Spectral Alignment of Graphs

Feizi, Soheil; Quon, Gerald; Recamonde‐Mendoza, Mariana; Médard, Muriel; Kellis, M; Jadbabaie, Ali

doi:10.1109/tnse.2019.2913233

Cited by 44 publications

(38 citation statements)

References 85 publications

(167 reference statements)

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“…Obviously, this leads to loss of performance in LRM. Also, it can be inferred that if, in a real multiplex network, the multiplexity of layers is unknown at first, then an initial phase of network alignment [45] is helpful for finding the right one-to-one mapping of nodes. Then, LRM works if layers show enough similarity w.r.t.…”

Section: Discussionmentioning

confidence: 99%

Link prediction in real-world multiplex networks via layer reconstruction method

et al. 2020

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Networks are invaluable tools to study real biological, social and technological complex systems in which connected elements form a purposeful phenomenon. A higher resolution image of these systems shows that the connection types do not confine to one but to a variety of types. Multiplex networks encode this complexity with a set of nodes which are connected in different layers via different types of links. A large body of research on link prediction problem is devoted to finding missing links in single-layer (simplex) networks. In recent years, the problem of link prediction in multiplex networks has gained the attention of researchers from different scientific communities. Although most of these studies suggest that prediction performance can be enhanced by using the information contained in different layers of the network, the exact source of this enhancement remains obscure. Here, it is shown that similarity w.r.t. structural features (eigenvectors) is a major source of enhancements for link prediction task in multiplex networks using the proposed layer reconstruction method and experiments on real-world multiplex networks from different disciplines. Moreover, we characterize how low values of similarity w.r.t. structural features result in cases where improving prediction performance is substantially hard.

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Section: Discussionmentioning

confidence: 99%

Link prediction in real-world multiplex networks via layer reconstruction method

et al. 2020

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“…We first introduce, in Section 2, the graph Jaccard index (GJI), a natural objective function for the network alignment problem. For a given alignment, the GJI rewards correct matches while simultaneously penalizing mismatches, overcoming limitations of previous approaches (Feizi et al, 2019).…”

Section: The Construction Of a Mapping Between Network Nodes Correspomentioning

confidence: 99%

Network alignment and similarity reveal atlas-based topological differences in structural connectomes

Frigo¹,

Cruciani

Coudert

et al. 2020

Preprint

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The interactions between different brain regions can be modeled as a graph, called connectome, whose nodes correspond to parcels from a predefined brain atlas. The edges of the graph encode the strength of the axonal connectivity between regions of the atlas which can be estimated via diffusion Magnetic Resonance Imaging (MRI) tractography. Herein, we aim at providing a novel perspective on the problem of choosing a suitable atlas for structural connectivity studies by assessing how robustly an atlas captures the network topology across different subjects in a homogeneous cohort. We measure this robustness by assessing the alignability of the connectomes, namely the possibility to retrieve graph matchings that provide highly similar graphs. We introduce two novel concepts. First, the graph Jaccard index (GJI), a graph similarity measure based on the well-established Jaccard index between sets; the GJI exhibits natural mathematical properties that are not satisfied by previous approaches. Second, we devise WL-align, a new technique for aligning connectomes obtained by adapting the Weisfeiler-Lehman (WL) graph-isomorphism test. We validated the GJI and WL-align on data from the Human Connectome Project database, inferring a strategy for choosing a suitable parcellation for structural connectivity studies. Code and data are publicly available.

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“…A number of other works have investigated seeded matching [18,19,20]. Feizi et al used a spectral method to recover an alignment of dense graphs with side information restricting the set of possible alignments [21]. Lyzinski et al explored the limitations of some convex programming methods, which have presented a barrier to the development of efficient algorithms [22].…”

Section: Related Workmentioning

confidence: 99%

Partial Recovery of Erdðs-Rényi Graph Alignment via k-Core Alignment

Cullina

Kiyavash

Mittal

et al. 2019

Proc. ACM Meas. Anal. Comput. Syst.

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We determine information theoretic conditions under which it is possible to partially recover the alignment used to generate a pair of sparse, correlated Erdős-Rényi graphs. To prove our achievability result, we introduce the k-core alignment estimator. This estimator searches for an alignment in which the intersection of the correlated graphs using this alignment has a minimum degree of k. We prove a matching converse bound. As the number of vertices grows, recovery of the alignment for a fraction of the vertices tending to one is possible when the average degree of the intersection of the graph pair tends to infinity. It was previously known that exact alignment is possible when this average degree grows faster than the logarithm of the number of vertices. *

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Spectral Alignment of Graphs

Cited by 44 publications

References 85 publications

Link prediction in real-world multiplex networks via layer reconstruction method

Link prediction in real-world multiplex networks via layer reconstruction method

Network alignment and similarity reveal atlas-based topological differences in structural connectomes

Partial Recovery of Erdðs-Rényi Graph Alignment via k-Core Alignment

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