Graph Signal Processing

Research in Graph Signal Processing (GSP) aims to develop tools for processing data defined on irregular graph domains. In this paper we first provide an overview of core ideas in GSP and their connection to conventional digital signal processing. We then summarize recent developments in developing basic GSP tools, including methods for sampling, filtering or graph learning. Next, we review progress in several application areas using GSP, including processing and analysis of sensor network data, biological data, and applications to image processing and machine learning. We finish by providing a brief historical perspective to highlight how concepts recently developed in GSP build on top of prior research in other areas.

[1]  José M. F. Moura,et al.  Discrete Signal Processing on Graphs , 2012, IEEE Transactions on Signal Processing.

[2]  José M. F. Moura,et al.  Signal Processing on Graphs: Causal Modeling of Unstructured Data , 2015, IEEE Transactions on Signal Processing.

[3]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[4]  Antonio Ortega,et al.  Energy-efficient data representation and routing for wireless sensor networks based on a distributed wavelet compression algorithm , 2006, 2006 5th International Conference on Information Processing in Sensor Networks.

[5]  Alan V. Oppenheim,et al.  Discrete-Time Signal Pro-cessing , 1989 .

[6]  Pascal Frossard,et al.  Learning Parametric Dictionaries for Signals on Graphs , 2014, IEEE Transactions on Signal Processing.

[7]  José M. F. Moura,et al.  Bi-Virus SIS Epidemics over Networks: Qualitative Analysis , 2015, IEEE Transactions on Network Science and Engineering.

[8]  José M. F. Moura,et al.  DCT/DST and Gauss-Markov fields: conditions for equivalence , 1998, IEEE Trans. Signal Process..

[9]  O. Sporns.  Networks of the Brain , 2010 .

[10]  Xiao-Ping Zhang,et al.  On the Shift Operator, Graph Frequency, and Optimal Filtering in Graph Signal Processing , 2015, IEEE Transactions on Signal Processing.

[11]  Yue M. Lu,et al.  Uncertainty principles for signals defined on graphs: Bounds and characterizations , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[12]  Mikhail Belkin,et al.  Using manifold structure for partially labelled classification , 2002, NIPS 2002.

[13]  Vassilis Kalofolias,et al.  How to Learn a Graph from Smooth Signals , 2016, AISTATS.

[14]  Antonio Ortega,et al.  Graph Learning From Data Under Laplacian and Structural Constraints , 2016, IEEE Journal of Selected Topics in Signal Processing.

[15]  Sergio Barbarossa,et al.  Signals on Graphs: Uncertainty Principle and Sampling , 2015, IEEE Transactions on Signal Processing.

[16]  Jingxin Zhang,et al.  Techniques for Constructing Biorthogonal Bipartite Graph Filter Banks , 2015, IEEE Transactions on Signal Processing.

[17]  Markus Püschel,et al.  Algebraic Signal Processing Theory: Cooley–Tukey Type Algorithms for Real DFTs , 2008, IEEE Transactions on Signal Processing.

[18]  P. P. Vaidyanathan,et al.  Extending Classical Multirate Signal Processing Theory to Graphs—Part I: Fundamentals , 2017, IEEE Transactions on Signal Processing.

[19]  Jessika Weiss,et al.  Graphical Models In Applied Multivariate Statistics , 2016 .

[20]  Quanzheng Li,et al.  A Spectral Graph Regression Model for Learning Brain Connectivity of Alzheimer’s Disease , 2015, PloS one.

[21]  Gregory Gutin,et al.  Digraphs - theory, algorithms and applications , 2002 .

[22]  R. Clarke,et al.  Relation between the Karhunen Loève and cosine transforms , 1981 .

[23]  James H. Garrett,et al.  Semi-Supervised Multiresolution Classification Using Adaptive Graph Filtering With Application to Indirect Bridge Structural Health Monitoring , 2014, IEEE Transactions on Signal Processing.

[24]  Yuichi Tanaka,et al.  Spectral Domain Sampling of Graph Signals , 2017, IEEE Transactions on Signal Processing.

