Diffusion maps

By Ronald R. Coifman, Stéphane Lafon. 2006

Subfields: Representation & Self-Supervised Learning

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Citations in the corpus

Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering (2016, methodology): “On the other hand, we will also improve this framework with tools developed in GSP, including graph wavelet operators [14, 9, 11, 6, 30], spectral graph coarsening techniques [33], and improved localization properties [36, 26, 27].”
UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction (2018, methodology): “Algorithms such as PCA [8], MDS [9], and Sammon mapping [20] fall into the former category while t-SNE [15] [26], Isomap [24], LargeVis [22], Laplacian eigenmaps [1] [2], diffusion maps [4], NeRV [28], and JSE [12] all fall into the latter category.”
Geometric Deep Learning: Going beyond Euclidean data (2016, background): “referred to as the diffusion distance [30].”
Community detection in graphs (2009, neutral): “B) and in a recent analysis by Nadler et al. (Nadler et al., 2006), one defined a dissimilarity measure called “diffusion distance”, which is derived from the probability that the walker visits the target after a fixed number of steps.”
Diffusion maps, spectral clustering and reaction coordinates of dynamical systems (2005, background): “An example where the density plays no role but the geometry Ω defines the structure of the eigenvalues and eigenvectors is described in [23].”
A spectral notion of Gromov–Wasserstein distance and related methods (2011, methodology): “By directly conceiving their procedures using heat diffusions, the proposals of [17,28,41,44] already encode a certain notion of scale, which is given by the time parameter governing the diffusion.”
Relaxation-based coarsening and multiscale graph organization (2010, unknown): “An ingenious rigorous definition of distances in a general graph, introduced in [18], is called diffusion distance.”
Riemannian Manifold Learning (2008, background): “Among the family of dimensionality reduction approaches, manifold learning1 algorithms have attracted extensive attention recently due to their nonlinear nature, geometric intuition, and computational feasibility.”
See all by looking at a few: Sparse modeling for finding representative objects (2012, methodology): “Because datasets consist of high-dimensional data, most dimensionality reduction methods aim at reducing the feature-space dimension for all the data, e.g., PCA [25], LLE [34], Isomap [36], Diffusion Maps [7], etc.”
Intrinsic shape context descriptors for deformable shapes (2012, methodology): “The studies of diffusion geometry are based on the theoretical works by Berard et al. [4] and later by Coif-man and Lafon [13] who suggested to use the eigenvalues and eigenvectors of the Laplace-Beltrami operator associated with the shape to construct invariant metrics known as diffusion distances.”
Learning with Partially Absorbing Random Walks (2012, background): “…leading to a variety of models including PageRank [14] for web page ranking, hitting and commute times [8] for similarity measure between vertices, harmonic functions [20] for semi-supervised learning, diffusion maps [7] for dimensionality reduction, and normalized cuts [12] for clustering.”
Vector Diffusion Maps and the Connection Laplacian (2011, methodology): “In the past decade we have been witnessed to the emergence of non-linear dimensionality reduction methods, such as locally linear embedding (LLE) [33], ISOMAP [39], Hessian LLE [12], Laplacian eigenmaps [2] and diffusion maps [9].”
Randomized Near Neighbor Graphs, Giant Components, and Applications in Data Science (2017, methodology): “There are a great many other methods of dimensionality reduction that start by constructing a graph that roughly approximates the data, for example tdistributed Stochastic Neighborhood Embedding (t-SNE) [16, 31], diffusion maps [7] or Laplacian Eigenmaps [2].”