Graph wavelets for spatial traffic analysis

By Mark Crovella, Eric D. Kolaczyk. 2003

263 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition, Statistical and Nonlinear Physics, Graph Learning, Signal Processing

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In Computer Vision and Pattern Recognition

In Statistical and Nonlinear Physics

In Graph Learning

In Signal Processing

Citations in the corpus

The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains (2012, methodology): “The graph wavelets of Crovella and Kolaczyk [53] are functions ψk,i : V → R, localized with respect to a range of scale/location indices (k, i), which at a minimum satisfy ∑ j∈V ψk,i(j) = 0 (i.”
Wavelets on Graphs via Spectral Graph Theory (2009, neutral): “Crovella and Kolaczyk [30] defined wavelets on unweighted graphs for analyzing computer network traffic.”
Spectral Graph Skeletons for 3D Action Recognition (2014, methodology): “One of the earliest works on graph wavelets include a method by Crovella and Kolaczyk [6] for analyzing computer traﬃc data on unweighted graphs.”
A Multiscale Pyramid Transform for Graph Signals (2013, background): “Part of this work appeared in the master’s thesis [1] and was presented at the Duke Workshop on Sensing and Analysis of HighDimensional Data in July 2011.”
Wavelet transform on manifolds: Old and new approaches (2010, methodology): “Several approaches to this problem have already been considered, although with quite different mathematical formulations and properties: • In [13], simple compactly supported wavelets are constructed using the hop distance neighborhoods on graphs and applied to Internet traffic data.”
Wavelets on Graphs via Deep Learning (2013, methodology): “A number of approaches for constructing wavelets on graphs have been proposed, including, but not limited to the CKWT [7], Haar-like wavelets [24, 10], diffusion wavelets [6], spectral wavelets [12], tree-based wavelets [19], average-interpolating wavelets [21], and separable filterbank wavelets [17”
Global and Local Uncertainty Principles for Signals on Graphs (2016, background): “The major research thrust to date in the emerging area of signal processing on graphs [1, 2] has been to design multiscale wavelet and vertex-frequency transforms [3]-[24].”
Structural analysis of network traffic flows (2004, background): “However, a wide range of important problems fa ced by network researchers today require modeling and analysis of traffic on all links simulta neously, including traffic engineering, traffic matrix estimation [17, 31, 32], anomaly detection [6 , 1], attack detection [30], traffic forecasting and capa”
Graph Signal Processing: Overview, Challenges, and Applications (2017, background): “Vertex domain designs such as [100] or [101] have the advantage of defining exactly localized basis functions on the graph, but do”
Perfect Reconstruction Two-Channel Wavelet Filter Banks for Graph Structured Data (2011, background): “Crovella and Kolaczyk [2] designed wavelet like transforms on graphs which are localized in space.”
Image denoising with nonlocal spectral graph wavelets (2010, methodology): “These include vertex-domain methods based on n-hop distance [14], lifting schemes [15], and methods restricted to trees [16].”