目录
一、数据探索
1.数据来源
http://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/
2.数据描述
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1
ID
ID 号
2
Diagnosis
诊断
3
radius
半径
4
texture
纹理
5
perimete
周长
6
area
面积
7
细胞一
smoothness
平滑度
8
compactness
紧密度
9
concavity
凹度
10
concave points
凹点
11
symmetry
对称性
12
fractal dimension
分形维数
13
radius
半径
14
texture
纹理
15
perimete
周长
16
area
面积
17
细胞二
smoothness
平滑度
18
compactness
紧密度
19
concavity
凹度
20
concave points
凹点
21
symmetry
对称性
22
fractal dimension
分形维数
23
radius
半径
24
texture
纹理
25
perimete
周长
26
area
面积
27
细胞三
smoothness
平滑度
28
compactness
紧密度
29
concavity
凹度
30
concave points
凹点
31
symmetry
对称性
32
fractal dimension
分形维数
3.查看数据
查看数据以及查看数据
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4.数据描述性分析
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5.研究各特征相互关系
将数据集中三个细胞的十个特征值分为三个数据集data1，data2，data3，分别研究三个子数据集的各个特征值相互关系
特征矩阵
Data1特征矩阵：
Data2特征矩阵：
Data3特征矩阵：
特征相关系数图
总特征相关系数图
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Data1数据集中各个数据特征值相关系数图
Data1数据集中半径与周长、面积是大于0.90严格相关的，凹度凹点以及紧密度也是相关系数大于0.70的相关。
Data2数据集中各个数据特征值相关系数图
Data2数据集中半径与周长、面积是大于0.90严格相关的，凹度凹点以及紧密度也是相关系数大于0.70的相关。
Data3数据集中各个数据特征值相关系数图
Data3数据集中半径与周长、面积是大于0.90的严格相关的，凹度凹点以及紧密度也是相关系数大于0.70的相关。
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二、数据预处理
1.处理缺失值
a)查看缺失值
b）缺失值处理
由于缺失值仅有13条，因此删除对应缺失值所在行不会大幅度影响结果聚类，因此在本次实验中采取删除缺失值所在行的缺失值处理方法
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c）查看处理后的结果
用查看缺失值的方式查看
2.查看异常值
查看异常值
尝试着查看数据集data_new的异常值，由于总属性种类过多，对分析结果造成较大影响，因此还是将数据依照三个细胞分为三个子数据集查看异常值
Data1异常值查看
异常值结果如下图所示
Data2异常值查看
异常值结果如下图所示
Data3异常值查看
异常值结果如下图所示
3.处理相关值
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结果如下图所示
将处理好的data_new数据依次分给子数据集
聚类时时，由于ID与判断是否得病两列会影响聚类，因此把两列特征值删去
三、数据分析（聚类）
1.k-means
a）k值评估
数据集评估
肘部法则
人工选择k值存在偶然性以及误差，因此查阅资料可知，通过肘部发展迭代K值最终在快速下降趋于平缓下降的转折点选择出聚类的最好情况。
（kmeans聚类分析——Python实现_thisissally的博客-CSDN博客）
由图可以看出在2 ，3 类都有可能成为聚类情况，因此再对2 ，3 类用系数评估
当k=2时聚类
显示中心点
当k=3时
查看中心点
b)查看聚类效果
聚类效果好坏的判断有三种方式，本实验选用Calinski-Harabasz(CH)方式判定聚类效果。
K=2
K=3
输出聚类结果
c)聚类可视化
可视化三维图时data_new1特征值数据的横向分布不利于绘图，因此将分散的属性值结合为一个，因此转换为data_new2数据做聚类可视化分析。
2.k-medoids
a)k-中点聚类
直接使用data_new2数据框进行k-中点聚类
下载pyclust库，使用pyclust库下的k-Medoids板块
聚类结果如下，
b)聚类可视化
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3.层次聚类
a）层次聚类
先进行sklearn的层次聚类
聚类结果如下
b)聚类可视化
结果如下
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4.SOM
a)聚类准备
下载Minisom库
开始聚类
查看聚类结果
b)聚类可视化
热力图：
散点图
综上分为三类
合并最终聚类结果
四、实验结果对比
在各种聚类方式中，k-medoids需要进行大量的机器运算，结果出来的也十分缓慢，在实际研究中不建议采用，尤其当实验数据较大时，严重耽误时间导致效率过低，在运行集中聚类方式时，更建议采用k-means算法，该算法较为完善且在网络上有大量参考文献与资料，可视化也是多种多样的，其次就是SOM算法，运行速度较快，结果较清晰明显。
