Cumulative Explained Variance for PCA in Python

Question

I have a simple R script for running FactoMineR's PCA on a tiny dataframe in order to find the cumulative percentage of variance explained for each variable:

library(FactoMineR)
a <- c(1, 2, 3, 4, 5)
b <- c(4, 2, 9, 23, 3)
c <- c(9, 8, 7, 6, 6)
d <- c(45, 36, 74, 35, 29)

df <- data.frame(a, b, c, d)

df_pca <- PCA(df, ncp = 4, graph=F)
print(df_pca$eig$`cumulative percentage of variance`)

Which returns:

> print(df_pca$eig$`cumulative percentage of variance`)
[1]  58.55305  84.44577  99.86661 100.00000

I'm trying to do the same in Python using scikit-learn's decomposition package as follows:

import pandas as pd
from sklearn import decomposition, linear_model

a = [1, 2, 3, 4, 5]
b = [4, 2, 9, 23, 3]
c = [9, 8, 7, 6, 6]
d = [45, 36, 74, 35, 29]

df = pd.DataFrame({'a': a,
                  'b': b,
                  'c': c, 
                  'd': d})

pca = decomposition.PCA(n_components = 4)
pca.fit(df)
transformed_pca = pca.transform(df)

# sum cumulative variance from each var
cum_explained_var = []
for i in range(0, len(pca.explained_variance_ratio_)):
    if i == 0:
        cum_explained_var.append(pca.explained_variance_ratio_[i])
    else:
        cum_explained_var.append(pca.explained_variance_ratio_[i] + 
                                 cum_explained_var[i-1])
print(cum_explained_var)

But this results in:

[0.79987089715487936, 0.99224337624509307, 0.99997254568237226, 1.0]

As you can see, both correctly add up to 100%, but it seems the contributions of each variable differ between the R and Python versions. Does anyone know where these differences are coming from or how to correctly replicate the R results in Python?

EDIT: Thanks to Vlo, I now know that the differences stem from the FactoMineR PCA function scaling the data by default. By using the sklearn preprocessing package (pca_data = preprocessing.scale(df)) to scale my data before running PCA, my results match the

summary(prcomp(df)) summary(princomp(df)) PCA(df, scale.unit = F)$eig Note the scale.unit argument. — Vlo
I'm a bit confused by what you mean with these three snippets of code. Is this for replicating the python output in R? — Nizag
Run the snippets, especially the last one. Read the documentation on the argument scale.unit in the function PCA() — Vlo
Ok I see. So the differences between the two PCA functions are due to the FactoMiner scaling the data by default so I need to look into how it's scaling the data and how to do that in python. Thanks for the help! — Nizag

Nizag Nizag · Accepted Answer · 2017-04-11T20:36:37

Thanks to Vlo, I learned that the differences between the FactoMineR PCA function and the sklearn PCA function is that the FactoMineR one scales the data by default. By simply adding a scaling function to my python code, I was able to reproduce the results.

import pandas as pd
from sklearn import decomposition, preprocessing

a = [1, 2, 3, 4, 5]
b = [4, 2, 9, 23, 3]
c = [9, 8, 7, 6, 6]
d = [45, 36, 74, 35, 29]
e = [35, 84, 3, 54, 68]


df = pd.DataFrame({'a': a,
                  'b': b,
                  'c': c, 
                  'd': d})


pca_data = preprocessing.scale(df)

pca = decomposition.PCA(n_components = 4)
pca.fit(pca_data)
transformed_pca = pca.transform(pca_data)

cum_explained_var = []
for i in range(0, len(pca.explained_variance_ratio_)):
    if i == 0:
        cum_explained_var.append(pca.explained_variance_ratio_[i])
    else:
        cum_explained_var.append(pca.explained_variance_ratio_[i] + 
                                 cum_explained_var[i-1])

print(cum_explained_var)

Output:

[0.58553054049052267, 0.8444577483783724, 0.9986661265687754, 0.99999999999999978]

Cumulative Explained Variance for PCA in Python

1 Answers