* 18 pages. We propose a novel invertible dimension reduction process
for manifold learning with a neural network implementation, and explore the
inherent difficulty of manifold learning in real-world secnarios by the way Access Paper or Ask Questions
* TMM: submitted on 2018.07.17, accepted on 2019.07.01. arXiv admin
note: text overlap with arXiv:1805.07193, arXiv:1805.00123 by other authors Access Paper or Ask Questions
* Journal extension of our previous conference paper: arXiv:1809.02693.
arXiv admin note: text overlap with arXiv:1901.02350 by other authors Access Paper or Ask Questions
