The conference paper gives in the first section a brief and easy understandable introduction into the basics of Riemannian geometry. Furthermore, it gives a review of classical methods for mapping data into a low-dimensional manifold / nonlinear dimensionality reduction like Local Linear Embedding (LLE), Isometric Feature Mapping (ISOMAP) and Local Riemannian Manifold Learning (LRML).
Link to the resource (fulltext):
https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8250223