[25]  José M. F. Moura,et al.  Algebraic Signal Processing Theory: Cooley–Tukey Type Algorithms for DCTs and DSTs , 2007, IEEE Transactions on Signal Processing.

[26]  Yuantao Gu,et al.  A Distributed Tracking Algorithm for Reconstruction of Graph Signals , 2015, IEEE Journal of Selected Topics in Signal Processing.

[27]  Romualdo Pastor-Satorras,et al.  Competing activation mechanisms in epidemics on networks , 2011, Scientific Reports.

[28]  P. Lancaster,et al.  The theory of matrices : with applications , 1985 .

[29]  Muhammad Tayyab Asif,et al.  Wavelets on graphs with application to transportation networks , 2014, 17th International IEEE Conference on Intelligent Transportation Systems (ITSC).

[30]  J. Tenenbaum,et al.  A global geometric framework for nonlinear dimensionality reduction. , 2000, Science.

[31]  Zoubin Ghahramani,et al.  Combining active learning and semi-supervised learning using Gaussian fields and harmonic functions , 2003, ICML 2003.

[32]  José M. F. Moura,et al.  Role of subgraphs in epidemics over finite-size networks under the scaled SIS process , 2014, J. Complex Networks.

[33]  Pierre Vandergheynst,et al.  Wavelets on Graphs via Spectral Graph Theory , 2009, ArXiv.

[34]  Daniel A. Spielman,et al.  Fitting a graph to vector data , 2009, ICML '09.

[35]  Cyrus Shahabi,et al.  Graph Convolutional Recurrent Neural Network: Data-Driven Traffic Forecasting , 2017, ArXiv.

[36]  Yuichi Tanaka,et al.  Oversampled Graph Laplacian Matrix for Graph Filter Banks , 2014, IEEE Transactions on Signal Processing.

[37]  Donald F. Towsley,et al.  The effect of network topology on the spread of epidemics , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[38]  José M. F. Moura,et al.  Signal processing on graphs: Performance of graph structure estimation , 2016, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[39]  José M. F. Moura,et al.  The Algebraic Approach to the Discrete Cosine and Sine Transforms and Their Fast Algorithms , 2003, SIAM J. Comput..

[40]  Antonio Ortega,et al.  Localization bounds for the graph translation , 2016, 2016 IEEE Global Conference on Signal and Information Processing (GlobalSIP).

[41]  Antonio Ortega,et al.  Graph-based transforms for inter predicted video coding , 2015, 2015 IEEE International Conference on Image Processing (ICIP).

[42]  Yuejie Chi,et al.  Compressive graph clustering from random sketches , 2015, 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[43]  J. Besag.  Spatial Interaction and the Statistical Analysis of Lattice Systems , 1974 .

[44]  José M. F. Moura,et al.  Algebraic Signal Processing Theory , 2006, ArXiv.

[45]  Sunil K. Narang,et al.  Signal processing techniques for interpolation in graph structured data , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[46]  Ted G. Lewis,et al.  Network Science: Theory and Applications , 2009 .

[47]  Pierre Vandergheynst,et al.  Stationary Signal Processing on Graphs , 2016, IEEE Transactions on Signal Processing.

[48]  Charles T. Loop,et al.  Point cloud attribute compression with graph transform , 2014, 2014 IEEE International Conference on Image Processing (ICIP).

[49]  D. Marpe,et al.  The H . 264 / AVC Video Coding Standard , 2004 .

[50]  V. Koltchinskii,et al.  Empirical graph Laplacian approximation of Laplace–Beltrami operators: Large sample results , 2006, math/0612777.

[51]  José M. F. Moura,et al.  Diffusion in Social Networks as SIS Epidemics: Beyond Full Mixing and Complete Graphs , 2014, IEEE Journal of Selected Topics in Signal Processing.

[52]  S T Roweis,et al.  Nonlinear dimensionality reduction by locally linear embedding. , 2000, Science.

[53]  Steffen L. Lauritzen,et al.  Graphical models in R , 1996 .

