Invertible Manifold Learning for Dimension Reduction

It is widely believed that a dimension reduction (DR) process drops information inevitably in most practical scenarios. Thus, methods try to preserve some essential of data after DR, as well manifold based DR methods. However, they usually fail yield satisfying results, especially high-dimensional cases. In the context learning, we think good low-dimensional representation should topological and geometric properties manifolds, which involve exactly entire manifolds. this paper, define problem information-lossless NLDR with assumption propose novel two-stage method, called invertible learning (inv-ML), tackle problem. A local isometry constraint preserving geometry applied under inv-ML. Firstly, homeomorphic sparse coordinate transformation learned find without losing information. Secondly, linear compression performed on coding, trade-off between target incurred loss. Experiments are conducted seven datasets neural network implementation inv-ML, i-ML-Enc, demonstrate proposed inv-ML not only achieves comparison typical existing but also reveals characteristics manifolds through interpolation latent space. Moreover, reliability tangent space approximated by neighborhood real-world key success algorithms. The code will be made available soon.