_Y.append(C[i][j][1])        pl.scatter(coo_X, coo_Y, marker='x', color=colValue[i%len(colValue)], label=i)    pl.legend(loc='upper right')    pl.show()C = AGNES(dataset, dist_avg, 3)draw(C)

这是采用dist_avg函数运行的结果图。