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Stationary Graph Processes and Spectral Estimation

Antonio G. Marques, Santiago Segarra, Geert Leus, Alejandro Ribeiro
2017 IEEE Transactions on Signal Processing  

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2016 pre-print arXiv:1603.04667v1 fatcat:qyzwv6r3s5az5hn62apqce3qka

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2017 accepted
arXiv:1603.04667v2 fatcat:q5yonwpiufbnnpw5auytxk2brm
Finally, we illustrate the power spectral density estimation in synthetic and real-world graphs.  ...  Our definition requires that stationary graph processes can be modeled as the output of a linear graph filter applied to a white input.  ...  Given that stationary processes were shown to be diagonalized by the Graph Fourier basis, the concept of power spectral density for graph processes was introduced and several estimation methods were studied  ... 
doi:10.1109/tsp.2017.2739099 fatcat:fvfs4jj7hvdb3g5ifm73bki6qm
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Antonio G. Marques, Santiago Segarra, Geert Leus, Alejandro Ribeiro. "Stationary Graph Processes and Spectral Estimation." IEEE Transactions on Signal Processing 65.22 (2017) 5911-5926

Subsampling for Graph Power Spectrum Estimation [article]

Sundeep Prabhakar Chepuri, Geert Leus
2016 arXiv   pre-print

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Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks.  ...  In this paper we focus on subsampling stationary random processes that reside on the vertices of undirected graphs.  ...  Graph spectral domain Consider the problem of estimating the graph power spectrum of the second-order stationary graph process x ∈ R N from a set of K ≪ N linear observations stacked in the vector y ∈  ... 
arXiv:1603.03697v1 fatcat:q2animaujbc2rew67lzj7vqhvq
Citation

Sundeep Prabhakar Chepuri, Geert Leus. "Subsampling for Graph Power Spectrum Estimation." arXiv (2016)

Point Cloud Segmentation based on Hypergraph Spectral Clustering [article]

Songyang Zhang, Shuguang Cui, Zhi Ding
2020 arXiv   pre-print

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2020 pre-print
arXiv:2001.07797v1 fatcat:4g7xlaaomrcaxbfdccoq3nvfdi
2020 pre-print
arXiv:2001.07797v2 fatcat:qvqrpngb2ncztpk33gz7w5kbw4
Hypergraph spectral analysis has emerged as an effective tool processing complex data structures in data analysis.  ...  This work investigates the power of hypergraph spectral analysis in unsupervised segmentation of 3D point clouds. We estimate and order the hypergraph spectrum from observed point cloud coordinates.  ...  In [20] , a graph stationary process is defined within the GSP framework to describe the stationary property of the graph shifting.  ... 
arXiv:2001.07797v3 fatcat:s37e4rl24vfexpuceoga2yjrmu
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Songyang Zhang, Shuguang Cui, Zhi Ding. "Point Cloud Segmentation based on Hypergraph Spectral Clustering." arXiv (2020)

Fitting Graphical Interaction Models to Multivariate Time Series [article]

Michael Eichler
2012 arXiv   pre-print

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Furthermore, we discuss maximum likelihood estimation based on Whittle's approximation to the log-likelihood function and propose an iterative method for solving the resulting likelihood equations.  ...  In this paper, we present a parametric approach for graphical interaction modelling of multivariate stationary time series.  ...  {a,b} (λ) of a process X V : letf V V (λ) be an estimate of the spectral matrix such as a nonparametric kernel spectral estimate and letĝ V V (λ) =f V V (λ) −1 its inverse; then the partial spectral coherences  ... 
arXiv:1206.6839v1 fatcat:osp2ar72nzhq7dchnuvzk546ci
Citation

Michael Eichler. "Fitting Graphical Interaction Models to Multivariate Time Series." arXiv (2012)

Partial correlation graphs for continuous-parameter time series [article]

Vicky Fasen-Hartmann, Lea Schenk
2024 arXiv   pre-print

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In this paper, we establish the partial correlation graph for multivariate continuous-time stochastic processes, assuming only that the underlying process is stationary and mean-square continuous with  ...  expectation zero and spectral density function.  ...  In the high-frequency sampling scheme, the smoothed periodogram and the lag-window spectral density estimator are popular estimators for the spectral density as for discrete-time processes (Anderson,  ... 
arXiv:2401.16970v1 fatcat:mk5rfjo6djfclj4njvbf7y5z4y
Citation

Vicky Fasen-Hartmann, Lea Schenk. "Partial correlation graphs for continuous-parameter time series." arXiv (2024)

Statistical Graph Signal Processing: Stationarity and Spectral Estimation [chapter]

