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机器学习 —— 聚类算法

发布时间:2022/11/15 0:34:15

K均值算法(K-means)聚类

一、K-means算法原理

聚类的概念:一种无监督的学习,事先不知道类别,自动将相似的对象归到同一个簇中。

K-Means算法是一种聚类分析(cluster analysis)的算法,其主要是来计算数据聚集的算法,主要通过不断地取离种子点最近均值的算法。

K-Means算法主要解决的问题如下图所示。我们可以看到,在图的左边有一些点,我们用肉眼可以看出来有四个点群,但是我们怎么通过计算机程序找出这几个点群来呢?于是就出现了我们的K-Means算法

这个算法其实很简单,如下图所示:

从上图中,我们可以看到,A,B,C,D,E是五个在图中点。而灰色的点是我们的种子点,也就是我们用来找点群的点。有两个种子点,所以K=2。

然后,K-Means的算法如下:

  1. 随机在图中取K(这里K=2)个种子点。
  2. 然后对图中的所有点求到这K个种子点的距离,假如点Pi离种子点Si最近,那么Pi属于Si点群。(上图中,我们可以看到A,B属于上面的种子点,C,D,E属于下面中部的种子点)
  3. 接下来,我们要移动种子点到属于他的“点群”的中心。(见图上的第三步)
  4. 然后重复第2)和第3)步,直到,种子点没有移动(我们可以看到图中的第四步上面的种子点聚合了A,B,C,下面的种子点聚合了D,E)。

这个算法很简单,重点说一下“求点群中心的算法”:欧氏距离(Euclidean Distance):差的平方和的平方根

K-Means主要最重大的缺陷——都和初始值有关:

K是事先给定的,这个K值的选定是非常难以估计的。很多时候,事先并不知道给定的数据集应该分成多少个类别才最合适。(ISODATA算法通过类的自动合并和分裂,得到较为合理的类型数目K)

K-Means算法需要用初始随机种子点来搞,这个随机种子点太重要,不同的随机种子点会有得到完全不同的结果。(K-Means++算法可以用来解决这个问题,其可以有效地选择初始点)

总结:K-Means算法步骤:

  1. 从数据中选择k个对象作为初始聚类中心;
  2. 计算每个聚类对象到聚类中心的距离来划分;
  3. 再次计算每个聚类中心
  4. 计算标准测度函数,直到达到最大迭代次数,则停止,否则,继续操作。
  5. 确定最优的聚类中心

二、实战

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline

1、聚类实例

导包,使用make_blobs生成随机点

  • from sklearn.datasets import make_blobs
from sklearn.datasets import make_blobs

data,target = make_blobs()

plt.scatter(data[:,0],data[:,1],c=target)

建立模型,训练数据,并进行数据预测,使用相同数据

无监督的情况下进行计算,预测 现在机器学习没有目标

  • from sklearn.cluster import KMeans, DBSCAN
# cluster : 聚类
from sklearn.cluster import KMeans, DBSCAN

# 创建

# n_clusters=8 : 默认8个组(簇),k = 8
kmeans = KMeans(n_clusters=4)

# 训练

# 聚类算法:不需要提供 target
kmeans.fit(data)

labels_ : 每个样本点的标签

kmeans.labels_
'''
array([3, 3, 2, 0, 2, 0, 2, 2, 1, 3, 2, 3, 3, 1, 1, 2, 2, 0, 3, 3, 3, 1,
       1, 2, 1, 2, 0, 3, 1, 3, 3, 1, 2, 3, 2, 1, 1, 3, 1, 1, 1, 3, 2, 1,
       1, 1, 2, 1, 2, 2, 1, 3, 2, 2, 1, 1, 1, 3, 3, 3, 2, 1, 2, 3, 2, 1,
       3, 1, 2, 3, 1, 3, 2, 1, 1, 3, 0, 1, 2, 2, 1, 1, 0, 0, 1, 3, 2, 2,
       1, 2, 3, 3, 3, 3, 2, 3, 0, 1, 2, 2])
'''

plt.scatter(data[:,0],data[:,1],c=kmeans.labels_)

重要参数:

