Python的kml库

Kmeans算法介绍

基本原理

伪代码

聚类结果评估

编程实现

封装，KMeansCluster_Class.py

# -*- coding: utf-8 -*-


"""
Created on Mon May  4 16:26:05 2020


@author: Hja
@Company：北京师范大学珠海分校
@version: V1.0
@contact: [e-mail] 2018--2020
@software: Spyder
@file: KMeansCluster_Class.py
@time: 2020/4/22 9:02
@Desc：kMeans聚类
"""


import time
from copy import deepcopy
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
from sklearn.datasets import make_blobs
from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
import mglearn
import warnings
warnings.filterwarnings("ignore")#消除警告
#   初始化图形参数
plt.rcParams['figure.figsize'] = (16,9)#  设置大小
#  图形美化
plt.style.use('ggplot')



class KMeansCluster(object):
    '''KMeans聚类'''
    
    
    def __init__(self,n_clusters = 8,max_iter = 300):
        '''
        n_clusters: ，默认= 8,形成的簇数以及生成的质心数
        max_iter :默认为300,单次运行的k均值算法的最大迭代次数
        '''
        self.n_clusters = n_clusters
        self.max_iter = max_iter
        self.X_train = None#  训练集
        self.n_iter = None#  运行迭代的次数
        self.Center_point = None#   保存当前中心点的坐标
        self.Center_point_old = None#   用于保存中心点更新前的坐标
        self.clusters = None#  用于保存数据所属的中心点
        self.iteration_flag = None# 迭代标识位，通过计算新旧中心点的距离
        self.labels_ = None#  保存训练数据类标,标签本身并没有先验意义
#        self.DBI = None#  度量聚类优劣的指标,  DBI指数,越小越好
        self.Intra_Dis = None#  存放所有类内距离之和
        self.score = None#   存放   类间间距/类内间距   来衡量聚类结果的好坏，越大越好
        
    def dist(self,matrix_a,matrix_b,ax = 1):
        #  linalg=linear（线性）+algebra（代数），norm则表示范数，默认二范数
        #  axis=1表示按行向量处理，求多个行向量的范数
        '''
        matrix_a like :
        array([[12., 40.],
               [80., 22.],
               [10.,  4.]], dtype=float32)
        matrix_b like:
            array([[0., 0.],
                   [0., 0.],
                   [0., 0.]])
        
        if axis = 1,即按行求范数
        return array([41.76122604, 82.96987405, 10.77032961])
        
        or axis = 0,按列求范数
        returnarray([81.51073549, 45.82575695])
        '''
        return np.linalg.norm(matrix_a - matrix_b,axis = ax)
    
    
    
    
    def fit(self,X_train):
        self.X_train = X_train
        #   X_train is a np.array
        
        #  Center_point  是一个n_clusters行，X_train.shape[1]列的矩阵
        self.Center_point = np.zeros((self.n_clusters,self.X_train.shape[1]),dtype = np.float32)#  存放随机初始化的中心点
#        print(self.Center_point)
        
        
        #  随机获得中心点
        for i in range(self.X_train.shape[1]):#  面对多维数据集
#            print(i)
            self.Center_point[:,i] =  np.random.choice(self.X_train[:,i],size = self.n_clusters)
            #  Center_point 的第i列从 X_train的第i列中随机抽取长度为  n_clusters
#            print('第{}列：{}'.format(i,self.Center_point[:,i]))
            
            
            
        self.Center_point_old = np.zeros(self.Center_point.shape,dtype = np.float32)#  初始化
        #  用于保存数据所属的中心点
        self.clusters = np.zeros(len(self.X_train),dtype = np.int)
        # 迭代标识位，通过计算新旧中心点的距离
#        self.iteration_flag = self.dist(self.Center_point,self.Center_point_old,1)
        self.iteration_flag = np.ones(self.n_clusters)
            
        #  记录迭代次数
        self.n_iter = 1
        #  若中心点不再变化 or 循环次数超过300次,则退出循环
        print('-'*25,'The kmeans is running...','-'*25)
        while self.iteration_flag.any() != 0 and self.n_iter < self.max_iter:
            #  同时满足两个条件则继续循环
            #  iteration_flag like：array([0,0,0]) 则会退出循环
            
