An introduction to hypergraph signal processing

Barbarossa, Sergio; Tsitsvero, Mikhail

doi:10.1109/icassp.2016.7472914

Cited by 47 publications

(48 citation statements)

References 18 publications

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“…3 shows inferred traffic flows on the Minnesota road network. 3 Consistent results are obtained with other accuracy metrics, e.g., the relative L 2 error. Figure 5: Graph-based SSL for real-world traffic flows.…”

Section: Learning Synthetic Edge Flowssupporting

confidence: 71%

Graph-based Semi-Supervised & Active Learning for Edge Flows

Jia

Segarra

Benson

2019

Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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We present a graph-based semi-supervised learning (SSL) method for learning edge flows defined on a graph. Specifically, given flow measurements on a subset of edges, we want to predict the flows on the remaining edges. To this end, we develop a computational framework that imposes certain constraints on the overall flows, such as (approximate) flow conservation. These constraints render our approach different from classical graph-based SSL for vertex labels, which posits that tightly connected nodes share similar labels and leverages the graph structure accordingly to extrapolate from a few vertex labels to the unlabeled vertices.We derive bounds for our method's reconstruction error and demonstrate its strong performance on synthetic and real-world flow networks from transportation, physical infrastructure, and the Web. Furthermore, we provide two active learning algorithms for selecting informative edges on which to measure flow, which has applications for optimal sensor deployment. The first strategy selects edges to minimize the reconstruction error bound and works well on flows that are approximately divergence-free. The second approach clusters the graph and selects bottleneck edges that cross cluster-boundaries, which works well on flows with global trends.

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Section: Learning Synthetic Edge Flowssupporting

confidence: 71%

Graph-based Semi-Supervised & Active Learning for Edge Flows

Jia

Segarra

Benson

2019

Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery &Amp; Data Mining

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“…Furthermore, we believe that graph representations are only the beginning of the story, as they are built incorporating only pairwise relations. More sophisticated tools may be envisaged by enlarging the horizon to include multi-way relations, using for example simplicial complexes or hypergraphs, as suggested in [54], or multilayer network representations [55], [56]. Furthermore, in this work, we have basically restricted our attention to time-invariant graph representations and to linear models.…”

Section: Discussionmentioning

confidence: 99%

The Edge Cloud: A Holistic View of Communication, Computation, and Caching

Barbarossa

Sardellitti

Ceci

et al. 2018

Cooperative and Graph Signal Processing

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The evolution of communication networks shows a clear shift of focus from just improving the communications aspects to enabling new important services, from Industry 4.0 to automated driving, virtual/augmented reality, Internet of Things (IoT), and so on. This trend is evident in the roadmap planned for the deployment of the fifth generation (5G) communication networks. This ambitious goal requires a paradigm shift towards a vision that looks at communication, computation and caching (3C) resources as three components of a single holistic system. The further step is to bring these 3C resources closer to the mobile user, at the edge of the network, to enable very low latency and high reliability services. The scope of this chapter is to show that signal processing techniques can play a key role in this new vision. In particular, we motivate the joint optimization of 3C resources. Then we show how graph-based representations can play a key role in building effective learning methods and devising innovative resource allocation techniques.

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“…Fewer works have been done by using hypergraphs : hypergraphs can be seen as generalization of “plain graphs” where hyperedges can connect two or more nodes. In other words, hypergraphs extend the modeling capabilities offered by graphs ( Section 1 ) in cases where multi-way relations are of interest; indeed, graphs take into account only pairwise relations [ 55 , 56 , 57 , 58 , 59 ]. A straightforward example may regard a scientific collaboration network in which n authors co-authored a paper: if one has to model this scenario using a graph, then one might consider nodes as authors which are connected by

edges.…”

Section: Related Work On Graph Kernelsmentioning

confidence: 99%

(Hyper)graph Kernels over Simplicial Complexes

Martino

2020

Entropy

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Graph kernels are one of the mainstream approaches when dealing with measuring similarity between graphs, especially for pattern recognition and machine learning tasks. In turn, graphs gained a lot of attention due to their modeling capabilities for several real-world phenomena ranging from bioinformatics to social network analysis. However, the attention has been recently moved towards hypergraphs, generalization of plain graphs where multi-way relations (other than pairwise relations) can be considered. In this paper, four (hyper)graph kernels are proposed and their efficiency and effectiveness are compared in a twofold fashion. First, by inferring the simplicial complexes on the top of underlying graphs and by performing a comparison among 18 benchmark datasets against state-of-the-art approaches; second, by facing a real-world case study (i.e., metabolic pathways classification) where input data are natively represented by hypergraphs. With this work, we aim at fostering the extension of graph kernels towards hypergraphs and, more in general, bridging the gap between structural pattern recognition and the domain of hypergraphs.

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An introduction to hypergraph signal processing

Cited by 47 publications

References 18 publications

Graph-based Semi-Supervised & Active Learning for Edge Flows

Graph-based Semi-Supervised & Active Learning for Edge Flows

The Edge Cloud: A Holistic View of Communication, Computation, and Caching

(Hyper)graph Kernels over Simplicial Complexes

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