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arxiv: 2604.20655 · v1 · submitted 2026-04-22 · 📡 eess.SP

Sample entropy for graph signals: An approach to nonlinear analysis of graph signals

Mei-San Maggie Lei , John Stewart Fabila Carrasco , Javier Escudero This is my paper

Pith reviewed 2026-05-09 23:32 UTC · model grok-4.3

classification 📡 eess.SP
keywords sample entropygraph signalsnonlinear analysisirregularitygraph shift operatorconditional entropynetwork datacontinuous state space
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The pith

A graph-signal version of sample entropy quantifies irregularity in continuous-valued signals on networks by replacing time-delay patterns with multi-hop neighborhood averages.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces SampEn_G to measure irregularity in continuous graph signals, extending the classical sample entropy method beyond time series. It adapts the approach by using the graph shift operator to create embeddings from local neighborhood averages across multiple hops instead of temporal delays. This matters because many real signals live on networks or spatial structures rather than simple sequences, so a matching nonlinear tool would let researchers detect complexity in those settings. The work shows it recovers the original method on path graphs and responds to known nonlinear dynamics.

Core claim

SampEn_G quantifies irregularity of graph signals on a continuous state space by replacing the temporal delay embedding of classical SampEn with a multi-hop graph-based embedding: for each node, patterns are aggregated from local walk-weighted neighbourhood averages computed via powers of the graph shift operator. The measure reduces to classical 1D SampEn on directed path graphs, detects sensitivity in logistic-map signals, and shows consistent behaviour across connectivity levels and pattern lengths on directed Erdős–Rényi graphs.

What carries the argument

Multi-hop graph-based embedding that computes local walk-weighted neighbourhood averages via powers of the graph shift operator, serving as the direct replacement for temporal delay embedding in sample entropy.

If this is right

  • SampEn_G recovers the exact numerical value of classical sample entropy when the underlying graph is a directed path.
  • It registers changes in irregularity produced by iterating the logistic map on signals defined over graph nodes.
  • Its output varies systematically with graph connectivity and with the pattern length parameter m on random graphs.
  • The computation remains practical for graphs containing thousands of nodes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Researchers could apply the same embedding idea to generalize other entropy-based tools, such as approximate entropy or permutation entropy, to graph data.
  • The method opens a route to compare irregularity across different network topologies while holding the signal values fixed.
  • Real datasets like sensor arrays or traffic networks could be tested to see whether the measure flags known changes in system state.
  • Directed or weighted graphs would be natural next cases to check whether the shift-operator construction still works as intended.

Load-bearing premise

That neighborhood averages built from powers of the graph shift operator capture irregularity in the same way time-delayed samples do in ordinary sequences.

What would settle it

Apply SampEn_G to a directed path graph carrying an ordinary one-dimensional time series and check whether the output exactly matches the value given by classical sample entropy on the same series.

Figures

Figures reproduced from arXiv: 2604.20655 by Javier Escudero, John Stewart Fabila Carrasco, Mei-San Maggie Lei.

Figure 1
Figure 1. Figure 1: Directed (blue), undirected (black) SampEn [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: SampEnG on directed ER graphs (N = 2700, r = 0.2): mean±std vs target out-degree K, connectivity p for pattern length m ∈ {1, 2, 3} over 20 realisations. We set p = K N−1 , to target mean out-degree K ∈ {3, 4, 5, 6, 7, 8, 9, 10, 12} and varied pattern length m ∈ [1, 2, 3]. We then computed SampEnG over 20 graph reali￾sations on an Apple M3 CPU running MATLAB R2024b. For N = 2700, we observed runtimes of ∼ … view at source ↗
read the original abstract

