Mean of data scaled with sklearn StandardScaler is not zero

Question

I have the following code

import pandas as pd
from sklearn.preprocessing import StandardScaler
import numpy as np

df.columns=['sepal_len', 'sepal_wid', 'petal_len', 'petal_wid', 'class']
df.dropna(how="all", inplace=True) # drops the empty line at file-end 

X = df.ix[:,0:4].values
y = df.ix[:,4].values

Next I am scaling the data and get the mean values:

X_std = StandardScaler().fit_transform(X)
mean_vec = np.mean(X_std, axis=0)

What I do not get is that my output is this:

[ -4.73695157e-16  -6.63173220e-16   3.31586610e-16  -2.84217094e-16]

I do understand how these values can be anything other than 0. If I scale it, it should be 0 zero right?

Could anyone explain to me what happens here?

Answer 1

In practice those values are so close to 0 that you can consider them to be 0.

The scaler tries to set the mean to be zero, but due to limitations with numerical representation it can only get the mean really close to 0.

Check this question on the precision of floating point arithmetics.

Also interesting is the concept of Machine Epsilon and that for a float 64 is something like 2.22e-16