  • n_clusters:聚类的个数

重要属性:

  • cluster_centers_ : [n_clusters, n_features]的数组,表示聚类中心点的坐标
  • labels_ : 每个样本点的标签
# 分组的个数
kmeans.n_clusters
# 4

# 聚类中心
kmeans.cluster_centers_
'''
array([[-4.46626315, -8.14085978],
       [ 1.44224349,  4.81770399],
       [-7.01852833, -6.6710513 ],
       [-3.74353854, -6.23186778]])
'''

绘制图形中心点,显示聚类结果kmeans.cluster_centers

plt.scatter(data[:,0],data[:,1],c=kmeans.labels_)

# 话聚类中心
plt.scatter(kmeans.cluster_centers_[:,0],kmeans.cluster_centers_[:,1],c='r',s=100)

2、 实战,三问中国足球几多愁?

读取数据

football = pd.read_csv('../data/AsiaFootball.txt',header=None)
football

列名修改为:"国家","2006世界杯","2010世界杯","2007亚洲杯"

football.columns = ["国家","2006世界杯","2010世界杯","2007亚洲杯"]
football

data = football.iloc[:,1:].copy()

使用K-Means进行数据处理,对亚洲球队进行分组,分三组

kmeans = KMeans(n_clusters=3)
kmeans.fit(data)

# labels
kmeans.labels_
# array([0, 1, 1, 2, 2, 0, 0, 0, 2, 0, 0, 0, 2, 2, 0])

country = football['国家'].values
country
'''
array(['中国', '日本', '韩国', '伊朗', '沙特', '伊拉克', '卡塔尔', '阿联酋', '乌兹别克斯坦', '泰国',
       '越南', '阿曼', '巴林', '朝鲜', '印尼'], dtype=object)
'''

for循环打印输出分组后的球队

0 == kmeans.labels_
'''
array([ True, False, False, False, False,  True,  True,  True, False,
        True,  True,  True, False, False,  True])
'''

country[0 == kmeans.labels_]
'''
array(['中国', '伊拉克', '卡塔尔', '阿联酋', '泰国', '越南', '阿曼', '印尼'], dtype=object)
'''


for i in range(3):
    print(country[i == kmeans.labels_])
'''
['中国' '伊拉克' '卡塔尔' '阿联酋' '泰国' '越南' '阿曼' '印尼']
['日本' '韩国']
['伊朗' '沙特' '乌兹别克斯坦' '巴林' '朝鲜']
'''

3、K-Means图片颜色点分类

  • from sklearn.datasets import load_sample_image
  • load_sample_image()
from sklearn.datasets import load_sample_image

china = load_sample_image('china.jpg')
plt.imshow(china)

flower = load_sample_image('flower.jpg')
plt.imshow(flower)

china
'''
array([[[174, 201, 231],
        [174, 201, 231],
        [174, 201, 231],
        ...,
        [250, 251, 255],
        [250, 251, 255],
        [250, 251, 255]],

       [[172, 199, 229],
        [173, 200, 230],
        [173, 200, 230],
        ...,
        [251, 252, 255],
        [251, 252, 255],
        [251, 252, 255]],

       [[174, 201, 231],
        [174, 201, 231],
        [174, 201, 231],
        ...,
        [252, 253, 255],
        [252, 253, 255],
        [252, 253, 255]],

       ...,

       [[ 88,  80,   7],
        [147, 138,  69],
        [122, 116,  38],
        ...,
        [ 39,  42,  33],
        [  8,  14,   2],
        [  6,  12,   0]],

       [[122, 112,  41],
        [129, 120,  53],
        [118, 112,  36],
        ...,
        [  9,  12,   3],
        [  9,  15,   3],
        [ 16,  24,   9]],

       [[116, 103,  35],
        [104,  93,  31],
        [108, 102,  28],
        ...,
        [ 43,  49,  39],
        [ 13,  21,   6],
        [ 15,  24,   7]]], dtype=uint8)
'''

china.shape
# (427, 640, 3)

保留主要的颜色,使用聚类成64种

  • kmeans = KMeans(64)
  • kmeans.fit(data)
kmeans = KMeans(64)