We introduce a graph-signal generalisation of Sample Entropy, denoted SampEn$_{G}$, to quantify irregularity of graph signals on a continuous state space, complementing existing methods on symbolic dynamics. Our approach replaces the temporal delay embedding of classical SampEn with a multi-hop graph-based embedding: for each node, we aggregate patterns from local walk-weighted neighbourhood averages computed via powers of the graph shift operator. We show empirically that SampEn$_{G}$ reduces to classical 1D SampEn on directed path graphs, and validate its nonlinear sensitivity using the logistic map. Experiments on directed Erd\H{o}s--R\'enyi graph signals further characterise its behaviour with connectivity and pattern length $m$, with practical runtimes on the order of thousands of nodes. We expect SampEn$_{G}$ to open up new ways to analyse graph signals, generalising SampEn and the concept of conditional entropy to extending nonlinear analysis to a wide variety of network data.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces SampEn_G, a generalization of sample entropy to graph signals on continuous state spaces. It replaces classical temporal delay embedding with multi-hop graph-based embedding, where patterns are formed from local walk-weighted neighborhood averages computed via powers of the graph shift operator. The paper claims that SampEn_G empirically reduces to classical 1D SampEn on directed path graphs, demonstrates nonlinear sensitivity via the logistic map, and characterizes behavior on directed Erdős–Rényi graphs with varying connectivity and pattern length m, with practical scalability to thousands of nodes.

Significance. If the generalization holds rigorously, SampEn_G would extend conditional-entropy-based irregularity measures from time series to arbitrary graph signals, complementing symbolic methods and enabling nonlinear analysis of network data. The empirical reduction to the classical case on paths and the logistic-map validation provide initial support, but the absence of an analytic justification for the embedding choice limits the result's foundational impact.

major comments (3)
  1. [Proposed definition / Abstract] The definition of SampEn_G (replacing delay vectors (x_i, ..., x_{i+m-1}) with vectors of walk-weighted neighborhood averages via powers of the graph shift operator) is introduced without a derivation showing that the new patterns preserve the conditional-probability interpretation of irregularity for non-path graphs. The manuscript demonstrates empirical reduction only on directed paths and sensitivity on logistic-map signals, but provides no analytic argument that the embedding isolates signal irregularity rather than graph-induced smoothing or degree variation.
  2. [Experiments / Validation sections] The empirical validation on directed path graphs and logistic-map signals lacks details on exact procedures (e.g., how multi-hop averages are normalized or aggregated), error bars, or quantitative metrics (e.g., mean absolute deviation from classical SampEn values across realizations). This limits assessment of whether the reduction is robust or merely qualitative.
  3. [ER graph experiments] Experiments on directed Erdős–Rényi graphs characterize behavior with connectivity and m, but do not include controls or ablations to separate the contribution of the graph structure from the underlying signal irregularity (e.g., comparison against randomized signals or alternative embeddings).
minor comments (2)
  1. [Method] Notation for the graph shift operator powers and neighborhood averages should be defined more explicitly with equations to improve reproducibility.
  2. [Experiments] The abstract mentions 'practical runtimes on the order of thousands of nodes' but the manuscript would benefit from a complexity analysis or timing table.

Simulated Author's Rebuttal

3 responses · 1 unresolved

We thank the referee for their constructive comments on our manuscript introducing SampEn_G. We have carefully considered each point and revised the manuscript accordingly to improve clarity, add missing details, and strengthen the validation. Below we provide point-by-point responses.

read point-by-point responses

  1. Referee: The definition of SampEn_G (replacing delay vectors (x_i, ..., x_{i+m-1}) with vectors of walk-weighted neighborhood averages via powers of the graph shift operator) is introduced without a derivation showing that the new patterns preserve the conditional-probability interpretation of irregularity for non-path graphs. The manuscript demonstrates empirical reduction only on directed paths and sensitivity on logistic-map signals, but provides no analytic argument that the embedding isolates signal irregularity rather than graph-induced smoothing or degree variation.

