机器学习sklearn19.0聚类算法——Kmeans算法

一、关于聚类及相似度、距离的知识点

二、k-means算法思想与流程

三、sklearn中对于kmeans算法的参数

四、代码示例以及应用的知识点简介

（1）make_blobs：聚类数据生成器

sklearn.datasets.make_blobs(n_samples=100, n_features=2,centers=3, cluster_std=1.0, center_box=(-10.0, 10.0), shuffle=True, random_state=None)[source]

返回值为：

（2）np.vstack方法作用——堆叠数组

详细介绍参照博客链接：http://blog.csdn.net/csdn15698845876/article/details/73380803

#!/usr/bin/env python
# -*- coding:utf-8 -*-
# Author:ZhengzhengLiu

#k-means聚类算法

import numpy as np
import pandas as pd
import matplotlib as mpl
import matplotlib.pyplot as plt
import matplotlib.colors
import sklearn.datasets as ds
from sklearn.cluster import KMeans      #引入kmeans

#解决中文显示问题
mpl.rcParams['font.sans-serif'] = [u'SimHei']
mpl.rcParams['axes.unicode_minus'] = False

#产生模拟数据
N = 1500
centers = 4
#make_blobs:聚类数据生成器
data,y = ds.make_blobs(N,n_features=2,centers=centers,random_state=28)

data2,y2 = ds.make_blobs(N,n_features=2,centers=centers,random_state=28)
data3 = np.vstack((data[y==0][:200],data[y==1][:100],data[y==2][:10],data[y==3][:50]))
y3 = np.array([0]*200+[1]*100+[2]*10+[3]*50)

#模型的构建
km = KMeans(n_clusters=centers,random_state=28)
km.fit(data,y)
y_hat = km.predict(data)
print("所有样本距离聚簇中心点的总距离和:",km.inertia_)
print("距离聚簇中心点的平均距离:",(km.inertia_/N))
print("聚簇中心点:",km.cluster_centers_)

y_hat2 = km.fit_predict(data2)
y_hat3 = km.fit_predict(data3)

def expandBorder(a, b):
    d = (b - a) * 0.1
    return a-d, b+d

#画图
cm = mpl.colors.ListedColormap(list("rgbmyc"))
plt.figure(figsize=(15,9),facecolor="w")
plt.subplot(241)
plt.scatter(data[:,0],data[:,1],c=y,s=30,cmap=cm,edgecolors="none")

x1_min,x2_min = np.min(data,axis=0)
x1_max,x2_max = np.max(data,axis=0)
x1_min,x1_max = expandBorder(x1_min,x1_max)
x2_min,x2_max = expandBorder(x2_min,x2_max)
plt.xlim((x1_min,x1_max))
plt.ylim((x2_min,x2_max))
plt.title("原始数据")
plt.grid(True)

plt.subplot(242)
plt.scatter(data[:, 0], data[:, 1], c=y_hat, s=30, cmap=cm, edgecolors='none')
plt.xlim((x1_min, x1_max))
plt.ylim((x2_min, x2_max))
plt.title(u'K-Means算法聚类结果')
plt.grid(True)

m = np.array(((1, 1), (0.5, 5)))
data_r = data.dot(m)
y_r_hat = km.fit_predict(data_r)
plt.subplot(243)
plt.scatter(data_r[:, 0], data_r[:, 1], c=y, s=30, cmap=cm, edgecolors='none')

x1_min, x2_min = np.min(data_r, axis=0)
x1_max, x2_max = np.max(data_r, axis=0)
x1_min, x1_max = expandBorder(x1_min, x1_max)
x2_min, x2_max = expandBorder(x2_min, x2_max)

plt.xlim((x1_min, x1_max))
plt.ylim((x2_min, x2_max))
plt.title(u'数据旋转后原始数据图')
plt.grid(True)

