用 PCA 解释 K-Means 聚类 - Python

Question

我已经在一个数据集上实现了 K-Means 聚类，其中我使用 PCA 将维度减少到了 2 个特征。

Clustering analysis plot here

现在我想知道如何解释这个分析，因为轴上的变量有任何参考。 鉴于这种疑问，我还想知道在使用 PCA 调整大小的数据集上实施 K-Means 是否是一种好习惯。

如何解释这种聚类？

谢谢！

Answer 1

代码：

import statsmodels.api as sm
import numpy as np
import pandas as pd
import statsmodels.formula.api as smf
from statsmodels.stats import anova

mtcars = sm.datasets.get_rdataset("mtcars", "datasets", cache=True).data
df = pd.DataFrame(mtcars)
model = smf.ols(formula='np.log(mpg) ~ np.log(wt)', data=mtcars).fit()
print(anova.anova_lm(model))
print(anova.anova_lm(model).F["np.log(wt)"])



import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from sklearn.cluster import KMeans
from sklearn.decomposition import PCA

df.fillna(0, inplace = True)

x = df.iloc[:,2:]

wcss = []
for i in range(1,11):
   model = KMeans(n_clusters = i, init = "k-means++")
   model.fit(x)
   wcss.append(model.inertia_)
plt.figure(figsize=(10,10))
plt.plot(range(1,11), wcss)
plt.xlabel('Number of clusters')
plt.ylabel('WCSS')
plt.show()

pca = PCA(2)
data = pca.fit_transform(x)

plt.figure(figsize=(10,10))
var = np.round(pca.explained_variance_ratio_*100, decimals = 1)
lbls = [str(x) for x in range(1,len(var)+1)]
plt.bar(x=range(1,len(var)+1), height = var, tick_label = lbls)
plt.show()


centers = np.array(model.cluster_centers_)
model = KMeans(n_clusters = 6, init = "k-means++")
label = model.fit_predict(data)
plt.figure(figsize=(10,10))
uniq = np.unique(label)
for i in uniq:
   plt.scatter(data[label == i , 0] , data[label == i , 1] , label = i)
plt.scatter(centers[:,0], centers[:,1], marker="x", color='k')
#This is done to find the centroid for each clusters.
plt.legend()
plt.show()

df['label'] = label
df

最终结果：

等等等等等等