# %time kmeans.fit(china.reshape(-1,3))
# 计算量较大,速度很慢

随机获取1000个图片中的颜色, 进行训练

data = china.reshape(-1,3)
data.shape
# (273280, 3)

# pd.DataFrame(data).sample(1000)



from sklearn.utils import shuffle

# 先打乱顺序,然后取1000个
data2= data.copy()
data3 = shuffle(data2)[:1000]
data3
'''
array([[248, 249, 254],
       [ 63,  80,  36],
       [235, 243, 254],
       ...,
       [ 15,  26,   9],
       [101, 102,  94],
       [ 94, 104,  67]], dtype=uint8)
'''

data3.shape
# (1000, 3)

 使用KMeans进行聚类

kmeans = KMeans(64)

# 训练
kmeans.fit(data3)


#labels
labels = kmeans.labels_
labels
'''
array([40, 58, 37, 10, 36, 28,  5, 55, 40, 58, 48, 38,  4, 14, 47, 14,  1,
       15, 29, 56, 49, 35, 19, 17, 14, 36, 47, 33, 49,  2, 62, 17, 40, 47,
       40, 37, 40, 17, 17, 24, 57, 10, 28, 14, 55,  0, 14, 13, 34, 35,  3,
       17, 36,  3, 58, 44, 17, 57, 35, 40, 14, 56, 17, 10, 30,  4,  6, 23,
       31,  0, 43, 30, 36, 39, 35, 11, 55, 11, 11, 37, 40, 35, 48, 19, 17,
       63, 16,  1, 47, 58,  5, 10, 36, 30, 63,  6,  0,  4, 24,  3, 41, 47,
        3,  0, 46,  8, 31, 49, 38, 37, 36, 55, 27, 57,  6, 14,  0,  5, 50,
       55,  4, 28, 23, 14, 49, 17,  5,  7, 52, 37, 24, 23, 49, 46,  9, 17,
       39, 42, 14, 58,  0,  6, 37,  7, 14, 17, 19, 51, 14, 45,  5, 55, 10,
       49,  0, 50, 13, 38, 17, 10, 49, 13, 44, 58,  6,  3, 45,  9,  0, 52,
       40, 17, 58,  0, 14, 30, 63, 57, 35, 35,  0, 41, 11, 40, 10, 22, 50,
       47, 47, 10, 17, 51, 32,  3, 37,  7, 38, 14, 63, 37, 40, 35, 40, 52,
        0, 11, 28, 17, 54, 31, 37, 52, 63, 35, 14,  5,  9, 47, 10, 11, 17,
       17,  5, 11, 49,  6,  2, 10, 46,  0, 55, 40, 10, 52, 37, 49, 14, 35,
       30, 37, 52,  4,  9,  3, 52, 48, 24,  7, 25, 56, 13, 29, 12, 48, 49,
        0, 48, 35, 35,  0, 49, 41, 44, 19,  5, 10, 20, 47, 32,  0, 41, 47,
       39, 28, 34,  5, 26, 40, 17, 28, 58, 37,  8, 19, 42, 40, 37, 24, 31,
       56, 37,  6, 42, 59, 29, 47, 37, 63, 58, 34, 37, 16, 29, 41, 17, 44,
       47, 58, 51, 17,  3,  4,  0, 10, 44, 57, 14, 36,  4, 24, 30,  5, 37,
       30, 34, 11,  8,  0, 17, 51,  7, 34, 37, 19,  6,  4, 24, 63, 50, 40,
        2,  0, 37, 26, 36, 28, 34,  2, 39, 47, 16, 26, 32, 10,  2, 40,  6,
       39,  8, 37, 17, 43, 11, 28, 41,  7, 13, 35, 38, 49, 50, 50,  4, 31,
       53, 40, 43, 39, 53,  3, 48,  0, 37, 24, 62, 55,  6,  3, 28, 55, 41,
       31, 27, 10, 46,  0, 14,  1, 40, 34,  0, 14, 20, 56, 63, 40, 11,  0,
        2,  0, 33, 55,  3, 63, 37, 49, 10, 49, 35, 32, 35,  4, 46, 30, 14,
       28, 17, 13, 37, 37, 35, 43, 13, 35, 60, 29, 60,  7, 63, 50, 10, 35,