[54]  Pascal Frossard,et al.  Graph-Based Compression of Dynamic 3D Point Cloud Sequences , 2015, IEEE Transactions on Image Processing.

[55]  Oscar C. Au,et al.  Multiresolution Graph Fourier Transform for Compression of Piecewise Smooth Images , 2015, IEEE Transactions on Image Processing.

[56]  Mikhail Belkin,et al.  Laplacian Eigenmaps for Dimensionality Reduction and Data Representation , 2003, Neural Computation.

[57]  D. Donoho,et al.  Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[58]  A. Willsky.  Multiresolution Markov models for signal and image processing , 2002, Proc. IEEE.

[59]  Pascal Frossard,et al.  The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains , 2012, IEEE Signal Processing Magazine.

[60]  Urbashi Mitra,et al.  Structure-based learning in wireless networks via sparse approximation , 2012, EURASIP J. Wirel. Commun. Netw..

[61]  Antonio Ortega,et al.  Scalable variable complexity approximate forward DCT , 2004, IEEE Transactions on Circuits and Systems for Video Technology.

[62]  J. Leydold,et al.  Discrete Nodal Domain Theorems , 2000, math/0009120.

[63]  Sabrina Hirsch,et al.  Digital Signal Processing A Computer Based Approach , 2016 .

[64]  Camille Couprie,et al.  BRANE Clust: Cluster-Assisted Gene Regulatory Network Inference Refinement , 2018, IEEE/ACM Transactions on Computational Biology and Bioinformatics.

[65]  Gene Cheung,et al.  Graph-Based Joint Signal/Power Restoration for Energy Harvesting Wireless Sensor Networks , 2017, GLOBECOM 2017 - 2017 IEEE Global Communications Conference.

[66]  D. Edwards.  Introduction to graphical modelling , 1995 .

[67]  Michael I. Jordan.  Learning in Graphical Models , 1999, NATO ASI Series.

[68]  David W. Lewis,et al.  Matrix theory , 1991 .

[69]  Antonio Ortega,et al.  Spectral anomaly detection using graph-based filtering for wireless sensor networks , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[70]  Pierre Vandergheynst,et al.  Random sampling of bandlimited signals on graphs , 2015, NIPS 2015.

[71]  Vincent Gripon,et al.  Evaluating graph signal processing for neuroimaging through classification and dimensionality reduction , 2017, 2017 IEEE Global Conference on Signal and Information Processing (GlobalSIP).

[72]  Jelena Kovacevic,et al.  Multiresolution Representations for Piecewise-Smooth Signals on Graphs , 2018, ArXiv.

[73]  José M. F. Moura,et al.  Finding Non-Overlapping Clusters for Generalized Inference Over Graphical Models , 2011, IEEE Transactions on Signal Processing.

[74]  Vincent Gripon,et al.  Toward an uncertainty principle for weighted graphs , 2015, 2015 23rd European Signal Processing Conference (EUSIPCO).

[75]  J. Laurie Snell,et al.  Markov Random Fields and Their Applications , 1980 .

[76]  Pascal Frossard,et al.  Graph transform learning for image compression , 2017, 2016 Picture Coding Symposium (PCS).

[77]  Jelena Kovacevic,et al.  Signal Representations on Graphs: Tools and Applications , 2015, ArXiv.

[78]  Nikhil Balram,et al.  Recursive structure of noncausal Gauss-Markov random fields , 1992, IEEE Trans. Inf. Theory.

[79]  Samuel Madden,et al.  Distributed regression: an efficient framework for modeling sensor network data , 2004, Third International Symposium on Information Processing in Sensor Networks, 2004. IPSN 2004.

[80]  Antonio Ortega,et al.  Submitted to Ieee Transactions on Signal Processing 1 Efficient Sampling Set Selection for Bandlimited Graph Signals Using Graph Spectral Proxies , 2022 .

[81]  Xavier Bresson,et al.  Song recommendation with non-negative matrix factorization and graph total variation , 2016, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[82]  Ulrike von Luxburg,et al.  From Graphs to Manifolds - Weak and Strong Pointwise Consistency of Graph Laplacians , 2005, COLT.

