Kernels and Regularization on Graphs

By Alex Smola, Risi Kondor. 2003

1,002 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Computer Vision and Pattern Recognition

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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, 23, 29, 38, 49], none of which apply in our setting.”
Graph Kernels (2008, neutral): “We begin by providing some background, establishing some basic notation, and giving an outline of the paper.”
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains (2012, methodology): “References [4]– [11], [14, Chapter 5], and [28]–[30] discuss (15) and other energy minimization models in detail, as well as speciﬁc ﬁlters that arise as solutions, relations between these discrete graph spectral ﬁlters and ﬁlters arising out of continuous partial differential equations, and…”
Kernel methods in machine learning (2007, neutral): “Smola and Kondor [125] suggest kernels K = r(L) or K = r(L̃), which have desirable smoothness properties.”
Recurrent knowledge graph embedding for effective recommendation (2018, methodology): “It decomposes the user-item rating matrix, meanwhile adopting graph regularization [31] to constrain the distance of latent vectors of similar items that are connected by meta paths.”
Introduction to Semi-Supervised Learning (2009, methodology): “THE ASSUMPTION OF GRAPH-BASED METHODS∗ 55 walk [8, 168], harmonic function [210], local and global consistency [198], manifold regularization [17, 158, 155], kernels from the graph Laplacian [35, 51, 95, 101, 163, 211], spectral graph transducer [90], local averaging [179, 187], density-based regula”
Accelerated filtering on graphs using Lanczos method (2015, background): “In machine vision, automatic text classiﬁcation or more generally machine learning, graphs are used to represent similarities between data points and result in algorithms for semi-supervised learning [24, 19, 1, 23].”
Hyperparameter Learning for Graph Based Semi-supervised Learning Algorithms (2006, methodology): “In the second step, smoothing is applied globally, typically, based on the spectral transformation of the graph Laplacian [6] [10].”
Multi-Task Averaging (2011, methodology): “TA on the vectorized form of Y. 4.2 Regularized Laplacian Kernel The MTA solution matrix W= I+ T L 1 is similar to the regularized Laplacian kernel (RLK): Q= (I+ L) 1, introduced by Smola and Kondor (Smola and Kondor, 2003). In the RLK, the graph Laplacian matrix Lis assumed to be symmetric, but the”
Optimal Transport Kernels for Sequential and Parallel Neural Architecture Search (2020, background): “Previous work considers the neural network architectures as the graphs, then deﬁning various distances and kernels on graphs (Messmer & Bunke, 1998; Wallis et al., 2001; Kondor & Lafferty, 2002; Smola & Kondor, 2003; Gao et al., 2010; Ru et al., 2021).”
Learning Laplacian Matrix in Smooth Graph Signal Representations (2014, methodology): “has shown in [3] that graph Laplacian can be used to define various kernels related to regularization, diffusion, and random walk processes associated with graphs.”
Network Topology Inference from Spectral Templates (2016, neutral): “These include processes generated by graph ﬁlters with time-varying coefﬁcients or those generated by the so-called diffusion Laplacian kernels [27], to name a few.”
TriRank: Review-aware Explainable Recommendation by Modeling Aspects (2015, methodology): “Although there are various kernels [25], we have purposefully chosen this one (originally introduced by [36]) due to its effective encoding of the CF effect in bipartite graph scenarios.”
Multiscale methods for data on graphs and irregular multidimensional situations (2009, background): “See Smola and Kondor (2003) and Belkin et al. (2004) for other work on regularization of functions on graphs.”