Manifold learning, aka manifold estimation, are methods that extract the geometric structure of data.

Manifold learning as nonlinear dimensionality reduction (NLDR)

Manifold learning is also viewed as a subset of topological data analysis [@Wasserman2018].

Preservation of (Global) Mutual Distances

Isometric embedding: multi-dimensional scaling (MDS) [@Schoenberg1937]; ISOMAP [@Tenenbaum2000].

Low Lipschitz distortion, randomized embedding [@Johnson and Lindenstrauss, 1984].

Kernel-based Manifold Learning

All kernel-based manifold learning methods are all special cases of kernel principal component analysis (kernel PCA) [@Ham2004].

local linear embedding (LLE) [@Roweis2000]

local tangent space alignment (LTSA) [@ZhangZY2004]

Laplacian eigenmaps [@Belkin2003]

Hessian eigenmaps [@Donoho2003]

Geometric Diffusion

diffusion maps [@Coifman2005a; @Coifman2006a]

geometric harmonics [@Coifman2005b; @Coifman2006b]

🏷 Category=Manifold