[83]  Yuichi Tanaka,et al.  Critically sampled graph filter banks with polynomial filters from regular domain filter banks , 2017, Signal Process..

[84]  Pierre Vandergheynst,et al.  Learning class‐specific descriptors for deformable shapes using localized spectral convolutional networks , 2015, SGP '15.

[85]  José M. F. Moura,et al.  Big Data Analysis with Signal Processing on Graphs: Representation and processing of massive data sets with irregular structure , 2014, IEEE Signal Processing Magazine.

[86]  Pierre Vandergheynst,et al.  Compressive Spectral Clustering , 2016, ICML.

[87]  Urbashi Mitra,et al.  Reduced dimension policy iteration for wireless network control via multiscale analysis , 2012, 2012 IEEE Global Communications Conference (GLOBECOM).

[88]  Pierre Borgnat,et al.  Graph Wavelets for Multiscale Community Mining , 2014, IEEE Transactions on Signal Processing.

[89]  Martin J. Wainwright,et al.  Major Advances and Emerging Developments of Graphical Models [From the Guest Editors] , 2010 .

[90]  Laurent Najman,et al.  Extending the Power Watershed Framework Thanks to Γ-Convergence , 2017, SIAM J. Imaging Sci..

[91]  Thomas Hofmann,et al.  Semi-supervised Learning on Directed Graphs , 2004, NIPS.

[92]  Pierre Vandergheynst,et al.  Geodesic Convolutional Neural Networks on Riemannian Manifolds , 2015, 2015 IEEE International Conference on Computer Vision Workshop (ICCVW).

[93]  Paulo Gonçalves,et al.  Translation on Graphs: An Isometric Shift Operator , 2015, IEEE Signal Processing Letters.

[94]  José M. F. Moura,et al.  Signal Recovery on Graphs: Variation Minimization , 2014, IEEE Transactions on Signal Processing.

[95]  Pierre Vandergheynst,et al.  Vertex-Frequency Analysis on Graphs , 2013, ArXiv.

[96]  Ulrik Brandes,et al.  What is network science? , 2013, Network Science.

[97]  Antonio Ortega,et al.  Bipartite Approximation for Graph Wavelet Signal Decomposition , 2017, IEEE Transactions on Signal Processing.

[98]  Paul M. Thompson,et al.  Localizing Sources of Brain Disease Progression with Network Diffusion Model , 2016, IEEE Journal of Selected Topics in Signal Processing.

[99]  Mark Newman,et al.  Networks: An Introduction , 2010 .

[100]  Christos Boutsidis,et al.  Spectral Clustering via the Power Method - Provably , 2013, ICML.

[101]  Scott T. Grafton,et al.  Dynamic reconfiguration of human brain networks during learning , 2010, Proceedings of the National Academy of Sciences.

[102]  Pascal Frossard,et al.  Learning Heat Diffusion Graphs , 2016, IEEE Transactions on Signal and Information Processing over Networks.

[103]  Rémi Munos,et al.  Spectral Bandits for Smooth Graph Functions , 2014, ICML.

[104]  George J. Pappas,et al.  Analysis and Control of Epidemics: A Survey of Spreading Processes on Complex Networks , 2015, IEEE Control Systems.

[105]  Leonhard Held,et al.  Gaussian Markov Random Fields: Theory and Applications , 2005 .

[106]  Rushil Anirudh,et al.  Bootstrapping Graph Convolutional Neural Networks for Autism Spectrum Disorder Classification , 2017, ICASSP 2019 - 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[107]  Yue M. Lu,et al.  A Spectral Graph Uncertainty Principle , 2012, IEEE Transactions on Information Theory.

[108]  José M. F. Moura,et al.  Fitting graph models to big data , 2015, 2015 49th Asilomar Conference on Signals, Systems and Computers.

[109]  I. Pesenson.  Sampling in paley-wiener spaces on combinatorial graphs , 2008, 1111.5896.

[110]  Markus Püschel,et al.  Algebraic Signal Processing Theory: Foundation and 1-D Time , 2008, IEEE Transactions on Signal Processing.