            
            #  循环计算每个点对应的最近中心点
            for i in range(len(self.X_train)):
                #  计算出每个点与中心点的距离
                distances = self.dist(self.X_train[i],self.Center_point,1)#x[i] like :  array([17.93671, 15.78481])
                #  distances like :array([44.3666806 , 81.91375025, 10.73731025])
                #  其中第一个值是x[i] 到 Center_point中第一个点的距离
                
                #   记录x[i] 离Center_point中最近的点
                culuster = np.argmin(distances)#  np.argmin(a)返回 a 中最小元素的索引
                #   记录每个样例点与那个中心点距离最近
                self.clusters[i] = culuster
            
            
            #  用深度拷贝将当前的中心点保存
            self.Center_point_old = deepcopy(self.Center_point)
            '''
            为什么用深度拷贝？
            d = Center_point
            d like:array([[12., 40.],
                           [80., 22.],
                           [10.,  4.]], dtype=float32)
            Center_point  like:
                array([[12., 40.],
                       [80., 22.],
                       [10.,  4.]], dtype=float32)
            Then
            Center_point[0] = np.array([1,1])
            d  = 
            array([[ 1.,  1.],
               [80., 22.],
               [10.,  4.]], dtype=float32)
            '''
#            print(self.Center_point_old)
            #  从属于同一中心点放到一个数组中，然后按照列的方向取平均值更新中心点
            for i in range(self.n_clusters):
                #  第  i 个类簇
                points = [self.X_train[j] for j in range(len(self.X_train)) if self.clusters[j] == i]
                
                if points == []:#  如果某一类并没有分到数据点，points = []，那么np.mean()后会返回nan，影响后续计算
#                    In:  np.mean([])
#                     Out:   nan
                    self.Center_point[i] = np.zeros(self.X_train.shape[1],dtype = np.float32)
                else:
                    #  更新中心点
                    self.Center_point[i] = np.mean(points,axis = 0)#  按照列的方向取平均值
                
                
                
            print(u'**循环第%d次**'%self.n_iter)
            self.n_iter += 1
#              更新新旧中心点的距离
            self.iteration_flag = self.dist(self.Center_point,self.Center_point_old,1)
            print("新中心点与旧点的距离：", self.iteration_flag)
        

    
        self.labels_ = self.clusters#  存放数据类别
        self.Intra_class_spacing()#  运行该函数，给self.Intra_Dis 赋值
        self.score = self.Inter_class_spacing() / self.Intra_Dis #  衡量聚类结果
#        self.DBI = self.Davies_Bouldin()#  计算DBI系数


    def predict(self,X_test):
        
        '''
        根据当前的中心点
        对X_test进行预测
        标签本身并没有先验意义
        '''
        
        clusters_pred = np.zeros(len(X_test))#  存放类标
        for i in range(len(X_test)):#  循环计算每个点对应的最近中心点
            distances = self.dist(X_test[i],self.Center_point,1)#  计算距离
            cluster = np.argmin(distances)#  得出类别，其实就是索引
            clusters_pred[i] = cluster
        
        return clusters_pred

    
    
    def Intra_class_spacing(self):
        '''
        计算类内间距
        return like :{0: 17.75349746798756, 1: 18.41602776546014, 2: 17.605171601877746}
        0类 类内间距：17.75...  1类 类内间距:18.41.....     2类 类内间距:17.6.....
        '''
        Intra_dic = {}
        Intra_dis = 0.0
        
        for i in range(self.n_clusters):
            #  取出第   i 类的数据点
            points = [self.X_train[j] for j in range(len(self.X_train)) if self.clusters[j] == i]
            
            if points == []:#  健壮性
                continue
            
            else:
                dis = 0.0
                temp = 0.0
                for point in points:#   计算每一条数据与同类其他所有数据的距离
                    dis += np.sum(self.dist(point,points))#  求和
            
#                print(points)
                #  距离求和 除以  该类样本数 的平方
                temp = dis / len(points) ** 2
            
                Intra_dic[i] = temp#   第 i类的类内距离存放在字典中
                
                Intra_dis += temp#  将所有类内距离相加
        
        self.Intra_Dis = Intra_dis / float(self.n_clusters)#  取均值封装
        
        return Intra_dic
    
    
    