plt.subplot(244)
plt.scatter(data_r[:, 0], data_r[:, 1], c=y_r_hat, s=30, cmap=cm, edgecolors='none')
plt.xlim((x1_min, x1_max))
plt.ylim((x2_min, x2_max))
plt.title(u'数据旋转后预测图')
plt.grid(True)

plt.subplot(245)
plt.scatter(data2[:, 0], data2[:, 1], c=y2, s=30, cmap=cm, edgecolors='none')
x1_min, x2_min = np.min(data2, axis=0)
x1_max, x2_max = np.max(data2, axis=0)
x1_min, x1_max = expandBorder(x1_min, x1_max)
x2_min, x2_max = expandBorder(x2_min, x2_max)
plt.xlim((x1_min, x1_max))
plt.ylim((x2_min, x2_max))
plt.title(u'不同方差的原始数据')
plt.grid(True)

plt.subplot(246)
plt.scatter(data2[:, 0], data2[:, 1], c=y_hat2, s=30, cmap=cm, edgecolors='none')
plt.xlim((x1_min, x1_max))
plt.ylim((x2_min, x2_max))
plt.title(u'不同方差簇数据的K-Means算法聚类结果')
plt.grid(True)

plt.subplot(247)
plt.scatter(data3[:, 0], data3[:, 1], c=y3, s=30, cmap=cm, edgecolors='none')
x1_min, x2_min = np.min(data3, axis=0)
x1_max, x2_max = np.max(data3, axis=0)
x1_min, x1_max = expandBorder(x1_min, x1_max)
x2_min, x2_max = expandBorder(x2_min, x2_max)
plt.xlim((x1_min, x1_max))
plt.ylim((x2_min, x2_max))
plt.title(u'不同簇样本数量原始数据图')
plt.grid(True)

plt.subplot(248)
plt.scatter(data3[:, 0], data3[:, 1], c=y_hat3, s=30, cmap=cm, edgecolors='none')
plt.xlim((x1_min, x1_max))
plt.ylim((x2_min, x2_max))
plt.title(u'不同簇样本数量的K-Means算法聚类结果')
plt.grid(True)

plt.tight_layout(2, rect=(0, 0, 1, 0.97))
plt.suptitle(u'数据分布对KMeans聚类的影响', fontsize=18)
plt.savefig("k-means聚类算法.png")
plt.show()

#运行结果：
所有样本距离聚簇中心点的总距离和: 2592.9990199
距离聚簇中心点的平均距离: 1.72866601327
聚簇中心点: [[ -7.44342199e+00  -2.00152176e+00]
 [  5.80338598e+00   2.75272962e-03]
 [ -6.36176159e+00   6.94997331e+00]
 [  4.34372837e+00   1.33977807e+00]]

代码中用到的知识点：

#!/usr/bin/env python
# -*- coding:utf-8 -*-
# Author:ZhengzhengLiu

#kmean与mini batch kmeans 算法的比较

import time
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import matplotlib.colors
from sklearn.cluster import KMeans,MiniBatchKMeans
from sklearn.datasets.samples_generator import make_blobs
from sklearn.metrics.pairwise import pairwise_distances_argmin

#解决中文显示问题
mpl.rcParams['font.sans-serif'] = [u'SimHei']
mpl.rcParams['axes.unicode_minus'] = False

#初始化三个中心
centers = [[1,1],[-1,-1],[1,-1]]
clusters = len(centers)     #聚类数目为3
#产生3000组二维数据样本，三个中心点，标准差是0.7
X,Y = make_blobs(n_samples=300,centers=centers,cluster_std=0.7,random_state=28)

#构建kmeans算法
k_means =  KMeans(init="k-means++",n_clusters=clusters,random_state=28)
t0 = time.time()
k_means.fit(X)      #模型训练
km_batch = time.time()-t0       #使用kmeans训练数据消耗的时间
print("K-Means算法模型训练消耗时间:%.4fs"%km_batch)

