Our KernelPCA(fit_inverse_transform=True) implements the method of:

Learning to Find Pre-Images
Neural Information Processing Systems 16 (NIPS 2003)
Jason Weston, Bernhard Schölkopf, Gökhan Bakir

https://papers.nips.cc/paper/2003/hash/ac1ad983e08ad3304a97e147f522747e-Abstract.html

We might want to adapt this to make make_pipeline(Nystroem(), PCA()) a feature complete, scalable alternative to KernelPCA for denoising applications and novelty detection for instance.