    
    
    def Inter_class_spacing(self):
        '''
        计算类间间距
        '''
        Inter_dis = 0.0
        count = 0#  计数器
#        pass
        #   比如聚成3 类，即n_clusters = 3
        #  那么i = 0,j = [0,1,2,3),计算0-1类间的距离，0-2类间的距离
        #  那么i = 1,j = [1,2,3),计算1-2类间的距离
        #  那么i = 2,j = [2,3),不计算
        for i in range(self.n_clusters):
            for j in range(i + 1,self.n_clusters):
                if i != j:
                    count += 1
                    # 取出第   i  类的数据点
                    points_i = [self.X_train[k] for k in range(len(self.X_train)) if self.clusters[k] == i]
                    #  取出第   j  类的数据点
                    points_j = [self.X_train[k] for k in range(len(self.X_train)) if self.clusters[k] == j]
                    
                    if points_i == [] or points_j == []:#   如果某一类没有分配到数据点，在k值较大时会有这种情况，此时分母就为0
                        continue
                    else:
                        dis = 0.0#  存放距离的中间变量
                        for point in points_i:#  计算 i类 每一条数据与 j类 所有数据的距离
                            dis += np.sum(self.dist(point,points_j))
                            
                        temp = np.sum(dis) / (len(points_i) * len(points_j))
                        
                        
                        Inter_dis += temp#  将所有类间距离相加
        
        return Inter_dis / float(count)#  取平均

先跑一下正常的二维数据集，下面的接在上面代码下面

if __name__ == '__main__':

    # 导入数据集
    path = r'F:\大三下\李艳老师数据挖掘实践\实验八\KMeans数据集.csv'
    data = pd.read_csv(path,header = None)
    #print(data.shape)
    #print(data.head())

    X_train = np.array(data,dtype = np.float64)
    
    
    #  建模
    kmeans = KMeansCluster(n_clusters = 3,max_iter = 30)
    kmeans.fit(X_train)
    
    
    
    #  结果可视化
    colors = ['r','g','b','y','c','m']
    fig,ax = plt.subplots()
    #  不同的子集用不同的颜色
    for i in range(kmeans.n_clusters):
        points = np.array([X_train[j] for j in range(len(X_train)) if kmeans.clusters[j] == i])

        ax.scatter(points[:,0],points[:,1],s = 7,c = colors[i])
    ax.scatter(kmeans.Center_point[:, 0], kmeans.Center_point[:, 1], marker='*', s=200, c='black')
    plt.show()
    print('类间间距 / 类内间距 ：{:.2f}  越大代表结果越好'.format(kmeans.score))

运行结果

再尝试一下三维数据

if __name__ == '__main__':
    #  三维数据
    X,y = make_blobs(n_samples = 1000,n_features = 3,random_state = 1)
    kmeans = KMeansCluster(n_clusters = 3,max_iter = 30)
    kmeans.fit(X)
    
    #定义坐标轴
    fig = plt.figure()
    ax = plt.axes(projection='3d')
    
    
    colors = ['r','g','b','y','c','m']
##      不同的子集用不同的颜色
    for i in range(kmeans.n_clusters):
        points = np.array([X[j] for j in range(len(X)) if kmeans.clusters[j] == i])
        ax.scatter3D(points[:,0],points[:,1],points[:,2],s = 7,c = colors[i])
    ax.scatter3D(kmeans.Center_point[:, 0], kmeans.Center_point[:, 1],kmeans.Center_point[:,2], marker='*', s=200, c='black')
    plt.show()
    print('类间间距 / 类内间距 ：{:.2f}  越大代表结果越好'.format(kmeans.score))

运行结果

KMeans无法识别具有复杂形状的簇

if __name__ == '__main__':
    #  KMeans无法识别具有复杂形状的簇
    from sklearn.datasets import make_moons
    X,y = make_moons(n_samples = 5000,noise = 0.05,random_state = 1)
    # 将数据聚类成2个簇
    kmeans = KMeansCluster(n_clusters = 3,max_iter = 100)
    kmeans.fit(X)
    #  结果可视化
    colors = ['r','g','b','y','c','m']
    fig,ax = plt.subplots()
    #  不同的子集用不同的颜色
    for i in range(kmeans.n_clusters):
        points = np.array([X[j] for j in range(len(X)) if kmeans.clusters[j] == i])
        ax.scatter(points[:,0],points[:,1],s = 1,c = colors[i])
    ax.scatter(kmeans.Center_point[:, 0], kmeans.Center_point[:, 1], marker='*', s=200, c='black')
    plt.show()
    print('k = {}时  *类间间距 / 类内间距 ：{:.2f}*  越大代表结果越好'.format(kmeans.n_clusters,kmeans.score))

运行结果