#构建mini batch kmeans算法
batch_size = 100        #采样集的大小
mbk = MiniBatchKMeans(init="k-means++",n_clusters=clusters,batch_size=batch_size,random_state=28)
t0 = time.time()
mbk.fit(X)
mbk_batch = time.time()-t0
print("Mini Batch K-Means算法模型训练消耗时间:%.4fs"%mbk_batch)

#预测结果
km_y_hat = k_means.predict(X)
mbk_y_hat = mbk.predict(X)

#获取聚类中心点并对其排序
k_means_cluster_center = k_means.cluster_centers_
mbk_cluster_center = mbk.cluster_centers_
print("K-Means算法聚类中心点:
 center=",k_means_cluster_center)
print("Mini Batch K-Means算法聚类中心点:
 center=",mbk_cluster_center)
order = pairwise_distances_argmin(k_means_cluster_center,mbk_cluster_center)

#画图
plt.figure(figsize=(12,6),facecolor="w")
plt.subplots_adjust(left=0.05,right=0.95,bottom=0.05,top=0.9)
cm = mpl.colors.ListedColormap(['#FFC2CC', '#C2FFCC', '#CCC2FF'])
cm2 = mpl.colors.ListedColormap(['#FF0000', '#00FF00', '#0000FF'])

#子图1——原始数据
plt.subplot(221)
plt.scatter(X[:,0],X[:,1],c=Y,s=6,cmap=cm,edgecolors="none")
plt.title(u"原始数据分布图")
plt.xticks(())
plt.yticks(())
plt.grid(True)

#子图2：K-Means算法聚类结果图
plt.subplot(222)
plt.scatter(X[:,0], X[:,1], c=km_y_hat, s=6, cmap=cm,edgecolors='none')
plt.scatter(k_means_cluster_center[:,0], k_means_cluster_center[:,1],c=range(clusters),s=60,cmap=cm2,edgecolors='none')
plt.title(u'K-Means算法聚类结果图')
plt.xticks(())
plt.yticks(())
plt.text(-3.8, 3,  'train time: %.2fms' % (km_batch*1000))
plt.grid(True)

#子图三Mini Batch K-Means算法聚类结果图
plt.subplot(223)
plt.scatter(X[:,0], X[:,1], c=mbk_y_hat, s=6, cmap=cm,edgecolors='none')
plt.scatter(mbk_cluster_center[:,0], mbk_cluster_center[:,1],c=range(clusters),s=60,cmap=cm2,edgecolors='none')
plt.title(u'Mini Batch K-Means算法聚类结果图')
plt.xticks(())
plt.yticks(())
plt.text(-3.8, 3,  'train time: %.2fms' % (mbk_batch*1000))
plt.grid(True)
plt.savefig("kmean与mini batch kmeans 算法的比较.png")
plt.show()

#运行结果：
K-Means算法模型训练消耗时间:0.2260s
Mini Batch K-Means算法模型训练消耗时间:0.0230s
K-Means算法聚类中心点:
 center= [[ 0.96091862  1.13741775]
 [ 1.1979318  -1.02783007]
 [-0.98673669 -1.09398768]]
Mini Batch K-Means算法聚类中心点:
 center= [[ 1.34304199 -1.01641075]
 [ 0.83760683  1.01229021]
 [-0.92702179 -1.08205992]]

五、聚类算法的衡量指标

#!/usr/bin/env python
# -*- coding:utf-8 -*-
# Author:ZhengzhengLiu

#聚类算法评估

import time
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
import matplotlib.colors
from sklearn.cluster import KMeans,MiniBatchKMeans
from sklearn import metrics
from sklearn.metrics.pairwise import pairwise_distances_argmin
from sklearn.datasets.samples_generator import make_blobs

#解决中文显示问题
mpl.rcParams['font.sans-serif'] = [u'SimHei']
mpl.rcParams['axes.unicode_minus'] = False