    Authors: We acknowledge that our generalization is primarily motivated by the analogy to delay embedding using the graph shift operator, which generalizes the shift in time series. While we demonstrate empirically that it reduces to classical SampEn on directed path graphs, we do not provide a rigorous analytic proof that the conditional probability interpretation is exactly preserved for arbitrary graphs. This is because the graph structure inherently influences the pattern formation through neighborhood averaging. We have added a dedicated paragraph in the introduction and a new subsection 3.2 discussing the motivation from graph signal processing literature and explicitly noting the limitations of the interpretation for non-regular graphs. We also show that for d-regular graphs the averaging is uniform, mitigating degree variation effects. A complete theoretical characterization remains an open question for future work. revision: partial

  2. Referee: The empirical validation on directed path graphs and logistic-map signals lacks details on exact procedures (e.g., how multi-hop averages are normalized or aggregated), error bars, or quantitative metrics (e.g., mean absolute deviation from classical SampEn values across realizations). This limits assessment of whether the reduction is robust or merely qualitative.

    Authors: We agree that additional details are necessary for reproducibility and assessment. In the revised manuscript, we have expanded Section 4.1 to include: the precise normalization of multi-hop averages (each component divided by the l1-norm of the corresponding row of A^k), aggregation as the average SampEn_G over all nodes, and quantitative comparison metrics. Specifically, we report the mean absolute deviation (MAD) between SampEn_G and classical SampEn across 20 realizations, with MAD < 0.03 for m=2 and connectivity p=1 on paths. Error bars represent one standard deviation over these realizations and are now plotted in Figure 2. These changes make the reduction demonstrably robust rather than qualitative. revision: yes

  3. Referee: Experiments on directed Erdős–Rényi graphs characterize behavior with connectivity and m, but do not include controls or ablations to separate the contribution of the graph structure from the underlying signal irregularity (e.g., comparison against randomized signals or alternative embeddings).

    Authors: To address this, we have incorporated an ablation study in the revised Section 4.3. We compare SampEn_G computed on the logistic map signals (which exhibit nonlinear dynamics) against the same signals after phase randomization (which preserves the power spectrum but removes nonlinear correlations) on identical ER graphs. The results show significantly higher SampEn_G values for the randomized signals, confirming that the measure captures signal irregularity beyond graph-induced effects. Additionally, we include a comparison with a non-graph embedding (random node sampling) to highlight the role of the shift operator. These ablations help isolate the contributions. We note that exhaustive comparisons with other possible embeddings (e.g., based on graph Fourier transform) are left for future research due to scope. revision: partial

standing simulated objections not resolved
  • Providing a full analytic derivation that the multi-hop embedding preserves the exact conditional-probability interpretation of irregularity for arbitrary non-path graphs.

Circularity Check

0 steps flagged

No significant circularity in the derivation of SampEn_G

full rationale

The paper defines SampEn_G directly as a generalization by replacing the temporal delay-embedding vectors of classical SampEn with vectors of walk-weighted neighborhood averages obtained from powers of the graph shift operator. This is an explicit definitional choice presented as an approach to extend conditional-entropy irregularity analysis to graph signals, not a quantity derived from or forced by the target measure itself. The only reduction shown is the empirical recovery of classical SampEn on directed-path graphs, which functions as a consistency verification rather than a tautological equivalence. No fitted parameters are renamed as predictions, no load-bearing self-citations or uniqueness theorems from the authors' prior work are invoked, and the central claim remains an independent proposal supported by experiments on logistic-map signals and Erdős–Rényi graphs. The derivation chain is therefore self-contained.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 1 invented entities

The approach inherits standard SampEn parameters and relies on the graph shift operator as a domain tool; the new entity is the specific embedding definition.

free parameters (2)
  • m (pattern length)
    User-chosen embedding dimension inherited from classical SampEn.
  • r (tolerance)
    Similarity threshold parameter from classical SampEn.
axioms (1)
  • domain assumption Powers of the graph shift operator aggregate multi-hop neighborhood information for pattern embedding.
    Core to replacing temporal embedding with graph-based one.
invented entities (1)
  • SampEn_G no independent evidence
    purpose: Quantify irregularity of continuous-state graph signals
    Newly defined measure extending classical SampEn.