[111]  Nir Friedman,et al.  Probabilistic Graphical Models - Principles and Techniques , 2009 .

[112]  Alejandro Ribeiro,et al.  Collaborative filtering via graph signal processing , 2017, 2017 25th European Signal Processing Conference (EUSIPCO).

[113]  Sunil K. Narang,et al.  Downsampling graphs using spectral theory , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[114]  R. Coifman,et al.  Diffusion Wavelets , 2004 .

[115]  Jonathan Masci,et al.  Learning shape correspondence with anisotropic convolutional neural networks , 2016, NIPS.

[116]  Oscar C. Au,et al.  Optimal graph laplacian regularization for natural image denoising , 2015, 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[117]  Pascal Frossard,et al.  Distributed Signal Processing via Chebyshev Polynomial Approximation , 2011, IEEE Transactions on Signal and Information Processing over Networks.

[118]  Mark Crovella,et al.  Graph wavelets for spatial traffic analysis , 2003, IEEE INFOCOM 2003. Twenty-second Annual Joint Conference of the IEEE Computer and Communications Societies (IEEE Cat. No.03CH37428).

[119]  N. Balram,et al.  Noncausal Gauss Markov random fields: Parameter structure and estimation , 1993, IEEE Trans. Inf. Theory.

[120]  Jing Liao,et al.  Non-Intrusive Load Disaggregation Using Graph Signal Processing , 2018, IEEE Transactions on Smart Grid.

[121]  Andrew Knyazev,et al.  Chebyshev and conjugate gradient filters for graph image denoising , 2014, 2014 IEEE International Conference on Multimedia and Expo Workshops (ICMEW).

[122]  E. David,et al.  Networks, Crowds, and Markets: Reasoning about a Highly Connected World , 2010 .

[123]  Zhiping Lin,et al.  Design of Near Orthogonal Graph Filter Banks , 2015, IEEE Signal Processing Letters.

[124]  Cláudio T. Silva,et al.  Wavelet-based visualization of time-varying data on graphs , 2015, 2015 IEEE Conference on Visual Analytics Science and Technology (VAST).

[125]  Alejandro Ribeiro,et al.  Functional Alignment with Anatomical Networks is Associated with Cognitive Flexibility , 2016, Nature Human Behaviour.

[126]  Steven Skiena,et al.  DeepWalk: online learning of social representations , 2014, KDD.

[127]  Dimitri Van De Ville,et al.  Anatomically-adapted graph wavelets for improved group-level fMRI activation mapping , 2015, NeuroImage.

[128]  Selen Atasoy,et al.  Human brain networks function in connectome-specific harmonic waves , 2016, Nature Communications.

[129]  Ulrike von Luxburg,et al.  Graph Laplacians and their Convergence on Random Neighborhood Graphs , 2006, J. Mach. Learn. Res..

[130]  Gilbert Strang,et al.  The Discrete Cosine Transform , 1999, SIAM Rev..

[131]  Didier J. Le Gall,et al.  The MPEG video compression algorithm , 1992, Signal Process. Image Commun..

[132]  Pengfei Liu,et al.  Local-Set-Based Graph Signal Reconstruction , 2014, IEEE Transactions on Signal Processing.

[133]  Ilan Shomorony,et al.  Sampling large data on graphs , 2014, 2014 IEEE Global Conference on Signal and Information Processing (GlobalSIP).

[134]  Thomas Sikora,et al.  Trends and Perspectives in Image and Video Coding , 2005, Proceedings of the IEEE.

[135]  José M. F. Moura,et al.  Algebraic Signal Processing Theory: 1-D Space , 2008, IEEE Transactions on Signal Processing.

[136]  Xavier Bresson,et al.  Convolutional Neural Networks on Graphs with Fast Localized Spectral Filtering , 2016, NIPS.

[137]  Joshua B. Tenenbaum,et al.  Discovering Structure by Learning Sparse Graphs , 2010 .