       24, 11, 55, 55, 11, 56, 16, 42, 24, 31, 17, 11, 63, 14, 16, 37, 29,
       47, 43, 41, 35, 52, 37, 38, 58, 14, 63, 47,  3, 39,  6, 34, 41, 30,
       51, 55, 46,  3, 10,  4,  5, 63, 14,  0,  5, 47, 40,  2, 47, 58, 17,
       38, 33, 38, 34,  2, 49, 17, 37, 63, 35, 35, 63,  7, 45, 28, 60,  0,
       51, 35, 14,  5, 48, 14, 40, 47, 52, 58, 35, 57, 56, 62, 40, 17,  5,
       21,  0, 55,  1, 63, 56, 14, 28,  5, 28,  0,  2, 61, 33,  5, 38, 35,
       17,  3, 51, 14, 17,  6, 56,  9,  0, 24, 55, 40, 44,  5, 37,  0, 10,
       13,  8, 60,  5, 38, 38, 60, 28,  2,  4, 17, 40, 27, 55, 62,  7, 12,
        7,  4, 51, 11, 25, 28,  5, 41, 49,  0, 50, 28, 49,  9,  5, 30, 51,
       37,  6, 14, 51, 53,  0, 49, 14, 17, 20, 28, 63,  0, 22,  3, 10,  2,
       35,  6, 24, 55, 40, 37,  5, 14, 40,  0,  5, 40, 47, 40, 39, 17,  0,
       49, 11,  6, 33,  5, 63, 34, 31, 31, 49, 19, 41,  6, 11, 31, 37,  6,
       40, 38, 27, 37, 49, 63, 21, 30, 17, 25, 33, 17, 55, 31, 51, 34,  6,
       24, 51,  7, 18, 40, 40, 27, 28, 18, 48, 47, 28, 40,  1, 27,  0, 29,
       14, 28,  5, 11, 10, 39, 17, 47, 55, 39,  3, 48, 17,  1, 49, 22, 14,
       13, 56, 16, 29, 35, 33,  7, 34, 40, 34, 28,  0, 54, 56, 14, 37, 11,
        6,  0, 63, 63, 11, 51,  3, 14, 20, 40,  2, 38, 14, 29, 48, 28, 21,
        0, 11, 25, 19, 24, 34, 14, 40,  0, 35,  2,  6, 56, 55, 40, 11, 44,
       55, 57,  2, 14, 58, 31, 50, 10, 63, 48, 40, 52, 34, 59,  5, 48, 17,
       55, 39,  0, 10, 26, 34, 27, 47, 37, 10, 17,  5, 50, 37, 37, 49, 19,
        5, 11,  6, 37, 10, 15, 19, 53, 26, 55, 17, 17, 48, 14, 14, 47, 14,
       48, 49, 14, 11,  7, 24, 13, 63, 44, 10, 29, 41, 55, 28, 49, 31, 58,
       11, 17, 22, 29,  2, 53, 14, 58, 38, 37, 40, 49, 63, 17, 61, 18, 31,
       14, 37, 17,  6, 24, 26, 38,  5, 47, 37, 31,  3, 11, 32,  7, 51, 37,
       63, 37, 40, 43, 37, 34, 55, 39, 14, 17, 28, 22, 46, 14, 14, 37, 63,
       28,  9, 10, 14, 10, 37, 48,  0, 29, 37, 48, 53, 16, 44, 14, 55, 17,
       55, 34,  3, 40, 40, 17,  9, 17, 11,  6,  0,  4,  3, 47, 33, 10, 45,
       48, 30, 29, 56, 24,  9,  0,  0,  9, 28, 34, 37, 40,  0, 63,  6, 40,
       38, 22, 22, 34, 35, 58, 11, 48, 11, 17, 37, 11,  6, 14,  4, 35,  0,
       36, 28, 13, 37, 55, 14,  4, 50, 46,  0,  0, 49, 48, 14, 13, 37, 31,
       48, 24,  0, 63, 14, 10, 51, 31, 40, 10, 11, 20, 10, 47, 31, 47,  8,
       14, 52,  5,  4, 14, 18, 57, 63,  0, 50, 44, 47, 21, 56, 59, 54, 32,
       17, 14,  5, 45, 11, 49,  6, 48, 63, 53, 45, 28, 26, 38])
'''

