sklearn 上的 PCA - 如何解释 pca.components_ [英] PCA on sklearn - how to interpret pca.components_
问题描述
我使用这个简单的代码在具有 10 个特征的数据帧上运行 PCA:
pca = PCA()适合 = pca.fit(dfPca)pca.explained_variance_ratio_ 的结果显示:
array([ 5.01173322e-01, 2.98421951e-01, 1.00968655e-01,4.28813755e-02、2.46887288e-02、1.40976609e-02、1.24905823e-02、3.43255532e-03、1.84516942e-03、4.50314168e-16])我相信这意味着第一个 PC 解释了 52% 的方差，第二个分量解释了 29% 等等......
我不明白的是 pca.components_ 的输出.如果我执行以下操作:
df = pd.DataFrame(pca.components_, columns=list(dfPca.columns))我得到了下面的数据框，其中每一行都是一个主成分.我想了解的是如何解释该表.我知道如果我对每个组件上的所有特征进行平方并将它们相加，我会得到 1，但是 PC1 上的 -0.56 是什么意思?它是否说明了特征 E"，因为它是解释 52% 方差的分量的最高幅度?
谢谢
术语: 首先，PCA 的结果通常根据组件分数进行讨论，有时也称为因子分数(对应于特定数据点的转换变量值)和载荷(每个标准化原始变量应乘以得到分量分数的权重).
PART1:我解释了如何检查特征的重要性以及如何绘制双标图.
PART2:我解释了如何检查特征的重要性以及如何使用特征名称将它们保存到 Pandas 数据框中.
文章总结:Python 精简指南:
第 2 部分:
重要的特征是那些对组件影响较大的特征，因此对组件具有很大的绝对值.
要获取带有名称的 PC 上最重要的功能，并将它们保存到 pandas 数据框中，请使用以下方法:
from sklearn.decomposition import PCA将熊猫导入为 pd将 numpy 导入为 npnp.random.seed(0)# 10 个具有 5 个特征的样本train_features = np.random.rand(10,5)模型 = PCA(n_components=2).fit(train_features)X_pc = model.transform(train_features)# 组件数量n_pcs=model.components_.shape[0]# 获取每个组件上最重要特征的索引# 在这里列出理解most_important = [np.abs(model.components_[i]).argmax() for i in range(n_pcs)]initial_feature_names = ['a','b','c','d','e']# 获取名称most_important_names = [initial_feature_names[most_important[i]] for i in range(n_pcs)]# 再次列出理解dic = {'PC{}'.format(i): most_important_names[i] for i in range(n_pcs)}# 构建数据框df = pd.DataFrame(dic.items())打印:
<代码> 0 10 PC0 e1 台电脑1 天
所以在 PC1 上名为 e 的特性是最重要的，而在 PC2 上名为 d.
I ran PCA on a data frame with 10 features using this simple code:
pca = PCA()
fit = pca.fit(dfPca)
The result of pca.explained_variance_ratio_ shows:
array([ 5.01173322e-01, 2.98421951e-01, 1.00968655e-01,
4.28813755e-02, 2.46887288e-02, 1.40976609e-02,
1.24905823e-02, 3.43255532e-03, 1.84516942e-03,
4.50314168e-16])
I believe that means that the first PC explains 52% of the variance, the second component explains 29% and so on...
What I dont undestand is the output of pca.components_. If I do the following:
df = pd.DataFrame(pca.components_, columns=list(dfPca.columns))
I get the data frame bellow where each line is a principal component. What I'd like to understand is how to interpret that table. I know that if I square all the features on each component and sum them I get 1, but what does the -0.56 on PC1 mean? Dos it tell something about "Feature E" since it is the highest magnitude on a component that explains 52% of the variance?
Thanks
Terminology: First of all, the results of a PCA are usually discussed in terms of component scores, sometimes called factor scores (the transformed variable values corresponding to a particular data point), and loadings (the weight by which each standardized original variable should be multiplied to get the component score).
PART1: I explain how to check the importance of the features and how to plot a biplot.
PART2: I explain how to check the importance of the features and how to save them into a pandas dataframe using the feature names.
Summary in an article: Python compact guide: https://towardsdatascience.com/pca-clearly-explained-how-when-why-to-use-it-and-feature-importance-a-guide-in-python-7c274582c37e?source=friends_link&sk=65bf5440e444c24aff192fedf9f8b64f
PART 1:
In your case, the value -0.56 for Feature E is the score of this feature on the PC1. This value tells us 'how much' the feature influences the PC (in our case the PC1).
So the higher the value in absolute value, the higher the influence on the principal component.
After performing the PCA analysis, people usually plot the known 'biplot' to see the transformed features in the N dimensions (2 in our case) and the original variables (features).
I wrote a function to plot this.
Example using iris data:
import numpy as np
import matplotlib.pyplot as plt
from sklearn import datasets
import pandas as pd
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
iris = datasets.load_iris()
X = iris.data
y = iris.target
#In general it is a good idea to scale the data
scaler = StandardScaler()
scaler.fit(X)
X=scaler.transform(X)
pca = PCA()
pca.fit(X,y)
x_new = pca.transform(X)
def myplot(score,coeff,labels=None):
xs = score[:,0]
ys = score[:,1]
n = coeff.shape[0]
plt.scatter(xs ,ys, c = y) #without scaling
for i in range(n):
plt.arrow(0, 0, coeff[i,0], coeff[i,1],color = 'r',alpha = 0.5)
if labels is None:
plt.text(coeff[i,0]* 1.15, coeff[i,1] * 1.15, "Var"+str(i+1), color = 'g', ha = 'center', va = 'center')
else:
plt.text(coeff[i,0]* 1.15, coeff[i,1] * 1.15, labels[i], color = 'g', ha = 'center', va = 'center')
plt.xlabel("PC{}".format(1))
plt.ylabel("PC{}".format(2))
plt.grid()
#Call the function.
myplot(x_new[:,0:2], pca. components_)
plt.show()
Results
PART 2:
The important features are the ones that influence more the components and thus, have a large absolute value on the component.
TO get the most important features on the PCs with names and save them into a pandas dataframe use this:
from sklearn.decomposition import PCA
import pandas as pd
import numpy as np
np.random.seed(0)
# 10 samples with 5 features
train_features = np.random.rand(10,5)
model = PCA(n_components=2).fit(train_features)
X_pc = model.transform(train_features)
# number of components
n_pcs= model.components_.shape[0]
# get the index of the most important feature on EACH component
# LIST COMPREHENSION HERE
most_important = [np.abs(model.components_[i]).argmax() for i in range(n_pcs)]
initial_feature_names = ['a','b','c','d','e']
# get the names
most_important_names = [initial_feature_names[most_important[i]] for i in range(n_pcs)]
# LIST COMPREHENSION HERE AGAIN
dic = {'PC{}'.format(i): most_important_names[i] for i in range(n_pcs)}
# build the dataframe
df = pd.DataFrame(dic.items())
This prints:
0 1
0 PC0 e
1 PC1 d
So on the PC1 the feature named e is the most important and on PC2 the d.
Summary in an article: Python compact guide: https://towardsdatascience.com/pca-clearly-explained-how-when-why-to-use-it-and-feature-importance-a-guide-in-python-7c274582c37e?source=friends_link&sk=65bf5440e444c24aff192fedf9f8b64f
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