#初始化三个中心
centers = [[1,1],[-1,-1],[1,-1]]
clusters = len(centers)     #聚类数目为3
#产生3000组二维数据样本，三个中心点，标准差是0.7
X,Y = make_blobs(n_samples=300,centers=centers,cluster_std=0.7,random_state=28)

#构建kmeans算法
k_means =  KMeans(init="k-means++",n_clusters=clusters,random_state=28)
t0 = time.time()
k_means.fit(X)      #模型训练
km_batch = time.time()-t0       #使用kmeans训练数据消耗的时间
print("K-Means算法模型训练消耗时间:%.4fs"%km_batch)

#构建mini batch kmeans算法
batch_size = 100        #采样集的大小
mbk = MiniBatchKMeans(init="k-means++",n_clusters=clusters,batch_size=batch_size,random_state=28)
t0 = time.time()
mbk.fit(X)
mbk_batch = time.time()-t0
print("Mini Batch K-Means算法模型训练消耗时间:%.4fs"%mbk_batch)

km_y_hat = k_means.labels_
mbkm_y_hat = mbk.labels_

k_means_cluster_centers = k_means.cluster_centers_
mbk_means_cluster_centers = mbk.cluster_centers_
print ("K-Means算法聚类中心点:
center=", k_means_cluster_centers)
print ("Mini Batch K-Means算法聚类中心点:
center=", mbk_means_cluster_centers)
order = pairwise_distances_argmin(k_means_cluster_centers,
                                  mbk_means_cluster_centers)

#效果评估
### 效果评估
score_funcs = [
    metrics.adjusted_rand_score,    #ARI（调整兰德指数）
    metrics.v_measure_score,        #均一性与完整性的加权平均
    metrics.adjusted_mutual_info_score, #AMI（调整互信息）
    metrics.mutual_info_score,      #互信息
]

## 2. 迭代对每个评估函数进行评估操作
for score_func in score_funcs:
    t0 = time.time()
    km_scores = score_func(Y, km_y_hat)
    print("K-Means算法:%s评估函数计算结果值:%.5f；计算消耗时间:%0.3fs" % (score_func.__name__, km_scores, time.time() - t0))

    t0 = time.time()
    mbkm_scores = score_func(Y, mbkm_y_hat)
    print("Mini Batch K-Means算法:%s评估函数计算结果值:%.5f；计算消耗时间:%0.3fs
" % (score_func.__name__, mbkm_scores, time.time() - t0))

#运行结果：
K-Means算法模型训练消耗时间:0.6350s
Mini Batch K-Means算法模型训练消耗时间:0.0900s
K-Means算法聚类中心点:
center= [[ 0.96091862  1.13741775]
 [ 1.1979318  -1.02783007]
 [-0.98673669 -1.09398768]]
Mini Batch K-Means算法聚类中心点:
center= [[ 1.34304199 -1.01641075]
 [ 0.83760683  1.01229021]
 [-0.92702179 -1.08205992]]
K-Means算法:adjusted_rand_score评估函数计算结果值:0.72566；计算消耗时间:0.071s
Mini Batch K-Means算法:adjusted_rand_score评估函数计算结果值:0.69544；计算消耗时间:0.001s

K-Means算法:v_measure_score评估函数计算结果值:0.67529；计算消耗时间:0.004s
Mini Batch K-Means算法:v_measure_score评估函数计算结果值:0.65055；计算消耗时间:0.004s

K-Means算法:adjusted_mutual_info_score评估函数计算结果值:0.67263；计算消耗时间:0.006s
Mini Batch K-Means算法:adjusted_mutual_info_score评估函数计算结果值:0.64731；计算消耗时间:0.005s

K-Means算法:mutual_info_score评估函数计算结果值:0.74116；计算消耗时间:0.002s
Mini Batch K-Means算法:mutual_info_score评估函数计算结果值:0.71351；计算消耗时间:0.001s