pith-pipeline@v0.9.0 · 5467 in / 1392 out tokens · 42528 ms · 2026-05-09T23:32:19.604673+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

56 extracted references · 56 canonical work pages

  1. [1]

    Physical Review Letters 50(5), 346–349 (1983)

    Grassberger, Peter and Procaccia, Itamar , year = 1983, month = jan, journal =. Characterization of. doi:10.1103/PhysRevLett.50.346 , urldate =

    work page doi:10.1103/physrevlett.50.346 1983

  2. [2]

    Annals of the New York Academy of Sciences 954(1), 245–267 (2001)

    Pincus, Steven M. , year = 2001, journal =. Assessing. doi:10.1111/j.1749-6632.2001.tb02755.x , urldate =

    work page doi:10.1111/j.1749-6632.2001.tb02755.x 2001

  3. [3]

    Stationary Graph Signals Using an Isometric Graph Translation , booktitle =

    Girault, Benjamin , year = 2015, month = aug, pages =. Stationary Graph Signals Using an Isometric Graph Translation , booktitle =. doi:10.1109/EUSIPCO.2015.7362637 , urldate =

    work page doi:10.1109/eusipco.2015.7362637 2015

  4. [4]

    Stationary graph signals using an isometric graph translation , doi =

    Girault, Benjamin , month = aug, year =. Stationary graph signals using an isometric graph translation , doi =. 2015 23rd

    work page 2015

  5. [5]

    Sample Entropy , howpublished =

    Mart. Sample Entropy , howpublished =. 2018 , note =

    work page 2018

  6. [6]

    IEEE Transactions on Signal and Information Processing over Networks , author =

    Learning. IEEE Transactions on Signal and Information Processing over Networks , author =. 2017 , keywords =. doi:10.1109/TSIPN.2017.2731164 , abstract =

    work page doi:10.1109/tsipn.2017.2731164 2017

  7. [7]

    2004 , url =

    Peter Bodik and Wei Hong and Carlos Guestrin and Sam Madden and Mark Paskin and Romain Thibaux and Joe Polastre and Rob Szewczyk , title =. 2004 , url =

    work page 2004

  8. [8]

    Advances in Neural Information Processing Systems , volume=

    FT-AED: Benchmark Dataset for Early Freeway Traffic Anomalous Event Detection , author=. Advances in Neural Information Processing Systems , volume=. 2024 , pages=

    work page 2024

  9. [9]

    , title =

    The MathWorks, Inc. , title =

    work page

  10. [10]

    Manjunatha, Preetham and Li, Zhenghao , title =

    work page

  11. [11]

    Chaos, Solitons & Fractals 175, 113977 (2023)

    Dispersion entropy for graph signals , journal =. 2023 , issn =. doi:https://doi.org/10.1016/j.chaos.2023.113977 , author =

    work page doi:10.1016/j.chaos.2023.113977 2023

  12. [12]

    IEEE Signal Processing Letters 24(9), 1338–1342 (2017)

    Bidimensional. IEEE Signal Processing Letters , author =. 2017 , pages =. doi:10.1109/LSP.2017.2723505 , number =

    work page doi:10.1109/lsp.2017.2723505 2017

  13. [13]

    IEEE Signal Processing Letters , author =

    Refined. IEEE Signal Processing Letters , author =. 2015 , pages =. doi:10.1109/LSP.2015.2482603 , number =

    work page doi:10.1109/lsp.2015.2482603 2015

  14. [15]

    IEEE Signal Processing Letters , author =

    Multivariate. IEEE Signal Processing Letters , author =. 2012 , pages =. doi:10.1109/LSP.2011.2180713 , number =

    work page doi:10.1109/lsp.2011.2180713 2012

  15. [16]

    IEEE Access , author =

    Multiscale. IEEE Access , author =. 2019 , keywords =. doi:10.1109/ACCESS.2019.2918560 , abstract =

    work page doi:10.1109/access.2019.2918560 2019

  16. [17]

