Diffusion Kernels on Graphs and Other Discrete Input Spaces

By Risi Kondor, John D. Lafferty. 2002

931 citations recorded by the source corpus.

Subfields: Graph Learning, Statistical Learning Theory

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Graph Learning

In Statistical Learning Theory

Citations in the corpus

Neural Architecture Search with Bayesian Optimisation and Optimal Transport (2018, background): “The above work either define the distance/kernel between vertices or assume the same vertex (layer) set [9, 20, 26, 35, 46], none of which apply in our setting.”
The More You Know: Using Knowledge Graphs for Image Classification (2016, background): “There is also a substantial amount of work on various types of kernels defined for graphs [36] such as diffusion kernels [14], graphlet kernels [33], Weisfeiler-Lehman graph kernels [32], deep graph kernels [27], graph invariant kernels [26] and shortest-path kernels [1].”
Graph Kernels (2008, methodology): “(59) Since the product of any matrix with its transpose is p.s.d., we conclude thatKt is symmetric and p.s.d., and thus k(vi, vj) := [Kt]ij is a valid candidate for a kernel between graph vertices (Kondor and Lafferty, 2002).”
Wavelets on Graphs via Spectral Graph Theory (2009, neutral): “Some recent work has studied using the “diffusion kernel” Kt = e−tL for use with kernel-based machine learning algorithms [57].”
Metrics for Finite Markov Decision Processes (2004, background): “We are currently pursuing an interesting connection to diffusion kernels on graphs (Kondor & Lafferty, 2002).”
Propagation kernels: efficient graph kernels from propagated information (2014, methodology): “Measuring the structural similarity of local node neighborhoods has recently become popular for inference in networked data (Kondor and Lafferty 2002; Desrosiers and Karypis 2009; Neumann et al. 2013) where this idea has been used for designing kernels on graphs (kernels between the nodes of a graph”
Learning the Kernel Matrix with Semidefinite Programming (2002, methodology): “Such interaction graph allows to establish similarities among proteins through the construction of a corresponding diffusion kernel (Kondor and Lafferty, 2002).”
Neural methods for non-standard data (2004, methodology): “The approach [53] proposes to use the negative Laplacian as generator (cid:8) for the generic setting of an undirected graph as local neighborhood structure.”
Semi-supervised Penalized Output Kernel Regression for Link Prediction (2011, positive): “Typically, we use in this work the diﬀusion kernel (Kondor & Laﬀerty, 2002) matrix In the training information, the matrix A ℓ is now replaced by a positive semi-deﬁnite matrix K Y ℓ .”
Semi-Supervised Learning on Riemannian Manifolds (2004, background): “Some of these connections have been explored in a different form by Kondor and Lafferty (2002) in the context of developing kernels on graphs.”
A Comprehensive Survey of Neighborhood-based Recommendation Methods (2011, methodology): “Note that this measure is closely related to the Von Neumann Diffusion kernel [20, 40, 43]”
On Graph Kernels: Hardness Results and Efficient Alternatives (2003, background): “Diffusion kernels on graphs [12] allow for the computation of a kernel if the instance space has a graph structure.”
Diffusion Kernels on Statistical Manifolds (2005, background): “Kondor and Laﬀerty (2002) propose the use of discrete diﬀusion kernels and tools from spectral graph theory for data represented by graphs.”