Diffusion kernels on graphs and other discrete structures

By Risi Kondor. 2002

650 citations recorded by the source corpus.

Subfields: Representation & Self-Supervised Learning, Graph Learning

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Citations in the corpus

State-specific protein–ligand complex structure prediction with a multiscale deep generative model (2022, positive): “…pair update block updates the pair representations between the set of atomic nodes and frame nodes through discretized heat-kernel transformations 60 , such that they are capable of incorporating the molecular graph chirality and are able to explicitly encode long-range dependencies beyond…”
Kernel methods in machine learning (2007, neutral): “This has been proposed in Taskar et al. [132] for the soft margin maximization problem, as well as in Altun et al. [5] and Lafferty et al. [89] for conditional random fields and Gaussian processes.”
Metrics for Finite Markov Decision Processes (2004, background): “We are currently pursuing an interesting connection to diffusion kernels on graphs (Kondor & Lafferty, 2002).”
Kernels and Regularization on Graphs (2003, methodology): “From (26) we immediately obtain the corollary (see Kondor and Lafferty [2002]) that for diffusion processes on factor graphs the kernel on the factor graph is given by the product of kernels on the constituents, that is k((i, i), (j, j)) = k(i, j)k(i, j).”
A Comparison between Recursive Neural Networks and Graph Neural Networks (2006, background): “They extend support vector machines [11]–[14], neural networks [15]–[18] and SOMs [19] to structured data.”
Graph spectral image smoothing using the heat kernel (2008, methodology): “Recently, the heat kernel has been widely used in machine learning for dimensionality reduction, semi-supervised learning and data clustering [21,26,30,44].”
VisualRank: Applying PageRank to Large-Scale Image Search (2008, background): “Several other studies have explored the use of a similaritybased graph [22], [23] for semisupervised learning.”
A Network Diffusion Model of Disease Progression in Dementia (2012, neutral): “The main ﬁber bundles connecting these Theoreticalpredictionisbased onthesecondeigenmode oftheyounghealthy brain network’s Laplacian matrix H .”
Diffusion Improves Graph Learning (2019, background): “Two popular examples of graph diffusion are personalized PageRank (PPR) [57] and the heat kernel [36].”
A discriminative framework for clustering via similarity functions (2008, background): “For example, i n the diffusion kernelof [27], the similarityK(x, x) is related to the effective resistance between x and x in a weighted graph defined from distances in the original metric.”
Spectral Analysis of Signed Graphs for Clustering, Prediction and Visualization (2010, background): “Heat diffusion kernel By considering a process of heat diffusion on a graph one arrives at the heat diffusion kernel exp(−αL) [15].”