# 聚类中心
centers = kmeans.cluster_centers_
centers
'''
array([[241.42      , 246.04      , 253.34      ],
       [ 66.33333333,  95.66666667,  95.        ],
       [ 49.06666667,  25.        ,  22.46666667],
       [180.7       , 191.55      , 188.2       ],
       [123.52941176, 111.64705882,  92.58823529],
       [ 47.26666667,  48.93333333,  36.6       ],
       [205.76923077, 226.88461538, 249.65384615],
       [ 84.78571429,  74.64285714,  56.64285714],
       [218.33333333, 175.33333333, 136.16666667],
       [146.8       , 156.1       , 162.3       ],
       [209.65625   , 209.34375   , 214.59375   ],
       [ 14.06451613,  13.12903226,   6.96774194],
       [218.5       , 119.5       , 106.        ],
       [107.41666667, 110.08333333,  45.75      ],
       [186.38888889, 210.09259259, 236.55555556],
       [209.        ,  95.        ,  33.5       ],
       [111.28571429,  47.28571429,  28.14285714],
       [220.40816327, 236.42857143, 252.53061224],
       [157.5       , 128.75      , 106.75      ],
       [149.5       , 142.        , 130.8       ],
       [248.6       , 169.4       , 105.8       ],
       [167.        , 154.5       ,  85.25      ],
       [ 33.        ,  68.85714286,  73.        ],
       [ 80.        ,  15.33333333,   4.66666667],
       [ 86.38888889,  86.22222222,  32.27777778],
       [237.25      , 199.75      , 172.5       ],
       [102.57142857, 104.        ,  96.14285714],
       [172.57142857, 161.71428571, 134.28571429],
       [ 23.64285714,  27.14285714,  16.28571429],
       [170.76923077, 183.46153846, 175.07692308],
       [123.25      , 126.16666667, 113.91666667],
       [ 57.77777778,  53.94444444,  48.5       ],
       [170.83333333,  97.16666667,  81.5       ],
       [119.25      ,  74.625     ,  42.75      ],
       [193.4       , 203.        , 205.35      ],
       [200.06896552, 211.51724138, 225.72413793],
       [137.66666667, 140.33333333,  81.11111111],
       [231.72      , 242.08      , 253.46      ],
       [ 99.64705882,  96.58823529,  65.64705882],
       [219.25      , 223.58333333, 225.83333333],
       [249.93181818, 250.47727273, 253.84090909],
       [ 75.08333333,  79.66666667,  73.66666667],
       [145.75      ,  59.25      ,  48.25      ],
       [193.66666667, 146.83333333, 109.33333333],
       [ 84.6       ,  40.5       ,  31.3       ],
       [198.83333333, 126.16666667,  85.66666667],
       [ 18.25      ,  46.75      ,  45.75      ],
       [ 35.67857143,  36.35714286,  26.10714286],
       [  4.66666667,   3.33333333,   1.42857143],
       [240.03571429, 239.89285714, 241.92857143],
       [152.5       , 171.58333333, 181.5       ],
       [ 65.86666667,  69.6       ,  53.66666667],
       [123.27272727, 119.54545455,  61.18181818],
       [ 50.57142857,  46.28571429,   9.28571429],
       [164.        ,  83.66666667,  57.66666667],
       [230.10714286, 232.53571429, 237.71428571],
       [ 40.42857143,  12.28571429,  11.78571429],
       [131.875     , 152.        , 139.5       ],
       [ 67.47058824,  64.94117647,  23.35294118],
       [104.        , 102.33333333,  18.66666667],
       [104.6       , 117.2       , 118.4       ],
       [165.5       , 182.5       , 100.5       ],
       [131.75      ,  87.75      ,  78.75      ],
       [194.43333333, 218.43333333, 244.86666667]])
'''


centers.shape, labels.shape
# ((64, 3), (1000,))

