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Laplacian Spectral Properties of Graphs from Random Local Samples [article]

Zhengwei Wu, Victor M. Preciado
2013 arXiv   pre-print
In this paper, we propose techniques to estimate spectral properties of the normalized Laplacian matrix from a random collection of induced local subgraphs.  ...  Moreover, we propose a technique, based on convex optimization, to compute upper and lower bounds on the spectral radius of the normalized Laplacian matrix from local subgraphs.  ...  The combination of quality guarantee of moment se-quence and the optimization problems provides us with the estimation guarantee of the spectral radius.  ... 
arXiv:1310.4899v1 fatcat:q77jt2t7vfgwtgx65bpgwc6ryi

Laplacian Spectral Properties of Graphs from Random Local Samples [chapter]

Zhengwei Wu, Victor M. Preciado
2014 Proceedings of the 2014 SIAM International Conference on Data Mining  
In this paper, we propose techniques to estimate spectral properties of the normalized Laplacian matrix from a random collection of induced local subgraphs.  ...  Moreover, we propose a technique, based on convex optimization, to compute upper and lower bounds on the spectral radius of the normalized Laplacian matrix from local subgraphs.  ...  The combination of quality guarantee of moment se-quence and the optimization problems provides us with the estimation guarantee of the spectral radius.  ... 
doi:10.1137/1.9781611973440.39 dblp:conf/sdm/WuP14 fatcat:rjvr5rckbnfg7nypl2g7ananny

The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains

D. I. Shuman, S. K. Narang, P. Frossard, A. Ortega, P. Vandergheynst
2013 IEEE Signal Processing Magazine  
The emerging field of signal processing on graphs merges algebraic and spectral graph theoretic concepts with computational harmonic analysis to process such signals on graphs.  ...  that have been proposed to efficiently extract information from high-dimensional data on graphs.  ...  The authors would like to thank the anonymous reviewers and Dorina Thanou for their constructive comments on earlier versions of this article. AuthorS  ... 
doi:10.1109/msp.2012.2235192 fatcat:6srji3b4i5dgredt5p2m3rb2ae

Metrics for Graph Comparison: A Practitioner's Guide [article]

Peter Wills, Francois G. Meyer
2019 arXiv   pre-print
We put forward a multi-scale picture of graph structure, in which the effect of global and local structure upon the distance measures is considered.  ...  Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees in data in these fields yields insight into the generative mechanisms and functional properties of the graph  ...  Acknowledgments The authors are grateful to the anonymous reviewers and the Academic Editor for their insightful comments and suggestions that greatly improved the content and presentation of this manuscript  ... 
arXiv:1904.07414v2 fatcat:3xhzagkrifhxpa3uisljivk4ce

Spectral Properties of Unimodular Lattice Triangulations

Benedikt Krüger, Ella M. Schmidt, Klaus Mecke
2016 Journal of statistical physics  
For random triangulations we find a qualitative agreement of the spectral properties with well-known random graph models.  ...  The considered spectral properties can be applied to transport problems on triangulation graphs and the crossover behaviour allows a tuning of important transport quantities.  ...  Important properties of graphs can be found by examining spectral properties (the set of eigenvalues) of matrices associated with graphs.  ... 
doi:10.1007/s10955-016-1493-0 fatcat:fdzlfluk5je6thhitdxyd4xepm

Metrics for graph comparison: A practitioner's guide

Peter Wills, François G. Meyer, Pin-Yu Chen
2020 PLoS ONE  
We put forward a multi-scale picture of graph structure wherein we study the effect of global and local structures on changes in distance measures.  ...  Discovery and comparison of structures such as modular communities, rich clubs, hubs, and trees yield insight into the generative mechanisms and functional properties of the graph.  ...  Acknowledgments The authors are grateful to the anonymous reviewers and the Academic Editor for their insightful comments and suggestions that greatly improved the content and presentation of this manuscript  ... 
doi:10.1371/journal.pone.0228728 pmid:32050004 pmcid:PMC7015405 fatcat:igitnxkvcrdotafcbex5kt75mq

NetLSD

Anton Tsitsulin, Davide Mottin, Panagiotis Karras, Alexander Bronstein, Emmanuel Müller
2018 Proceedings of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining - KDD '18  
NetLSD extracts a compact signature that inherits the formal properties of the Laplacian spectrum, specifically its heat or wave kernel; thus, it hears the shape of a graph.  ...  In this paper, we propose the Network Laplacian Spectral Descriptor (NetLSD): the first, to our knowledge, permutation- and size-invariant, scale-adaptive, and efficiently computable graph representation  ...  Size-invariance postulates that if two graphs originate from the sampling of the same domain M, they should be deemed similar. Property 3 (Size-invariance).  ... 
doi:10.1145/3219819.3219991 dblp:conf/kdd/TsitsulinMKBM18 fatcat:jf2ownxrrfcu3fppip3kbks7c4

