Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps.

By Ronald R. Coifman, Stéphane Lafon, Ann B. Lee, Mauro Maggioni, Boaz Nadler, F. Warner, Steven W. Zucker. Proceedings of the National Academy of Sciences of the United States of America, 2005

1,850 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Radiology, Nuclear Medicine and Imaging

View Paper: https://www.semanticscholar.org/paper/01b24de15cf337c55b9866c4b534596ca3d93abe

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Citations in the corpus

Spectral clustering and the high-dimensional stochastic blockmodel (2010, background): “Researchers have explored the performance of other clustering algorithms under the Stochastic Blockmodel.”
Spectral Methods for Dimensionality Reduction (2006, neutral): “For example, the discrete graph Laplacian arises in the description of diffusion on graphs and can be related to Green's functions and heat kernels in this way [Kondor and Lafferty, 2002, Coifman et al., 2005].”
Learning Sets with Separating Kernels (2012, background): “This latter idea has triggered a large number of different algorithmic and theoretical studies (see for example [4, 5, 19, 20, 36, 54]).”
Kinetic distance and kinetic maps from molecular dynamics simulation. (2015, background): “Diffusion maps model the observed data as emerging from a diffusion process [11, 13].”
Bayesian Inference of Bijective Non-Rigid Shape Correspondence (2016, background): “These problems are becoming increasingly important due to the emergence of affordable 3D sensing technology.”
Construction of approximation spaces for reinforcement learning (2013, background): “Diffusion distances compare the probabilities to end up in the same states (see, e.g., Coifman et al., 2005, and Section 4.1).”
Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization (2006, methodology): “Below, we review the diffusion framework that first appeared in [10] and put it into the context of eigenmaps, dimensionality reduction, and Markov random walk learning on graphs.”
Characterization of cell fate probabilities in single-cell data with Palantir (2019, positive): “14).”
Wishbone identifies bifurcating developmental trajectories from single-cell data (2016, methodology): “Wishbone overcomes this problem by use of diffusion maps [7], a dimensionality reduction technique, to reduce noise and eliminate short circuits.”
Diffusion maps for high-dimensional single-cell analysis of differentiation data (2015, methodology): “Here, we propose diffusion maps (Coifman et al., 2005) as a tool for analysing single-cell differentiation data.”
(2014). Online quality assessment of human movement from skeleton data . Paper presented at British Machine Vision Conference, (2014, methodology): “An approximation of P is computed following [4] from the matrix W.”