inverse_transform in KernelPCA does not account for the mean

[lrjball]

Describe the bug

KernelPCA.inverse_transform gives back a zero-meaned dataset, even if the data used to fit the PCA did not have zero mean.

Steps/Code to Reproduce

Example:

from sklearn.datasets import make_blobs
from sklearn.decomposition import KernelPCA

X, _ = make_blobs(n_samples=100, centers=[[1, 1]], random_state=0)

kp = KernelPCA(n_components=2, fit_inverse_transform=True)
X_trans = kp.fit_transform(X)
X_inv = kp.inverse_transform(X_trans)

print(X.mean(axis=0))
print(X_inv.mean(axis=0))

Expected Results

[0.99904232 1.14277867]
[0.99904232 1.14277867]

The mean of the data after transforming and then inverse transforming should be the same, or at least very similar (maybe there are rounding errors etc.) to the mean of the original dataset.

Actual Results

[0.99904232 1.14277867]
[-5.07371922e-16  2.21767049e-16]

(The inverse transformed data still has zero mean)

Versions

System:
python: 3.6.8 (default, Oct 7 2019, 12:59:55) [GCC 8.3.0]
executable: /home//.virtualenvs/kernelpca_issue/bin/python3
machine: Linux-4.15.0-88-generic-x86_64-with-Ubuntu-18.04-bionic

Python dependencies:
pip: 20.0.2
setuptools: 45.2.0
sklearn: 0.22.2.post1
numpy: 1.18.1
scipy: 1.4.1
Cython: None
pandas: None
matplotlib: None
joblib: 0.14.1

Built with OpenMP: True

[lrjball]

After some digging, this bug is not exclusive to non-centered data, see:

import numpy as np
from sklearn.datasets import make_blobs
from sklearn.decomposition import KernelPCA

X, _ = make_blobs(n_samples=100, random_state=0)
X = X - X.mean(axis=0)
kp = KernelPCA(n_components=2, fit_inverse_transform=True)
X_trans = kp.fit_transform(X)
X_inv = kp.inverse_transform(X_trans)

assert np.isclose(X, X_inv).all()

which will still raise an AssertionError