层次聚类分析与k-medoids在实验中的运行速度以及运行效果并没有另外两种好。
五、参考资料
k-means
- k-means+python︱scikit-learn中的KMeans聚类实现( + MiniBatchKMeans) – 知识天地 – 博客园
- kmeans聚类分析——Python实现_thisissally的博客-CSDN博客
k-medoids
层次聚类
- （数据科学学习手札13）K-medoids聚类算法原理简介&Python与R的实现 – 费弗里 – 博客园
- 【Python-ML】SKlearn库层次聚类凝聚AgglomerativeClustering模型_医疗影像检索-CSDN博客_python sklearn 层次聚类
- 机器学习之层次聚类（hierarchical clustering）_Cherish0719的博客-CSDN博客_机器学习层次聚类
- 聚类热图分类注释_Python可视化matplotlib&seborn15-聚类热图clustermap（建议收藏）…_伥鬼的博客-CSDN博客
som
- https://github.com/JustGlowing/minisom
- 自组织神经网络（SOM）的Python第三方库minisom聚类功能实现_应无所住而生其心-CSDN博客_minisom python
- SOM(自组织映射神经网络)——案例篇 – 知乎
六、源码
导入相关包
import numpy as np
import pandas as pd
from numpy import nan
%matplotlib inline
import matplotlib.pyplot as plt
plt.style.use(‘seaborn’)
import seaborn as sns
sns.set_style(“whitegrid”)
k-means
from sklearn.cluster import KMeans
from sklearn import metrics
from mpl_toolkits.mplot3d import Axes3D
plt.rcParams[‘font.sans-serif’]=[‘SimHei’] #用来正常显示中文标签
plt.rcParams[‘axes.unicode_minus’]=False #用来正常显示负号
k-medoid
from matplotlib import pyplot
from pyclust import KMedoids
from sklearn.manifold import TSNE
层次聚类
from scipy.spatial.distance import pdist,squareform
from scipy.cluster.hierarchy import linkage
from scipy.cluster.hierarchy import dendrogram
from sklearn.cluster import AgglomerativeClustering
plt.rcParams[‘font.sans-serif’]=[‘SimHei’] #用来正常显示中文标签
plt.rcParams[‘axes.unicode_minus’]=False #用来正常显示负号
SOM
from sklearn.model_selection import train_test_split
from minisom import MiniSom
import math
导入数据集
查看数据
data = pd.read_csv(‘D:\数据挖掘\实验二\wdbc.csv’)
data.info()
print(data.describe())
%matplotlib inline
import matplotlib.pyplot as plt
plt.style.use(‘seaborn’)
import seaborn as sns
sns.set_style(“whitegrid”)
数据探索
l1 = [‘ radius’,’texture’,’perimeter’,’area’,’smoothness’,’compactness’,’concavity’,’concave points’,’symmetry’,’fractal dimension’]
l2 = [‘ radius.1′,’texture.1′,’perimeter.1′,’area.1′,’smoothness.1′,’compactness.1′,’concavity.1′,’concave points.1′,’symmetry.1′,’fractal dimension.1’]
l3 = [‘ radius.2′,’texture.2′,’perimeter.2′,’area.2′,’smoothness.2′,’compactness.2′,’concavity.2′,’concave points.2′,’symmetry.2′,’fractal dimension.2’]
data1 = data[[‘ID’,’diagnosis’,’ radius’,’texture’,’perimeter’,’area’,’smoothness’,’compactness’,’concavity’,’concave points’,’symmetry’,’fractal dimension’]]
data2 = data[[‘ID’,’diagnosis’,’ radius.1′,’texture.1′,’perimeter.1′,’area.1′,’smoothness.1′,’compactness.1′,’concavity.1′,’concave points.1′,’symmetry.1′,’fractal dimension.1′]]