# 预测
y_pred = kmeans.predict(data)
y_pred.shape
# (273280,)

y_pred
# array([14, 14, 14, ...,  5, 11, 11])

上面已经对 27万个 像素值 预测出了结果,结果的范围是0~63,共64组

接下来,我们用64个聚类中心点,分布替换每一个分组的所有像素值

plt.imshow(china)

centers.shape
# (64, 3)

centers[y_pred].shape
# (273280, 3)

# 新图
new_china = centers[y_pred].reshape(427,640,3)
new_china
'''
array([[[186.38888889, 210.09259259, 236.55555556],
        [186.38888889, 210.09259259, 236.55555556],
        [186.38888889, 210.09259259, 236.55555556],
        ...,
        [249.93181818, 250.47727273, 253.84090909],
        [249.93181818, 250.47727273, 253.84090909],
        [249.93181818, 250.47727273, 253.84090909]],

       [[186.38888889, 210.09259259, 236.55555556],
        [186.38888889, 210.09259259, 236.55555556],
        [186.38888889, 210.09259259, 236.55555556],
        ...,
        [249.93181818, 250.47727273, 253.84090909],
        [249.93181818, 250.47727273, 253.84090909],
        [249.93181818, 250.47727273, 253.84090909]],

       [[186.38888889, 210.09259259, 236.55555556],
        [186.38888889, 210.09259259, 236.55555556],
        [186.38888889, 210.09259259, 236.55555556],
        ...,
        [249.93181818, 250.47727273, 253.84090909],
        [249.93181818, 250.47727273, 253.84090909],
        [249.93181818, 250.47727273, 253.84090909]],

       ...,

       [[ 86.38888889,  86.22222222,  32.27777778],
        [137.66666667, 140.33333333,  81.11111111],
        [107.41666667, 110.08333333,  45.75      ],
        ...,
        [ 35.67857143,  36.35714286,  26.10714286],
        [ 14.06451613,  13.12903226,   6.96774194],
        [  4.66666667,   3.33333333,   1.42857143]],

       [[107.41666667, 110.08333333,  45.75      ],
        [123.27272727, 119.54545455,  61.18181818],
        [107.41666667, 110.08333333,  45.75      ],
        ...,
        [ 14.06451613,  13.12903226,   6.96774194],
        [ 14.06451613,  13.12903226,   6.96774194],
        [ 23.64285714,  27.14285714,  16.28571429]],

       [[107.41666667, 110.08333333,  45.75      ],
        [104.        , 102.33333333,  18.66666667],
        [104.        , 102.33333333,  18.66666667],
        ...,
        [ 47.26666667,  48.93333333,  36.6       ],
        [ 14.06451613,  13.12903226,   6.96774194],
        [ 14.06451613,  13.12903226,   6.96774194]]])
'''

plt.imshow(new_china / 255)

DBSCAN聚类算法

导包

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline

from sklearn.cluster import KMeans, DBSCAN

生成数据make_blobs()

  • from sklearn.datasets import make_blobs
from sklearn.datasets import make_blobs

data,target = make_blobs()

plt.scatter(data[:,0],data[:,1],c=target)

使用DBSCAN

# eps:半径
# min_samples:形成组(簇)的最小样本数
dbscan = DBSCAN(eps=1,min_samples=3)

dbscan.fit(data)

# 标签,分组结果
dbscan.labels_
# -1:离群点/噪声点
'''
array([ 0,  0,  1, -1,  0,  1,  2,  2,  1,  0,  2,  1,  2,  1,  0,  1,  2,
        0,  0,  2,  0,  0,  2,  0,  2,  1,  2,  0,  0,  2,  1,  2,  2,  2,
        2,  2,  1,  2,  1,  2,  2, -1,  0,  0,  0,  1,  0,  0,  1,  0,  2,
        0,  0,  0,  2,  1, -1,  2,  1, -1,  1,  0,  0,  0,  0,  1,  2,  0,
        2,  1,  2,  2,  1,  1,  1,  0,  0,  2,  1,  2,  1,  2,  1,  1,  1,
        0,  2,  0,  1,  1,  0,  1,  2,  1,  0,  2, -1,  1,  0,  2],
      dtype=int64)
'''

plt.scatter(data[:,0],data[:,1],c=dbscan.labels_)