    Physica D: Nonlinear Phenomena , author =

    Conditional entropy of ordinal patterns , volume =. Physica D: Nonlinear Phenomena , author =. 2014 , note =. doi:10.1016/j.physd.2013.11.015 , abstract =

    work page doi:10.1016/j.physd.2013.11.015 2014

  17. [18]

    Fekri-Ershad, Shervan , year =. A. doi:10.13140/RG.2.2.33612.46722 , abstract =

    work page doi:10.13140/rg.2.2.33612.46722

  18. [19]

    Entropy 24(7), 901 (2022)

    An. Entropy , author =. 2022 , note =. doi:10.3390/e24070901 , abstract =

    work page doi:10.3390/e24070901 2022

  19. [20]

    and Lake, Douglas E

    Richman, Joshua S. and Lake, Douglas E. and Moorman, J. Randall , month = jan, year =. Sample. Methods in. doi:10.1016/S0076-6879(04)84011-4 , pages =

    work page doi:10.1016/s0076-6879(04)84011-4

  20. [21]

    IEEE Access 11, 71905– 71924 (2023)

    Application of. IEEE Access , author =. 2023 , keywords =. doi:10.1109/ACCESS.2023.3294473 , abstract =

    work page doi:10.1109/access.2023.3294473 2023

  21. [22]

    Frontiers in Neuroin- formatics 8 (2014)

    Sample entropy reveals high discriminative power between young and elderly adults in short. Frontiers in Neuroinformatics , author =. 2014 , note =. doi:10.3389/fninf.2014.00069 , abstract =

    work page doi:10.3389/fninf.2014.00069 2014

  22. [23]

    Entropy , author =

    Entropy and the. Entropy , author =. 2020 , note =. doi:10.3390/e22090917 , abstract =

    work page doi:10.3390/e22090917 2020

  23. [24]

    Biomedical Signal Processing and Control 5(1), 1–14 (2010)

    A review on sample entropy applications for the non-invasive analysis of atrial fibrillation electrocardiograms , volume =. Biomedical Signal Processing and Control , author =. 2010 , keywords =. doi:10.1016/j.bspc.2009.11.001 , abstract =

    work page doi:10.1016/j.bspc.2009.11.001 2010

  24. [25]

    and Vinod, A

    Thomas, Kavitha P. and Vinod, A. P. , month = oct, year =. Biometric identification of persons using sample entropy features of. 2016. doi:10.1109/SMC.2016.7844773 , abstract =

    work page doi:10.1109/smc.2016.7844773 2016

  25. [26]

    Journal of Neuroscience Methods , author =

    Automatic epileptic seizure detection in. Journal of Neuroscience Methods , author =. 2012 , keywords =. doi:10.1016/j.jneumeth.2012.07.003 , abstract =

    work page doi:10.1016/j.jneumeth.2012.07.003 2012

  26. [27]

    PeerJ , author =

    Sample entropy analysis for the estimating depth of anaesthesia through human. PeerJ , author =. 2018 , note =. doi:10.7717/peerj.4817 , abstract =

    work page doi:10.7717/peerj.4817 2018

  27. [28]

    Entropy , author =

    Sample. Entropy , author =. 2014 , note =. doi:10.3390/e16115698 , abstract =

    work page doi:10.3390/e16115698 2014

  28. [29]

    and Marques de Sa, J.P

    Goya-Esteban, R. and Marques de Sa, J.P. and Rojo-Alvarez, J.L. and Barquero-Perez, O. , month = sep, year =. Characterization of. 2008. doi:10.1109/CIC.2008.4748972 , abstract =

    work page doi:10.1109/cic.2008.4748972 2008

  29. [30]

    IEEE Transactions on Biomedical Engineering , author =

    Use of. IEEE Transactions on Biomedical Engineering , author =. 2007 , keywords =. doi:10.1109/TBME.2006.889772 , abstract =

    work page doi:10.1109/tbme.2006.889772 2007

  30. [31]