data3 = data[[‘ID’,’diagnosis’,’ radius.2′,’texture.2′,’perimeter.2′,’area.2′,’smoothness.2′,’compactness.2′,’concavity.2′,’concave points.2′,’symmetry.2′,’fractal dimension.2′]]
各特征值与结果的关系
设置颜色主题
antV = [‘#1890FF’, ‘#2FC25B’, ‘#FACC14’, ‘#223273’, ‘#8543E0’, ‘#13C2C2’, ‘#3436c7’, ‘#F04864’]
生成各特征之间的关系矩阵图
g = sns.pairplot(data=data1, palette=antV)
f = sns.pairplot(data=data2, palette=antV)
k = sns.pairplot(data=data3, palette=antV)
查看特征间的相关性
总特征相关系数图
pearson_mat = data.corr(method=’spearman’)
plt.figure(figsize=(15,15))
ax = sns.heatmap(pearson_mat,square=True,annot=True,cmap=’YlGnBu’)
bottom, top = ax.get_ylim()
ax.set_ylim(bottom + 0.5, top – 0.5)
plt.show()
data1
pearson_mat = data1.corr(method=’spearman’)
plt.figure(figsize=(15,15))
ax = sns.heatmap(pearson_mat,square=True,annot=True,cmap=’Purples’)
bottom, top = ax.get_ylim()
ax.set_ylim(bottom + 0.5, top – 0.5)
plt.show()
data2
pearson_mat = data2.corr(method=’spearman’)
plt.figure(figsize=(15,15))
ax = sns.heatmap(pearson_mat,square=True,annot=True,cmap=’OrRd’)
bottom, top = ax.get_ylim()
ax.set_ylim(bottom + 0.5, top – 0.5)
plt.show()
data3
pearson_mat = data3.corr(method=’spearman’)
plt.figure(figsize=(15,15))
ax = sns.heatmap(pearson_mat,square=True,annot=True,cmap=’Greens’)
bottom, top = ax.get_ylim()
ax.set_ylim(bottom + 0.5, top – 0.5)
plt.show()
数据预处理
缺失值处理
按列统计零的值
num_missing = (data == 0).astype(int).sum(axis=0)
输出结果
print(num_missing)
标记缺失值
data = data.replace(0, nan)
处理缺失值少的特征值删除这两列中缺失值对应的行数
data_new = data.dropna(axis=0,subset = [“concavity”, “concave points”])
num_missing_new = (data_new == 0).astype(int).sum(axis=0)
print(num_missing_new)
查看异常值
data1
numeric_columns = []
object_columns = []
for c in data1.columns[0:-1]:
if data1[c].dtype == ‘object’:
object_columns.append(c)
else:
numeric_columns.append(c)
fig = plt.figure(figsize=(20,20))
for i,col in enumerate(numeric_columns):
ax = fig.add_subplot(5,3,i+1)
sns.boxplot(data1[col],orient=’v’,ax=ax)
plt.xlabel(col)
plt.show()
data2
numeric_columns = []
object_columns = []
for c in data2.columns[0:-1]:
if data2[c].dtype == ‘object’:
object_columns.append(c)
else:
numeric_columns.append(c)
fig = plt.figure(figsize=(20,20))
for i,col in enumerate(numeric_columns):
ax = fig.add_subplot(5,3,i+1)
sns.boxplot(data2[col],orient=’v’,ax=ax)
plt.xlabel(col)
plt.show()
data3
numeric_columns = []
object_columns = []
for c in data3.columns[0:-1]:
if data3[c].dtype == ‘object’:
object_columns.append(c)
else:
numeric_columns.append(c)
fig = plt.figure(figsize=(20,20))
for i,col in enumerate(numeric_columns):
ax = fig.add_subplot(5,3,i+1)
sns.boxplot(data3[col],orient=’v’,ax=ax)