 

分别使用KMeans和DBSCAN算法

画圆

  • from sklearn.datasets import make_circles
  • 使用make_circles()
from sklearn.datasets import make_circles

# 画圆
data,target = make_circles(
    n_samples=300,  # 样本数
    noise=0.09,# 噪声
    factor=0.4,# 可理解为两堆点的离散程度,值小于 1
)

plt.figure(figsize=(6,6))
plt.scatter(data[:,0],data[:,1],c=target)

 

# 使用 DBSCAN
dbscan = DBSCAN(eps=0.2,min_samples=3)
dbscan.fit(data)

plt.scatter(data[:,0],data[:,1],c=dbscan.labels_)

使用KMeans 查看效果区别

kmeans = KMeans(n_clusters=2)

kmeans.fit(data)

plt.scatter(data[:,0],data[:,1],c=kmeans.labels_)

轮廓系数

聚类算法的评估指标,轮廓系数

聚类评估:轮廓系数(Silhouette Coefficient )

  • 计算样本i到同簇其他样本的平均距离ai。ai 越小,说明样本i越应该被聚类到该簇。将ai 称为样本i的簇内不相似度。
  • 计算样本i到其他某簇Cj 的所有样本的平均距离bij,称为样本i与簇Cj 的不相似度。定义为样本i的簇间不相似度:bi =min{bi1, bi2, ..., bik}
  • si接近1,则说明样本i聚类合理
  • si接近-1,则说明样本i更应该分类到另外的簇
  • 若si 近似为0,则说明样本i在两个簇的边界上。
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline

加载数据

  • beer.txt
beer = pd.read_table('../data/beer.txt',sep=' ')
beer

data = beer.iloc[:,1:].copy()

导入KMeans

  • from sklearn.cluster import KMeans, DBSCAN
from sklearn.cluster import KMeans, DBSCAN

kmeans = KMeans(n_clusters=4)
kmeans.fit(data)

kmeans.labels_
# array([0, 0, 0, 2, 0, 0, 2, 0, 1, 1, 0, 1, 0, 0, 0, 3, 0, 0, 3, 1])

计算轮廓系数

  • silhouette_samples: 每个样本的轮廓系数
    • from sklearn.metrics import silhouette_samples
  • 平均轮廓系数得分
    • from sklearn.metrics import silhouette_score
from sklearn.metrics import silhouette_samples,silhouette_score

# silhouette_samples(data,kmeans.labels_)
'''
array([0.69616375, 0.59904896, 0.22209903, 0.33228274, 0.47164962,
       0.6803127 , 0.41274592, 0.53937684, 0.73244266, 0.58828484,
       0.70434972, 0.71134265, 0.52449913, 0.63186817, 0.45253349,
       0.72050474, 0.6934216 , 0.66869429, 0.68369738, 0.64876323])
'''

silhouette_score(data,kmeans.labels_)   # 平均轮廓系数
# 0.5857040721127795

如何根据轮廓系数选择最合适的K

  • 轮廓系数越大, K值越合适
# 提供不同的 K 值,分别计算轮廓系数
score_list = []
for k in range(2,20):
    kmeans = KMeans(k)
    kmeans.fit(data)
    score = silhouette_score(data,kmeans.labels_)
#     print(k,'得分',score)
    score_list.append(score)
    
# 画图
plt.plot(range(2,20),score_list)
plt.xticks(range(2,20))
plt.grid()
plt.show()

DBSCAN使用轮廓系数

from sklearn.cluster import KMeans, DBSCAN

score_list = []

for eps in range(2,26):
    dbscan = DBSCAN(eps=eps,min_samples=2)
    dbscan.fit(data)
    
    score = silhouette_score(data,dbscan.labels_)
    score_list.append(score)
    

# 画图
plt.plot(range(2,26),score_list)
plt.xticks(range(2,26))
plt.grid()
plt.show()

# eps半径 = 18到22时轮廓系数最大

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