Python之聚类（KMeans,KMeans++）

 # -*- coding: utf-8 -*-
 """
 Created on Mon Sep 17 16:41:46 2018

 @author: zhen
 """

 import numpy as np
 import matplotlib.pyplot as plt
 import sklearn.datasets as ds
 import matplotlib.colors
 from sklearn.cluster import KMeans
 from sklearn.cluster import MiniBatchKMeans

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

 if __name__ == "__main__":
     N = 400
     centers = 4
     data, y = ds.make_blobs(N, n_features=2, centers=centers, random_state=2)
     data2, y2 = ds.make_blobs(N, n_features=2, centers=centers, cluster_std=(1, 2.5, 0.5, 2), random_state=2)
     # 按行拼接numpy数组
     data3 = np.vstack((data[y == 0][:], data[y == 1][:50], data[y == 2][:20], data[y == 3][:5]))
     y3 = np.array([0] * 100 + [1] * 50 + [2] * 20 + [3] * 5)
     cls = KMeans(n_clusters=4, init='k-means++')
     y_hat = cls.fit_predict(data)
     y2_hat = cls.fit_predict(data2)
     y3_hat = cls.fit_predict(data3)

     m = np.array(((1, 1),(1, 3)))
     data_r = data.dot(m)
     y_r_hat = cls.fit_predict(data_r)

     matplotlib.rcParams['font.sans-serif'] = [u'SimHei']
     matplotlib.rcParams['axes.unicode_minus'] = False
     cm = matplotlib.colors.ListedColormap(list('rgbm'))
     plt.figure(figsize=(9, 10), facecolor='w')
     plt.subplot(421)
     plt.title(u'原始数据')
     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 = expand(x1_min, x1_max)
     x2_min, x2_max = expand(x2_min, x2_max)
     plt.xlim((x1_min, x1_max))
     plt.ylim((x2_min, x2_max))
     plt.grid(True)

     plt.subplot(422)
     plt.title(u'KMeans++聚类')
     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.grid(True)

     plt.subplot(423)
     plt.title(u'旋转后数据')
     plt.scatter(data[:, 0], data[:, 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 = expand(x1_min, x1_max)
     #x2_min, x2_max = expand(x2_min, x2_max)
     plt.ylim((x1_min, x1_max))
     plt.xlim((x2_min, x2_max))
     plt.grid(True)

     plt.subplot(424)
     plt.title(u'旋转后KMeans++聚类')
     plt.scatter(data[:, 0], data[:, 1], c=y_hat, s=30, cmap=cm, edgecolors='none')
     plt.ylim((x1_min, x1_max))
     plt.xlim((x2_min, x2_max))
     plt.grid(True)

     plt.subplot(425)
     plt.title(u'方差不相等数据')
     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 = expand(x1_min, x1_max)
     #x2_min, x2_max = expand(x2_min, x2_max)
     plt.xlim((x1_min, x1_max))
     plt.ylim((x2_min, x2_max))
     plt.grid(True)    

     plt.subplot(426)
     plt.title(u'方差不相等KMeans++聚类')
     plt.scatter(data2[:, 0], data2[:, 1], c=y2_hat, s=30, cmap=cm, edgecolors='none')
     plt.xlim((x1_min, x1_max))
     plt.ylim((x2_min, x2_max))
     plt.grid(True)

     plt.subplot(427)
     plt.title(u'数量不相等数据')
     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 = expand(x1_min, x1_max)
     #x2_min, x2_max = expand(x2_min, x2_max)
     plt.xlim((x1_min, x1_max))
     plt.ylim((x2_min, x2_max))
     plt.grid(True)  

     plt.subplot(428)
     plt.title(u'数量不相等KMeans++聚类')
     plt.scatter(data3[:, 0], data3[:, 1], c=y3_hat, s=30, cmap=cm, edgecolors='none')
     plt.xlim((x1_min, x1_max))
     plt.ylim((x2_min, x2_max))
     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.show()
     

结果：

总结：可知不同的超参数对聚类的效果影响很大，因此在聚类之前采样的数据要尽量保持均匀，各类的方差最好先进行预研，以便达到较好的聚类效果！