plt.xlabel(col)
plt.show()
处理相关值
删除特征值
data_new0 = data_new.drop([‘ radius’,’area’,’compactness’,’concave points’,’ radius.1′,’area.1′,’compactness.1′,’concave points.1′,’ radius.2′,’area.2′,’compactness.2′,’concave points.2′],axis=1,inplace=True)
data1 = data[[‘ID’,’diagnosis’,’texture’,’perimeter’,’smoothness’,’concavity’,’symmetry’,’fractal dimension’]]
data2 = data[[‘ID’,’diagnosis’,’texture.1′,’perimeter.1′,’smoothness.1′,’concavity.1′,’symmetry.1′,’fractal dimension.1′]]
data3 = data[[‘ID’,’diagnosis’,’texture.2′,’perimeter.2′,’smoothness.2′,’concavity.2′,’symmetry.2′,’fractal dimension.2′]]
k-means
将ID,diagnosis两列与数据类型不合的特征值删去
可视化
data_new1 = data_new.drop([‘ID’,’diagnosis’],axis=1)
将处理好的数据写入data_new2，所有聚类都使用data_new2数据集
data_new2 = pd.read_csv(‘D:\数据挖掘\实验二\data_new2.csv’)
寻找合适的K值
sse = []
for i in range(1,11): # 循环使用不同k测试结果
kmeans = KMeans(n_clusters = i, init = ‘k-means++’, random_state = 42)
kmeans.fit(data_new2)
sse.append(kmeans.inertia_) # kmeans.inertia_是每类数据到其中心点的距离之和。值越小，聚类越好。类别越多，k越大，值越小。
plt.plot(range(1,11), sse)
plt.title(‘The Elbow Method’)
plt.xlabel(‘Number of clusters’)
plt.ylabel(‘SSE’)
plt.show()
k值设为2
estimator = KMeans(n_clusters=2)#构造聚类器
estimator.fit(data_new2)#聚类
y = estimator.fit_predict(data_new2)
label_pred = estimator.labels_ #获取聚类标签
centroids = estimator.cluster_centers_ #获取聚类中心
inertia = estimator.inertia_ # 获取聚类准则的总和
查看聚类效果
metrics.calinski_harabasz_score(data_new2,y)
k值设为3
estimator = KMeans(n_clusters=3)#构造聚类器
estimator.fit(data_new2)#聚类
y = estimator.fit_predict(data_new2)
label_pred = estimator.labels_ #获取聚类标签
centroids = estimator.cluster_centers_ #获取聚类中心
inertia = estimator.inertia_ # 获取聚类准则的总和
metrics.calinski_harabasz_score(data_new2,y)
结果
输出原数据及类别
e=pd.concat([data_new2,pd.Series(label_pred,index=data_new2.index)],axis=1)
e.columns=list(data_new2.columns)+[‘result’]
可视化
雷达图
”’
未完成
labers = estimator.labels_.tolist()
newdata = pd.DataFrame(labers,index = [labers])
columns = [‘rank’, ‘title’, ‘cluster’, ‘genre’]
newdata [0].value_counts()
”’
3D图
labels = estimator.labels_
fig = plt.figure(1, figsize=(10, 10))
ax = Axes3D(fig, rect=[0, 0, .95, 1], elev=48, azim=134)
ax.scatter(data_new2.values[:, 1], data_new2.values[:, 0],data_new2.values[:, 3], c= labels.astype(np.float))
ax.w_xaxis.set_ticklabels([])
ax.w_yaxis.set_ticklabels([])
ax.w_zaxis.set_ticklabels([])
ax.set_xlabel(‘凹度’)
ax.set_ylabel(‘平滑度’)
ax.set_zlabel(‘纹理’)
ax.set_title(“3类”)
ax.dist = 12
plt.show()
k- medoids聚类
准备可视化需要的降维数据
data_TSNE = TSNE(learning_rate=10).fit_transform(data_new2)
data_TSNE
对不同的k进行试探性K-medoids聚类并可视化