Santiago Segarra, Sundeep Prabhakar Chepuri, Antonio G. Marques, Geert Leus
2018 Cooperative and Graph Signal Processing  

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Stationary graph processes are also characterized by a power spectral density (PSD) and this chapter provides a rigorous treatment of various PSD estimators, including nonparametric and parametric methods  ...  POWER SPECTRAL DENSITY ESTIMATORS We can exploit the fact that x is a stationary graph process in S = Vdiag( )V H to design efficient estimators of the covariance C x .  ... 
doi:10.1016/b978-0-12-813677-5.00012-2 fatcat:muflnsb4wjc6xbckyij4i4wbki
Citation

Santiago Segarra, Sundeep Prabhakar Chepuri, Antonio G. Marques, Geert Leus. "Statistical Graph Signal Processing: Stationarity and Spectral Estimation." Cooperative and Graph Signal Processing (2018) 325-347

Subsampling for graph power spectrum estimation

Sundeep Prabhakar Chepuri, Geert Leus
2016 2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)  

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Estimating the graph power spectrum forms a central component of stationary graph signal processing and related inference tasks.  ...  Second-order stationary graph signals are obtained by filtering white noise and they admit a well-defined power spectrum.  ...  In particular, we have focused on subsampling stationary graph signals for estimating the power spectral density.  ... 
doi:10.1109/sam.2016.7569707 dblp:conf/ieeesam/ChepuriL16 fatcat:hfpvtnmqxfeknmjweenbpxjz6m
Citation

Sundeep Prabhakar Chepuri, Geert Leus. "Subsampling for graph power spectrum estimation." 2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM) (2016) 1-5

BASES AND SCIENTIFIC-TECHNICAL AND APPLIED ASPECTS OF PROCESSING OF RHYTHMOCARDIOSIGNALS

Evheniya Yavorska
2017 Figshare  

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Methods of digital processing of rhythmocardiograms are developed and verification of the results had been made.  ...  Expressions of estimations of rhythmocardiogram characteristics are obtained and digital methods of their evaluation in the biomedical systems are developed.  ...  In Fig. 2 shows the graphs of the ensemble of the power spectral density of the stationary test The probability D p of a probable estimate of the power spectral density of a non-stationary test RCG:  ... 
doi:10.6084/m9.figshare.5230321 fatcat:u4jjt3vgz5e7ffqblxctjt2x44
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Citation

Evheniya Yavorska. "BASES AND SCIENTIFIC-TECHNICAL AND APPLIED ASPECTS OF PROCESSING OF RHYTHMOCARDIOSIGNALS." Figshare (2017)

Stationary Signal Processing on Graphs

Nathanael Perraudin, Pierre Vandergheynst
2017 IEEE Transactions on Signal Processing  

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2017 accepted
arXiv:1601.02522v5 fatcat:s7iudjwjqvbbba4gswcpfyxm6y
2016 pre-print
arXiv:1601.02522v1 fatcat:vktssonisnaa7clon6qveulf5q
2016 pre-print
arXiv:1601.02522v3 fatcat:4zhfistgfzhxtmpzmjuojduiku
2016 pre-print
arXiv:1601.02522v2 fatcat:h3ydkczaqfg2nbohs3ddpszo3i
2016 pre-print
arXiv:1601.02522v4 fatcat:xbsevavksrabzmwjutopciqlqa
We prove that stationary graph signals are characterized by a well-defined Power Spectral Density that can be efficiently estimated even for large graphs.  ...  Graphs are a central tool in machine learning and information processing as they allow to conveniently capture the structure of complex datasets.  ...  This work has been supported by the Swiss National Science Foundation research project Towards Signal Processing on Graphs, grant number: 2000_21/154350/1.  ... 
doi:10.1109/tsp.2017.2690388 fatcat:66biiwl65za7tdrip5j7rq3npu
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Nathanael Perraudin, Pierre Vandergheynst. "Stationary Signal Processing on Graphs." IEEE Transactions on Signal Processing 65.13 (2017) 3462-3477

Hypergraph Spectral Analysis and Processing in 3D Point Cloud [article]

Songyang Zhang, Shuguang Cui, Zhi Ding
2020 arXiv   pre-print

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We further evaluate the efficacy of hypergraph spectrum estimation in two common point cloud applications of sampling and denoising for which also we elaborate specific hypergraph filter design and spectral  ...  We introduce tensor-based methods to estimate hypergraph spectrum components and frequency coefficients of point clouds in both ideal and noisy settings.  ...  Furthermore, [18] introduces a method to estimate the graph spectrum space and graph diffusion for multiple observations based on the graph stationary process.  ... 
arXiv:2001.02384v1 fatcat:7wz4v3s5tbgrrpxjyfiwvnd7da
Citation