Local two-channel critically sampled filter-banks on graphs

Sunil K. Narang, Antonio Ortega
2010 2010 IEEE International Conference on Image Processing  
Designs precursor to more general filter-banks based on spectral properties of the graph.  ...  [4] 2008 Lifting wavelets on arbitrary graphs by Narang and Ortega 2009 [7] Spectral Transform Designs : Based on spectral properties of graph (eigen-values, eigen-vectors) Diffusion Wavelets on Graphs  ... 
doi:10.1109/icip.2010.5651072 dblp:conf/icip/NarangO10 fatcat:6sb64ksjs5ahfglw4jyrtfmtt4

Localized Spectral Graph Filter Frames: A Unifying Framework, Survey of Design Considerations, and Numerical Comparison (Extended Cut) [article]

David I Shuman
2020 arXiv   pre-print
In this article, we survey a particular class of dictionaries called localized spectral graph filter frames, whose atoms are created by localizing spectral patterns to different regions of the graph.  ...  After showing how this class encompasses a variety of approaches from spectral graph wavelets to graph filter banks, we focus on the two main questions of how to design the spectral filters and how to  ...  ACKNOWLEDGMENTS The author would like to thank the anonymous reviewers and Hamid Behjat for constructive feedback on earlier versions of this article.  ... 
arXiv:2006.11220v2 fatcat:2fhnkgrlgfau7o4m2aoisoflju

Metrics for Graph Comparison: A Practitioner's Guide [article]

Peter Wills, François G. Meyer
2019 bioRxiv   pre-print
We put forward a multi-scale picture of graph structure, in which the effect of global and local structure upon the distance measures is considered.  ...  used graph metrics and distance measures, and demonstrate their ability to discern between common topological features found in both random graph models and empirical datasets.  ...  λ L i i th eigenvalue of the Laplacian matrix λ L i i th eigenvalue of the normalized Laplacian matrix G {0,1} The {null,alternative} population of graphs G {0,1}Sample graph from G {0,1} D 0 G Degree  ... 
doi:10.1101/611509 fatcat:vvvdeofsj5aotesd65kbyczzwq

Spatial Data Mining with the Application of Spectral Clustering: A Trend Detection Approach

Arvind Sharma, R. K.
2017 International Journal of Computer Applications  
These algorithms and methods are used to scratch new knowledge from huge data sets having property of graphs.  ...  This paper extends the current spatial data mining algorithms to efficient mode of spectral clustering algorithms with the application of Laplacians graph properties and present new approach of spatial  ...  Now consider the properties of normalized graph Laplacians - The normalized form of graph Laplacian is based on two terms as symmetric and random walk.  ... 
doi:10.5120/ijca2017915252 fatcat:k6ryc4obuvboxmu3ccynzju6by

Spectral Networks and Locally Connected Networks on Graphs [article]

Joan Bruna, Wojciech Zaremba, Arthur Szlam, Yann LeCun
2014 arXiv   pre-print
In particular, we propose two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian.  ...  Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability to exploit the local translational invariance of signal classes over their  ...  We first sample 4096 random points S = {s j } j≤4096 from the unit sphere S 2 ⊂ R 3 .  ... 
arXiv:1312.6203v3 fatcat:ubgtphe57bgjvgctfd5i6xny6i

Approximating the Spectrum of a Graph [article]

David Cohen-Steiner, Weihao Kong, Christian Sohler, Gregory Valiant
2017 arXiv   pre-print
The spectrum of a network or graph G=(V,E) with adjacency matrix A, consists of the eigenvalues of the normalized Laplacian L= I - D^-1/2 A D^-1/2.  ...  In addition we study the implications of our algorithm to property testing in the bounded degree graph model.  ...  Return a random eigenvalue of the normalized Laplacian of C(v) Lemma 13. Algorithm SmallCCSpectrum samples a random eigenvalue from H.  ... 
arXiv:1712.01725v1 fatcat:gxoc2sd7tjguxmxohys3wy4z2m

Spectral and dynamical properties in classes of sparse networks with mesoscopic inhomogeneities

Marija Mitrović, Bosiljka Tadić
2009 Physical Review E  
Within the exhaustive spectral analysis for both the adjacency matrix and the normalized Laplacian matrix we identify the spectral properties which characterize the mesoscopic structure of sparse cyclic  ...  The number of distinct modules leads to an extra peak at the lower part of the Laplacian spectrum in cyclic graphs.  ...  We study the spectral properties of the adjacency matrix A and the related Laplacian matrix L ͑see Sec.  ... 
doi:10.1103/physreve.80.026123 pmid:19792216 fatcat:qwfc5mpchvgojhki6mn4i73x4m

Identifying network structure similarity using spectral graph theory

Ralucca Gera, L. Alonso, Brian Crawford, Jeffrey House, J. A. Mendez-Bermudez, Thomas Knuth, Ryan Miller
2018 Applied Network Science  
To test the scalability of our metric we use a random matrix theory approach while discovering Erdös-Rényi graphs.  ...  Our research utilizes a network visualization tool, which systematically discovers a network, producing a sequence of snapshots of the network.  ...  that the spectral properties of the graph above this value coincide with those of a system with maximal disorder.  ... 
doi:10.1007/s41109-017-0042-3 pmid:30839726 pmcid:PMC6214265 fatcat:6yaabbsbpvg3xpcq65eb3euu2q
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