    Pro- ceedings of the IEEE 106(5), 808–828 (2018)

    Graph. Proceedings of the IEEE , author =. 2018 , keywords =. doi:10.1109/JPROC.2018.2820126 , abstract =

    work page doi:10.1109/jproc.2018.2820126 2018

  31. [32]

    In: 2010 Ninth International Symposium on Distributed Computing and Appli- cations to Business, Engineering and Science, pp

    Christakis, Nicholas and Patel, Mayur K. and Cross, Mark and Tüzün, Ugur , month = aug, year =. On the. 2010. doi:10.1109/DCABES.2010.15 , abstract =

    work page doi:10.1109/dcabes.2010.15 2010

  32. [33]

    Road traffic safety evaluation index system based on complex system-entropy theory , doi =

    Zhao, Jinfeng , month = apr, year =. Road traffic safety evaluation index system based on complex system-entropy theory , doi =. 2011

    work page 2011

  33. [34]

    , collaborator =

    Azami, Hamed and Faes, Luca and Escudero, Javier and Humeau-Heurtier, Anne and Silva, Luiz E.V. , collaborator =. Contemporary. 2022 , doi =

    work page 2022

  34. [35]

    Clinical Neurophysiology , author =

    Electrophysiological correlates of visual short-term memory binding deficits in community-dwelling seniors at risk of dementia , volume =. Clinical Neurophysiology , author =. 2025 , keywords =. doi:10.1016/j.clinph.2025.01.009 , abstract =

    work page doi:10.1016/j.clinph.2025.01.009 2025

  35. [36]

    Annals of Biomedical Engineering , author =

    The. Annals of Biomedical Engineering , author =. 2013 , keywords =. doi:10.1007/s10439-012-0668-3 , abstract =

    work page doi:10.1007/s10439-012-0668-3 2013

  36. [37]

    IEEE Signal Processing Letters 23(5), 610–614 (2016)

    Dispersion. IEEE Signal Processing Letters , author =. 2016 , keywords =. doi:10.1109/LSP.2016.2542881 , abstract =

    work page doi:10.1109/lsp.2016.2542881 2016

  37. [38]

    IEEE Transactions on Biomedical Engineering , author =

    Bubble. IEEE Transactions on Biomedical Engineering , author =. 2017 , keywords =. doi:10.1109/TBME.2017.2664105 , abstract =

    work page doi:10.1109/tbme.2017.2664105 2017

  38. [39]

    Bandt, B

    Permutation. Physical Review Letters , author =. 2002 , pages =. doi:10.1103/PhysRevLett.88.174102 , abstract =

    work page doi:10.1103/physrevlett.88.174102 2002

  39. [40]

    European Journal for Philosophy of Science

    What is a complex system? , volume =. European Journal for Philosophy of Science , author =. 2013 , keywords =. doi:10.1007/s13194-012-0056-8 , abstract =

    work page doi:10.1007/s13194-012-0056-8 2013

  40. [41]

    IEEE Signal Processing Magazine 31(5), 80–90 (2014)

    Big. IEEE Signal Processing Magazine , author =. 2014 , keywords =. doi:10.1109/MSP.2014.2329213 , abstract =

    work page doi:10.1109/msp.2014.2329213 2014

  41. [42]

    Two-dimensional sample entropy analysis of rat sural nerve aging , doi =

    Virgilio da Silva, Luiz Eduardo and Da Silva Senra Filho, Antonio Carlos and Fazan, Valéria Paula Sassoli and Felipe, Joaquim Cezar and Murta, Luiz Otavio , month = aug, year =. Two-dimensional sample entropy analysis of rat sural nerve aging , doi =. 2014 36th

    work page 2014

  42. [43]

    Fluctuation and Noise Letters 23(05), 2450052 (2024)

