ENH Enrich docstring on `inverse_transform` of `KernelPCA`
@@ -346,6 +346,26 @@ class KernelPCA(TransformerMixin, BaseEstimator):
def inverse_transform(self, X):
"""Transform X back to original space.
+ ``inverse_transform`` approximates the inverse transformation using
+ a learned pre-image. The pre-image is learned by kernel ridge
+ regression of the original data on their low-dimensional representation
+ vectors.
+
+ .. note:
+ :meth:`~sklearn.decomposition.fit` internally uses a centered
+ kernel. As the centered kernel no longer contains the information
+ of the mean of kernel features, such information is not taken into
+ account in reconstruction.
+
+ .. note::
+ When users want to compute inverse transformation for 'linear'
+ kernel, it is recommended that they use
+ :class:`~sklearn.decomposition.PCA` instead. Unlike
+ :class:`~sklearn.decomposition.PCA`,
+ :class:`~sklearn.decomposition.KernelPCA`'s ``inverse_transform``
+ does not reconstruct the mean of data when 'linear' kernel is used
+ due to the use of centered kernel.
+
Parameters
----------
X : {array-like, sparse matrix} of shape (n_samples, n_components)
