Estimating Centrality Blindly From Low-Pass Filtered Graph Signals

He, Yiran; Wai, Hoi-To

doi:10.1109/icassp40776.2020.9053437

Cited by 16 publications

(16 citation statements)

References 31 publications

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“…Definition 1]. Notice that this is a sufficient condition to enable graph inference such as blind centrality estimation [14,15], as well as ensuring that the graph signal is smooth [10,11]. Formally, our task is to distinguish between the following two hypothesis: T0 : the graph filter H(S) is first-order lowpass T1 : the graph filter H(S) is not first-order lowpass (4) Note that T1 include highpass filters where Definition 1 is not satisfied for any K ∈ {1, ..., n}, as well as lowpass filters with a higher cutoff frequency at λK , K ≥ 2.…”

Section: Perron Frobenius Theorem and 1st-order Lowpass Filtermentioning

confidence: 99%

“…Inspired by the above, we model the COVID-19 data as a set of first-order lowpass graph signals (with outliers). Again, we can apply the blind centrality estimation method from [14,15] to rank the centrality of states. The results are illustrated in Fig.…”

Section: Numerical Experimentsmentioning

confidence: 99%

“…Our work is related to the recent developments in graph inference or learning which aim at learning the graph topology blindly This work is supported by CUHK Direct Grant #4055135. Emails: {yrhe,htwai}@se.cuhk.edu.hk [7,[10][11][12][13][14][15]. For instance, [10][11][12][13] infer topology from smooth graph signals which can be given by lowpass graph filtering, [7,14,15] consider blind inference of communities and centrality from lowpass graph signals; see [16,17].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Identifying First-Order Lowpass Graph Signals Using Perron Frobenius Theorem

Wai

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper is concerned with the blind identification of graph filters from graph signals. Our aim is to determine if the graph filter generating the graph signals is first-order lowpass without knowing the graph topology. Notice that lowpass graph filter is a common prerequisite for applying graph signal processing tools for sampling, denoising, and graph learning. Our method is inspired by the Perron Frobenius theorem, which observes that for first-order lowpass graph filter, the top eigenvector of output covariance would be the only eigenvector with elements of the same sign. Utilizing this observation, we develop a simple detector that answers if a given data set is produced by a first-order lowpass graph filter. We analyze the effects of finite-sample, graph size, observation noise, strength of lowpass filter, on the detector's performance. Numerical experiments on synthetic and real data support our findings.

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Section: Perron Frobenius Theorem and 1st-order Lowpass Filtermentioning

confidence: 99%

Section: Numerical Experimentsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Identifying First-Order Lowpass Graph Signals Using Perron Frobenius Theorem

Wai

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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“…To the best of our knowledge, TCEC sampling (Ruggeri and De Bacco 2020) is one of the first theoretical attempts in estimating eigenvalue centrality, which goes beyond heuristics or empirical reasoning. A closely related problem is that of estimating eigenvector centrality without observing any edge but only signals on nodes (Roddenberry and Segarra 2019;He and Wai 2020). A different but related research direction is to question the stability of centrality measures under perturbations (Segarra and Ribeiro 2015;Han and Lee 2016;Murai and Yoshida 2019).…”

Section: Related Workmentioning

confidence: 99%

Sampling on networks: estimating spectral centrality measures and their impact in evaluating other relevant network measures

Ruggeri

Bacco

2020

Appl Netw Sci

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We perform an extensive analysis of how sampling impacts the estimate of several relevant network measures. In particular, we focus on how a sampling strategy optimized to recover a particular spectral centrality measure impacts other topological quantities. Our goal is on one hand to extend the analysis of the behavior of TCEC (Ruggeri and De Bacco, in: Cherifi, Gaito, Mendes, Moro, Rocha (eds) Complex networks and their applications VIII, Springer, Cham, pp 90–101, 2020), a theoretically-grounded sampling method for eigenvector centrality estimation. On the other hand, to demonstrate more broadly how sampling can impact the estimation of relevant network properties like centrality measures different than the one aimed at optimizing, community structure and node attribute distribution. In addition, we analyze sampling behaviors in various instances of network generative models. Finally, we adapt the theoretical framework behind TCEC for the case of PageRank centrality and propose a sampling algorithm aimed at optimizing its estimation. We show that, while the theoretical derivation can be suitably adapted to cover this case, the resulting algorithm suffers of a high computational complexity that requires further approximations compared to the eigenvector centrality case. Main contributions (a) Extensive empirical analysis of the impact of the TCEC sampling method (optimized for eigenvector centrality recovery) on different centrality measures, community structure, node attributes and statistics related to specific network generative models; (b) extending TCEC to optimize PageRank estimation.

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“…Among others, the eigen-centrality is a popular centrality measure which assigns high importance to nodes that are connected to other important nodes. Recent works [7,8] suggested methods to estimate eigen-centrality blindly by only observing the graph signals on the graph.…”

Section: Introductionmentioning

confidence: 99%

Provably Fast Asynchronous And Distributed Algorithms For Pagerank Centrality Computation

Wai

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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This paper considers the PageRank centrality computation problem on large graphs. We study asynchronous and distributed algorithms which are operated by aggregating information from local neighbors iteratively. Unlike prior works which rely on stochastic gradient descent (SGD) applied on a least square objective, we derive a stochastic approximation (SA) scheme for solving the PageRank problem by discretizing a linear system of ordinary differential equations. Our approach results in a family of asynchronous and distributed algorithms applicable for fixed and random topologies. Convergence rates are analyzed for both settings. In the fixed topology setting, we prove that the SA-based PageRank algorithm converges faster than the prior SGD-based method for large graphs. Numerical experiments support our findings.

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Estimating Centrality Blindly From Low-Pass Filtered Graph Signals

Cited by 16 publications

References 31 publications

Identifying First-Order Lowpass Graph Signals Using Perron Frobenius Theorem

Identifying First-Order Lowpass Graph Signals Using Perron Frobenius Theorem

Sampling on networks: estimating spectral centrality measures and their impact in evaluating other relevant network measures

Provably Fast Asynchronous And Distributed Algorithms For Pagerank Centrality Computation

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