Songyang Zhang, Shuguang Cui, Zhi Ding. "Hypergraph Spectral Analysis and Processing in 3D Point Cloud." arXiv (2020)

Graph Sampling for Covariance Estimation [article]

Sundeep Prabhakar Chepuri, Geert Leus
2017 arXiv   pre-print

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Estimating the graph power spectrum forms an important component of stationary graph signal processing and related inference tasks such as Wiener prediction or inpainting on graphs.  ...  subsampled observations, and more importantly, without any spectral priors.  ...  We are interested in sampling and processing stationary graph signals, which are stochastic signals defined on graphs with second-order statistics that are invariant similar to time series, but in the  ... 
arXiv:1704.07661v1 fatcat:zqntirv6czaqrhr3yne55w5whe
Citation

Sundeep Prabhakar Chepuri, Geert Leus. "Graph Sampling for Covariance Estimation." arXiv (2017)

Network topology inference from non-stationary graph signals

Rasoul Shafipour, Santiago Segarra, Antonio G. Marques, Gonzalo Mateos
2017 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  

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on these spectral templates to estimate the eigenvalues by imposing desirable properties on the graph to be recovered.  ...  Different from the stationary setting where the GSO and the covariance matrix of the observed signals are simultaneously diagonalizable, here they are not.  ...  As a result, the novel approach is to first identify the GSO eigenvectors from a judicious graph filter estimate, and then we rely on these spectral templates to estimate the eigenvalues by imposing desirable  ... 
doi:10.1109/icassp.2017.7953282 dblp:conf/icassp/ShafipourSMM17 fatcat:6eiuhopxvjcdzlr3ju43at2b3i
Citation

Rasoul Shafipour, Santiago Segarra, Antonio G. Marques, Gonzalo Mateos. "Network topology inference from non-stationary graph signals." 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2017) 5870-5874

Supervised Graph-Based Processing for Sequential Transient Interference Suppression

Ronen Talmon, Israel Cohen, Sharon Gannot, Ronald R. Coifman
2012 IEEE Transactions on Audio, Speech, and Language Processing  

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In this paper, we present a supervised graph-based framework for sequential processing and employ it to the problem of transient interference suppression.  ...  We describe a graph construction using a noisy speech signal and training recordings of typical transients.  ...  They also thank the anonymous reviewers for their constructive comments and useful suggestions.  ... 
doi:10.1109/tasl.2012.2205243 fatcat:zzarsifuergp5ni7frqc7lbvwy
Citation

Ronen Talmon, Israel Cohen, Sharon Gannot, Ronald R. Coifman. "Supervised Graph-Based Processing for Sequential Transient Interference Suppression." IEEE Transactions on Audio, Speech, and Language Processing 20.9 (2012) 2528-2538

Towards a definition of local stationarity for graph signals

Benjamin Girault, Shrikanth S. Narayanan, Antonio Ortega
2017 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)  

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Finally, we take advantage of the knowledge of the spectrum of the atoms to give a new power spectrum estimator.  ...  We use this local power spectrum to characterize local stationarity and identify sources of non-stationarity through differences of local power spectrum.  ...  GRAPH SIGNAL PROCESSING We first state the concepts from graph signal processing that are used in this paper.  ... 
doi:10.1109/icassp.2017.7952935 dblp:conf/icassp/GiraultNO17 fatcat:yvj7oauarzdmpjwv4zh3jxigcu
Citation

Benjamin Girault, Shrikanth S. Narayanan, Antonio Ortega. "Towards a definition of local stationarity for graph signals." 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2017) 4139-4143

A Second Order Cumulant Spectrum Test That a Stochastic Process is Strictly Stationary and a Step Toward a Test for Graph Signal Strict Stationarity [article]

Denisa Roberts, Douglas Patterson
2020 arXiv   pre-print

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2018 pre-print
arXiv:1801.06727v1 fatcat:r6s5ij6yzfhtnhnxmws6ud3aem
Future areas of research include testing for strict stationarity of graph signals, with applications in learning convolutional neural networks on graphs, denoising, and inpainting.  ...  This article develops a statistical test for the null hypothesis of strict stationarity of a discrete time stochastic process in the frequency domain.  ...  Graph signal processing domain can lend mathematical tools such as spectral graph theory to handle the challenge.  ... 
arXiv:1801.06727v2 fatcat:nxmmco7norhphnclc6lpa5mfxu
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Denisa Roberts, Douglas Patterson. "A Second Order Cumulant Spectrum Test That a Stochastic Process is Strictly Stationary and a Step Toward a Test for Graph Signal Strict Stationarity." arXiv (2020)

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