机器学习 | 算法模型 —— 聚类：FCM模糊聚类算法

谁借莪１个温暖的怀抱￠ 2023-02-22 13:34 25阅读 0赞

# 1.FCM模糊聚类原理 #

> 模糊c均值聚类FCM算法融合了模糊理论的精髓，相较于k-means的硬聚类，FCM算法（Fuzzy C-Means，FCM）提供了更加灵活的聚类结果。***因为大部分情况下，数据集中的对象不能划分成为明显分离的簇，将一个对象划分到一个特定的簇有些生硬，不符合人的客观认知***。因此，对每个对象和每个簇赋予一个权值，指明对象属于该簇的程度即可。当然，基于概率的方法也可以给出这样的权值，但是有时候我们很难确定一个合适的统计模型，因此使用具有自然地、非概率特性的FCM聚类算法就是一个比较好的选择。

# 2.FCM模糊聚类流程 #

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> 
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# 3.FCM模糊聚类程序 #

from pylab import *
    from numpy import *
    import pandas as pd
    import numpy as np
    import operator
    import math
    import matplotlib.pyplot as plt
    import random
    
    
    # 数据保存在.csv文件中
    df_full = pd.read_csv("iris.csv")
    columns = list(df_full.columns)
    features = columns[:len(columns) - 1]
    # class_labels = list(df_full[columns[-1]])
    df = df_full[features]
    # 维度
    num_attr = len(df.columns) - 1
    # 分类数
    k = 3
    # 最大迭代数
    MAX_ITER = 100
    # 样本数
    n = len(df)  # the number of row
    # 模糊参数
    m = 2.00
    
    
    # 初始化模糊矩阵U
    def initializeMembershipMatrix():
        membership_mat = list()
        for i in range(n):
            random_num_list = [random.random() for i in range(k)]
            summation = sum(random_num_list)
            temp_list = [x / summation for x in random_num_list]  # 首先归一化
            membership_mat.append(temp_list)
        return membership_mat
    
    
    # 计算类中心点
    def calculateClusterCenter(membership_mat):
        cluster_mem_val = zip(*membership_mat)
        cluster_centers = list()
        cluster_mem_val_list = list(cluster_mem_val)
        for j in range(k):
            x = cluster_mem_val_list[j]
            xraised = [e ** m for e in x]
            denominator = sum(xraised)
            temp_num = list()
            for i in range(n):
                data_point = list(df.iloc[i])
                prod = [xraised[i] * val for val in data_point]
                temp_num.append(prod)
            numerator = map(sum, zip(*temp_num))
            center = [z / denominator for z in numerator]  # 每一维都要计算。
            cluster_centers.append(center)
        return cluster_centers
    
    
    # 更新隶属度
    def updateMembershipValue(membership_mat, cluster_centers):
        #    p = float(2/(m-1))
        data = []
        for i in range(n):
            x = list(df.iloc[i])  # 取出文件中的每一行数据
            data.append(x)
            distances = [np.linalg.norm(list(map(operator.sub, x, cluster_centers[j]))) for j in range(k)]
            for j in range(k):
                den = sum([math.pow(float(distances[j] / distances[c]), 2) for c in range(k)])
                membership_mat[i][j] = float(1 / den)
        return membership_mat, data
    
    
    # 得到聚类结果
    def getClusters(membership_mat):
        cluster_labels = list()
        for i in range(n):
            max_val, idx = max((val, idx) for (idx, val) in enumerate(membership_mat[i]))
            cluster_labels.append(idx)
        return cluster_labels
    
    
    def fuzzyCMeansClustering():
        # 主程序
        membership_mat = initializeMembershipMatrix()
        curr = 0
        while curr <= MAX_ITER:  # 最大迭代次数
            cluster_centers = calculateClusterCenter(membership_mat)
            membership_mat, data = updateMembershipValue(membership_mat, cluster_centers)
            cluster_labels = getClusters(membership_mat)
            curr += 1
        print(membership_mat)
        return cluster_labels, cluster_centers, data, membership_mat
    
    
    def xie_beni(membership_mat, center, data):
        sum_cluster_distance = 0
        min_cluster_center_distance = inf
        for i in range(k):
            for j in range(n):
                sum_cluster_distance = sum_cluster_distance + membership_mat[j][i] ** 2 * sum(
                    power(data[j, :] - center[i, :], 2))  # 计算类一致性
        for i in range(k - 1):
            for j in range(i + 1, k):
                cluster_center_distance = sum(power(center[i, :] - center[j, :], 2))  # 计算类间距离
                if cluster_center_distance < min_cluster_center_distance:
                    min_cluster_center_distance = cluster_center_distance
        return sum_cluster_distance / (n * min_cluster_center_distance)
    
    
    labels, centers, data, membership = fuzzyCMeansClustering()
    print(labels)
    print(centers)
    center_array = array(centers)
    label = array(labels)
    datas = array(data)
    
    # Xie-Beni聚类有效性
    print("聚类有效性：", xie_beni(membership, center_array, datas))
    xlim(0, 10)
    ylim(0, 10)
    # 做散点图
    fig = plt.gcf()
    fig.set_size_inches(16.5, 12.5)
    f1 = plt.figure(1)
    plt.scatter(datas[nonzero(label == 0), 0], datas[nonzero(label == 0), 1], marker='o', color='r', label='0', s=10)
    plt.scatter(datas[nonzero(label == 1), 0], datas[nonzero(label == 1), 1], marker='+', color='b', label='1', s=10)
    plt.scatter(datas[nonzero(label == 2), 0], datas[nonzero(label == 2), 1], marker='*', color='g', label='2', s=10)
    plt.scatter(center_array[:, 0], center_array[:, 1], marker='x', color='m', s=30)
    plt.show()

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