python - Recovering features names of explained_variance_ratio_ in PCA with sklearn

Question

I'm trying to recover from a PCA done with scikit-learn, which features are selected as relevant.

A classic example with IRIS dataset.

import pandas as pd
import pylab as pl
from sklearn import datasets
from sklearn.decomposition import PCA

# load dataset
iris = datasets.load_iris()
df = pd.DataFrame(iris.data, columns=iris.feature_names)

# normalize data
df_norm = (df - df.mean()) / df.std()

# PCA
pca = PCA(n_components=2)
pca.fit_transform(df_norm.values)
print pca.explained_variance_ratio_

This returns

In [42]: pca.explained_variance_ratio_
Out[42]: array([ 0.72770452,  0.23030523])

How can I recover which two features allow these two explained variance among the dataset ? Said diferently, how can i get the index of this features in iris.feature_names ?

In [47]: print iris.feature_names
['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)', 'petal width (cm)']

Thanks in advance for your help.

Answer 1

This information is included in the pca attribute: components_. As described in the documentation, pca.components_ outputs an array of [n_components, n_features], so to get how components are linearly related with the different features you have to:

Note: each coefficient represents the correlation between a particular pair of component and feature

import pandas as pd
import pylab as pl
from sklearn import datasets
from sklearn.decomposition import PCA

# load dataset
iris = datasets.load_iris()
df = pd.DataFrame(iris.data, columns=iris.feature_names)

# normalize data
from sklearn import preprocessing
data_scaled = pd.DataFrame(preprocessing.scale(df),columns = df.columns) 

# PCA
pca = PCA(n_components=2)
pca.fit_transform(data_scaled)

# Dump components relations with features:
print(pd.DataFrame(pca.components_,columns=data_scaled.columns,index = ['PC-1','PC-2']))

      sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)
PC-1           0.522372         -0.263355           0.581254          0.565611
PC-2          -0.372318         -0.925556          -0.021095         -0.065416

IMPORTANT: As a side comment, note the PCA sign does not affect its interpretation since the sign does not affect the variance contained in each component. Only the relative signs of features forming the PCA dimension are important. In fact, if you run the PCA code again, you might get the PCA dimensions with the signs inverted. For an intuition about this, think about a vector and its negative in 3-D space - both are essentially representing the same direction in space. Check this post for further reference.