[138]  Benjamin Girault.  Stationary graph signals using an isometric graph translation , 2015, 2015 23rd European Signal Processing Conference (EUSIPCO).

[139]  Antonio Ortega,et al.  Active semi-supervised learning using sampling theory for graph signals , 2014, KDD.

[140]  Pascal Frossard,et al.  Graph-based Isometry Invariant Representation Learning , 2017, ICML.

[141]  Anil K. Jain.  Fundamentals of Digital Image Processing , 2018, Control of Color Imaging Systems.

[142]  Ann B. Lee,et al.  Geometric diffusions as a tool for harmonic analysis and structure definition of data: multiscale methods. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[143]  Pascal Frossard,et al.  Learning Laplacian Matrix in Smooth Graph Signal Representations , 2014, IEEE Transactions on Signal Processing.

[144]  Hyeokho Choi,et al.  Distributed wavelet transform for irregular sensor network grids , 2005, IEEE/SP 13th Workshop on Statistical Signal Processing, 2005.

[145]  Yuichi Tanaka,et al.  M-Channel Oversampled Graph Filter Banks , 2014, IEEE Trans. Signal Process..

[146]  Camille Couprie,et al.  Dual constrained TV-based regularization , 2011, 2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[147]  Antonio Ortega,et al.  Joint Routing and 2D Transform Optimization for Irregular Sensor Network Grids Using Wavelet Lifting , 2008, 2008 International Conference on Information Processing in Sensor Networks (ipsn 2008).

[148]  R. Wagner.  Distributed Wavelet DeNoising for Sensor Networks , 2006 .

[149]  Antonio Ortega,et al.  A probabilistic interpretation of sampling theory of graph signals , 2015, 2015 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[150]  Dimitri Van De Ville,et al.  Tight Wavelet Frames on Multislice Graphs , 2013, IEEE Transactions on Signal Processing.

[151]  Michael I. Jordan,et al.  Graphical Models, Exponential Families, and Variational Inference , 2008, Found. Trends Mach. Learn..

[152]  Xavier Bresson,et al.  Transient networks of spatio-temporal connectivity map communication pathways in brain functional systems , 2017, NeuroImage.

[153]  Michael G. Rabbat,et al.  Approximating signals supported on graphs , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[154]  Alejandro Ribeiro,et al.  Brain signal analytics from graph signal processing perspective , 2017, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[155]  Deborah Estrin,et al.  Multiresolution storage and search in sensor networks , 2005, TOS.

[156]  Santiago Segarra,et al.  Network Topology Inference from Spectral Templates , 2016, IEEE Transactions on Signal and Information Processing over Networks.

[157]  Sunil K. Narang,et al.  Compact Support Biorthogonal Wavelet Filterbanks for Arbitrary Undirected Graphs , 2012, IEEE Transactions on Signal Processing.

[158]  Alessandro Vespignani,et al.  The role of the airline transportation network in the prediction and predictability of global epidemics , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[159]  Shih-Fu Chang,et al.  Graph construction and b-matching for semi-supervised learning , 2009, ICML '09.

[160]  Pascal Frossard,et al.  Learning of structured graph dictionaries , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[161]  Joan Bruna,et al.  Spectral Networks and Locally Connected Networks on Graphs , 2013, ICLR.

[162]  José M. F. Moura,et al.  Big Data + Big Cities: Graph Signals of Urban Air Pollution [Exploratory SP] , 2014, IEEE Signal Processing Magazine.

[163]  Sunil K. Narang,et al.  Perfect Reconstruction Two-Channel Wavelet Filter Banks for Graph Structured Data , 2011, IEEE Transactions on Signal Processing.

[164]  P. P. Vaidyanathan,et al.  Extending Classical Multirate Signal Processing Theory to Graphs—Part I: Fundamentals , 2017, IEEE Transactions on Signal Processing.

[165]  Michael G. Rabbat,et al.  Characterization and Inference of Graph Diffusion Processes From Observations of Stationary Signals , 2016, IEEE Transactions on Signal and Information Processing over Networks.

