Non-linear independent component analysis with diffusion maps

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Local Kernels and the Geometric Structure of Data (2014, unknown): “In Section 3, we connect this theory to the theory of nonlinear independent components of Itô processes, which was introduced in [22] and applied in [20, 10].”
An extension of slow feature analysis for nonlinear blind source separation (2014, background): “Singer & Coifman made a data-driven choice for the metric tensor through local inspection of the data manifold, and showed that the resulting diffusion maps can reconstruct the original sources in a toy example (Singer and Coifman, 2008) and extract slowly varying manifolds in time series data (Sing”
Anisotropic diffusion on sub-manifolds with application to Earth structure classification (2012, methodology): “To this end, our work contributes a generalization of the nonlinear ICA [4] in the sense that it computes the ICs of a-priory given data, but also provides an efficient extension for the ICs to any newly observed data.”
LanczosNet: Multi-Scale Deep Graph Convolutional Networks (2019, methodology): “Similarly, [55] uses the anisotropic Gaussian kernel deﬁned by the local Mahalanobis distances to extract independent components from nonlinear measurements of independent stochastic Itˆo processes.”