data_new2 = pd.read_csv(‘D:\数据挖掘\实验二\data_new2.csv’)
plt.figure(figsize=(12,8))
for i in range(2,6):
k = KMedoids(n_clusters=i,distance=’euclidean’,max_iter=1000).fit_predict(data_new2.values)
colors = ([[‘red’,’blue’,’black’,’yellow’,’green’][i] for i in k])
plt.subplot(219+i)
plt.scatter(data_TSNE[:,0],data_TSNE[:,1],c=colors,s=10)
plt.title(‘K-medoids Resul of ‘.format(str(i)))
结果
输出原数据及类别
k = KMedoids(n_clusters=3,distance=’euclidean’,max_iter=1000).fit_predict(data_new2.values)
i=pd.concat([data_new2,pd.Series(k,index=data_new2.index)],axis=1)
i.columns=list(data_new2.columns)+[‘result’]
i
层次聚类
标准化
data_new2 = pd.read_csv(‘D:\数据挖掘\实验二\data_new2.csv’)
a=round(
(data_new2-data_new2.min())/(data_new2.min()),
3)
k=3
model=AgglomerativeClustering(n_clusters=k,linkage=’ward’)
model.fit(a)
结果
输出原数据及类别
r=pd.concat([data_new2,pd.Series(model.labels_,index=data_new2.index)],axis=1)
r.columns=list(data_new2.columns)+[‘result’]
聚类可视化
plt.figure(figsize=(20,6))
Z = linkage(a, method=’ward’, metric=’euclidean’)
p = dendrogram(Z)
plt.show()
”’
未完成
style=[‘ro-‘,’go-‘,’bo-‘]
xlabels= [‘texture’,’perimeter’,’smoothness’,’concavity’,’symmetry’,’fractal dimension’]
for i in range(k): #注意作图、做出不同样式
plt.figure()
tmp=r[r[u’result’]==i].iloc[:,:4] # 提取每一类
for j in range(len(tmp)):
plt.plot(range(1,5),tmp.iloc[j],style[i])
plt.xticks(range(1,5),xlabels,rotation=20) #坐标标签
plt.subplots_adjust(bottom=0.15) # 调整底部
”’
SOM
data = data_new2 = pd.read_csv(‘D:\数据挖掘\实验二\data_new2.csv’)
数据规范化
data = (data – np.mean(data, axis=0)) / np.std(data, axis=0)
data = data.values
初始化和训练
som_shape = (1, 3)
som = MiniSom(som_shape[0], som_shape[1], data.shape[1], sigma=.5, learning_rate=.5,
neighborhood_function=’gaussian’, random_seed=10)
som.train_batch(data, 500, verbose=True)
每个神经元代表一个簇
winner_coordinates = np.array([som.winner(x) for x in data]).T
利用np.ravel_多重指数，我们将二维
一维索引的坐标
cluster_index = np.ravel_multi_index(winner_coordinates, som_shape)
结果
输出原数据及类别
o=pd.concat([data_new2,pd.Series(cluster_index,index=data_new2.index)],axis=1)
o.columns=list(data_new2.columns)+[‘result’]
o
使用data的前2个维度对簇进行一维索引绘制的坐标
for c in np.unique(cluster_index):
plt.scatter(data[cluster_index == c, 0],
data[cluster_index == c, 1], label=’cluster=’+str(c), alpha=.7)
绘制中心点
for centroid in som.get_weights():
plt.scatter(centroid[:, 0], centroid[:, 1], marker=’x’,
s=30, linewidths=35, color=’k’, label=’centroid’)
plt.legend()
Original: https://blog.csdn.net/weixin_46490924/article/details/122520267
Author: 平平无奇秃头小天才
Title: 数据挖掘-实战记录（二）乳腺癌数据聚类实验及其分析报告
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