[166]  Toshihisa Tanaka,et al.  Efficient sensor position selection using graph signal sampling theory , 2016, 2016 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[167]  Pascal Frossard,et al.  Inference of mobility patterns via Spectral Graph Wavelets , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[168]  O. Sporns,et al.  The economy of brain network organization , 2012, Nature Reviews Neuroscience.

[169]  Sergio Barbarossa,et al.  On the Graph Fourier Transform for Directed Graphs , 2016, IEEE Journal of Selected Topics in Signal Processing.

[170]  José M. F. Moura,et al.  Spectral Projector-Based Graph Fourier Transforms , 2017, IEEE Journal of Selected Topics in Signal Processing.

[171]  Lionel Martin,et al.  Fast Eigenspace Approximation using Random Signals , 2016, ArXiv.

[172]  Jelena Kovacevic,et al.  Discrete Signal Processing on Graphs: Sampling Theory , 2015, IEEE Transactions on Signal Processing.

[173]  Antonio Ortega,et al.  Towards a sampling theorem for signals on arbitrary graphs , 2014, 2014 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[174]  Sunil K. Narang,et al.  Local two-channel critically sampled filter-banks on graphs , 2010, 2010 IEEE International Conference on Image Processing.

[175]  Antonio Ortega,et al.  Bipartite Graph Filter Banks: Polyphase Analysis and Generalization , 2017, IEEE Transactions on Signal Processing.

[176]  Ann B. Lee,et al.  Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[177]  Antonio Ortega,et al.  Critical sampling for wavelet filterbanks on arbitrary graphs , 2017, 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[178]  Siheng Chen,et al.  Localization, Decomposition, and Dictionary Learning of Piecewise-Constant Signals on Graphs , 2016 .

[179]  Alán Aspuru-Guzik,et al.  Convolutional Networks on Graphs for Learning Molecular Fingerprints , 2015, NIPS.

[180]  Laurent Massoulié,et al.  Epidemics and Rumours in Complex Networks: Index , 2009 .

[181]  Alejandro Ribeiro,et al.  Graph Frequency Analysis of Brain Signals , 2015, IEEE Journal of Selected Topics in Signal Processing.

[182]  Michael Elad,et al.  Dual Graph Regularized Dictionary Learning , 2016, IEEE Transactions on Signal and Information Processing over Networks.

[183]  José M. F. Moura,et al.  Discrete Signal Processing on Graphs: Frequency Analysis , 2013, IEEE Transactions on Signal Processing.

[184]  R. Tibshirani,et al.  Sparse inverse covariance estimation with the graphical lasso. , 2008, Biostatistics.

[185]  Santiago Segarra,et al.  Stationary Graph Processes and Spectral Estimation , 2016, IEEE Transactions on Signal Processing.

[186]  Quanzheng Li,et al.  Matched signal detection on graphs: Theory and application to brain imaging data classification , 2016, NeuroImage.

[187]  C. T. Butts,et al.  Revisiting the Foundations of Network Analysis , 2009, Science.

[188]  Antonio Ortega,et al.  Lifting Based Wavelet Transforms on Graphs , 2009 .

[189]  Ireneusz Jabłoński,et al.  Graph Signal Processing in Applications to Sensor Networks, Smart Grids, and Smart Cities , 2017, IEEE Sensors Journal.

[190]  Peyman Milanfar,et al.  A Tour of Modern Image Filtering: New Insights and Methods, Both Practical and Theoretical , 2013, IEEE Signal Processing Magazine.

[191]  Camille Couprie,et al.  BRANE Cut: Biologically-Related A priori Network Enhancement with Graph cuts for Gene Regulatory Network Inference , 2015 .

[192]  Michael G. Rabbat,et al.  Graph spectral compressed sensing for sensor networks , 2012, 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).

[193]  W. Siebert.  Circuits, Signals and Systems , 1985 .

[194]  Y. Rozanov,et al.  Markov random fields , 1984 .

[195]  R.G. Baraniuk,et al.  An architecture for distributed wavelet analysis and processing in sensor networks , 2006, 2006 5th International Conference on Information Processing in Sensor Networks.