层次聚类算法

层次聚类算法的Python实现。

Python实现

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import math
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import pylab as pl
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# 数据处理：得到训练数据集dataset
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def get_dataset():
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    # 西瓜数据集：每三个一组（编号，密度，含糖量）
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    data = """
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    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,
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    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,
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    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,
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    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,
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    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,
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    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
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    """
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    a = data.split(',')
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    return [(float(a[i]), float(a[i+1])) for i in range(1, len(a)-1, 3)]
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# 计算两个元组的欧几里得距离
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def dist(a, b):
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    return math.sqrt(math.pow(a[0]-b[0], 2) + math.pow(a[1]-b[1], 2))
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# 计算两个聚类簇的平均距离
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def dist_avg(Ci, Cj):
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    return sum(dist(i, j) for i in Ci for j in Cj) / (len(Ci)*len(Cj))
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# 找到距离最小的下标及最小距离
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def find_Min(M):
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    min = 10000
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    x = 0
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    y = 0
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    for i in range(len(M)):
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        for j in range(len(M[i])):
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            if i != j and M[i][j] < min:
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                min = M[i][j]
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                x = i
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                y = j
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    return x, y, min
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# 算法模型
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# 参数：样本数据集, 距离计算函数，聚类簇数
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def AGNES(D, dist, k):
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    # 先初始化为|D|个类
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    C = []
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    M = []
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    for i in D:
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        Ci = []
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        Ci.append(i)
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        C.append(Ci)
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    # M存放C中两两间的距离
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    for i in C:
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        Mi = []
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        for j in C:
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            Mi.append(dist(i, j))
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        M.append(Mi)
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    # 实时聚类个数q
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    q = len(D)
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    # 合并更新
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    while q > k:
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        x, y, min = find_Min(M)
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        C[x].extend(C[y])
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        C.remove(C[y])
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        # 更新距离
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        M = []
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        for i in C:
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            Mi = []
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            for j in C:
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                Mi.append(dist(i, j))
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            M.append(Mi)
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        # 聚类数减一
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        q -= 1
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    return C
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# 训练结果可视化
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def draw(C):
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    color = ['r', 'y', 'g', 'b', 'c', 'k', 'm']
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    for i in range(len(C)):
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        x = []    # x坐标列表
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        y = []    # y坐标列表
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        for j in range(len(C[i])):
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            x.append(C[i][j][0])
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            y.append(C[i][j][1])
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        pl.scatter(x, y, marker='x', color=color[i%len(color)], label=i+1)
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    pl.legend(loc='upper left')
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    pl.title('AGNES')
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    pl.show()
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if __name__ == '__main__':
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    # 数据处理得到训练数据集
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    dataset = get_dataset()
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    # 设置聚类簇个数k
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    k = 4
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    # 层次聚类形成k个聚类簇
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    C = AGNES(dataset, dist_avg, k)
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    draw(C)

聚类结果