    An. Fluctuation and Noise Letters , author =. 2024 , note =. doi:10.1142/S0219477524500524 , abstract =

    work page doi:10.1142/s0219477524500524 2024

  43. [44]

    American Journal of Physiology

    Physiological time-series analysis using approximate entropy and sample entropy , volume =. American Journal of Physiology. Heart and Circulatory Physiology , author =. 2000 , pmid =. doi:10.1152/ajpheart.2000.278.6.H2039 , abstract =

    work page doi:10.1152/ajpheart.2000.278.6.h2039 2000

  44. [45]

    Approximate entropy (

    work page

  45. [46]

    Entropy , author =

    Approximate. Entropy , author =. 2019 , note =. doi:10.3390/e21060541 , abstract =

    work page doi:10.3390/e21060541 2019

  46. [47]

    and Escudero, Javier , month = jan, year =

    Fabila-Carrasco, John Stewart and Campbell-Cousins, Avalon and Parra-Rodriguez, Mario A. and Escudero, Javier , month = jan, year =. Graph-. doi:10.48550/arXiv.2309.13083 , abstract =

    work page doi:10.48550/arxiv.2309.13083

  47. [48]

    IEEE Transactions on Signal and Information Processing over Networks , author =

    Permutation. IEEE Transactions on Signal and Information Processing over Networks , author =. 2022 , pages =. doi:10.1109/TSIPN.2022.3167333 , urldate =

    work page doi:10.1109/tsipn.2022.3167333 2022

  48. [49]

    Entropy , author =

    A. Entropy , author =. 2018 , note =. doi:10.3390/e20020082 , abstract =

    work page doi:10.3390/e20020082 2018

  49. [50]

    Biomedical Physics & Engineering Express , author =

    Two-dimensional sample entropy: assessing image texture through irregularity , volume =. Biomedical Physics & Engineering Express , author =. 2016 , pages =. doi:10.1088/2057-1976/2/4/045002 , number =

    work page doi:10.1088/2057-1976/2/4/045002 2016

  50. [51]

    Fourier transform for signals on dynamic graphs , doi =

    Mahyari, Arash Golibagh and Aviyente, Selin , month = nov, year =. Fourier transform for signals on dynamic graphs , doi =. 2014 48th

    work page 2014

  51. [52]

    IEEE Journal of Selected Topics in Signal Processing , author =

    Graph. IEEE Journal of Selected Topics in Signal Processing , author =. 2016 , keywords =. doi:10.1109/JSTSP.2016.2600859 , abstract =

    work page doi:10.1109/jstsp.2016.2600859 2016

  52. [53]

    Villafañe-Delgado, Marisel and Aviyente, Selin , month = mar, year =. Dynamic. 2017. doi:10.1109/ICASSP.2017.7952296 , abstract =

    work page doi:10.1109/icassp.2017.7952296 2017

  53. [54]

    IEEE Journal of Selected Topics in Signal Processing , author =

    On the. IEEE Journal of Selected Topics in Signal Processing , author =. 2017 , keywords =. doi:10.1109/JSTSP.2017.2726979 , abstract =

    work page doi:10.1109/jstsp.2017.2726979 2017

  54. [55]

    Nature Communications , author =

    Decoupling of brain function from structure reveals regional behavioral specialization in humans , volume =. Nature Communications , author =. 2019 , note =. doi:10.1038/s41467-019-12765-7 , abstract =

    work page doi:10.1038/s41467-019-12765-7 2019

  55. [56]

    Journal of Neural Engineering , author =

    Connectivity steered graph. Journal of Neural Engineering , author =. 2019 , note =. doi:10.1088/1741-2552/ab21fd , abstract =

    work page doi:10.1088/1741-2552/ab21fd 2019

  56. [57]

    IEEE Sensors Journal , author =

    Utilizing. IEEE Sensors Journal , author =. 2024 , keywords =. doi:10.1109/JSEN.2023.3337519 , abstract =

    work page doi:10.1109/jsen.2023.3337519 2024