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 math import 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_min def dist_min(Ci, Cj):     return min(dist(i, j) for i in Ci for j in Cj) #dist_max def dist_max(Ci, Cj):     return max(dist(i, j) for i in Ci for j in Cj) #dist_avg def 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。