Signal Processing on Signed Graphs: Fundamentals and Potentials

Dittrich, Thomas; Matz, Gerald

doi:10.1109/msp.2020.3014060

Cited by 14 publications

(16 citation statements)

References 31 publications

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“…Here, we use S to denote the general shift matrix and select Laplacian matrix as the shift matrix for the specific discussion in Section III and Section IV, since Laplacian matrix is one of most popular shift matrix [13]- [15]. Most of the conclusions in this paper, however, apply to other shift matrices (see Figure 4).…”

Section: Graphsmentioning

confidence: 99%

“…Signed graphs are widely used in social networks, in which case person support/oppose each other, recommendation networks (likes/dislikes), and biological networks (promote and inhibit relationships between neurons) [15], [28], [29]. This article studies the most simplest signed graphs with weights equal to 1 or −1 introduced by Harary [30] in 1953, to deal with social relations including disliking, indifference, and liking.…”

Section: B Signed Graphsmentioning

confidence: 99%

“…The Laplacian matrix of signed graphs is defined as L sign = D sign − W , where D sign = j |w ij |, i.e., the sum of the absolute weights of incident edges [15], [31]. Signed graphs have two categories: balanced and unbalanced graphs.…”

Section: B Signed Graphsmentioning

confidence: 99%

“…Let G be a connected signed graph, i.e., a graph whose non-zero edge weights can take positive and negative values. The following conditions are equivalent [15], [34], [35]:…”

Section: Appendix Amentioning

confidence: 99%

See 3 more Smart Citations

How likely is a random graph shift-enabled?

Chen,

Cheng,

Stankovic

et al. 2021

Preprint

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The shift-enabled property of an underlying graph is essential in designing distributed filters. This article discusses when a random graph is shift-enabled. In particular, popular graph models Erdős-Rényi (ER), Watts-Strogatz (WS), Barabási-Albert (BA) random graph are used, weighted and unweighted, as well as signed graphs. Our results show that the considered unweighted connected random graphs are shiftenabled with high probability when the number of edges is moderately high. However, very dense graphs, as well as fully connected graphs, are not shift-enabled. Interestingly, this behaviour is not observed for weighted connected graphs, which are always shift-enabled unless the number of edges in the graph is very low.

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Section: Graphsmentioning

confidence: 99%

Section: B Signed Graphsmentioning

confidence: 99%

Section: B Signed Graphsmentioning

confidence: 99%

“…Let G be a connected signed graph, i.e., a graph whose non-zero edge weights can take positive and negative values. The following conditions are equivalent [15], [34], [35]:…”

Section: Appendix Amentioning

confidence: 99%

See 2 more Smart Citations

How likely is a random graph shift-enabled?

Chen,

Cheng,

Stankovic

et al. 2021

Preprint

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show abstract

“…It is known in graph spectral theory [28] that balanced signed graphs have unique spectral properties [29]; for example, the signed graph Laplacian matrix [30] has eigenvalue 0 iff the corresponding signed graph is balanced. In contrast, extending the original GCT [10], GDPA [11] states that the Gershgorin disc left-ends of a similarity transform SMS −1 of graph Laplacian M to a balanced graph can be perfectly aligned at λ min (M).…”

Section: Related Workmentioning

confidence: 99%

Projection-free Graph-based Classifier Learning using Gershgorin Disc Perfect Alignment

Yang

Cheung

Tan

et al. 2021

Preprint

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In semi-supervised graph-based binary classifier learning, a subset of known labels xi are used to infer unknown labels, assuming that the label signal x is smooth with respect to a similarity graph specified by a Laplacian matrix. When restricting labels x i to binary values, the problem is NP-hard. While a conventional semidefinite programming (SDP) relaxation can be solved in polynomial time using, for example, the alternating direction method of multipliers (ADMM), the complexity of iteratively projecting a candidate matrix M onto the positive semi-definite (PSD) cone (M 0) remains high. In this paper, leveraging a recent linear algebraic theory called Gershgorin disc perfect alignment (GDPA), we propose a fast projection-free method by solving a sequence of linear programs (LP) instead. Specifically, we first recast the SDP relaxation to its SDP dual, where a feasible solution H 0 can be interpreted as a Laplacian matrix corresponding to a balanced signed graph sans the last node. To achieve graph balance, we split the last node into two that respectively contain the original positive and negative edges, resulting in a new Laplacian H. We repose the SDP dual for solution H, then replace the PSD cone constraint H 0 with linear constraints derived from GDPAsufficient conditions to ensure H is PSD-so that the optimization becomes an LP per iteration. Finally, we extract predicted labels from our converged LP solution H. Experiments show that our algorithm enjoyed a 40× speedup on average over the next fastest scheme while retaining comparable label prediction performance.Preprint. Under review.

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On Generalized Signature Graphs

Matz

2024

ICASSP 2024 - 2024 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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Signal Processing on Signed Graphs: Fundamentals and Potentials

Cited by 14 publications

References 31 publications

How likely is a random graph shift-enabled?

How likely is a random graph shift-enabled?

Projection-free Graph-based Classifier Learning using Gershgorin Disc Perfect Alignment

On Generalized Signature Graphs

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