When can two unlabeled networks be aligned under partial overlap?

Kazemi, Ehsan; Yartseva, Lyudmila; Grossglauser, Matthias

doi:10.1109/allerton.2015.7446983

Cited by 41 publications

(46 citation statements)

References 26 publications

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“…For example, PROPER is a state-of-the-art algorithm that uses PGM-based methods to align two networks . There are several works on the theoretical and practical aspects of PGM algorithms [Narayanan and Shmatikov, 2009, Yartseva and Grossglauser, 2013, Korula and Lattanzi, 2014, Chiasserini et al, 2015a, Kazemi et al, 2015b, Kazemi, 2016, Shirani et al, 2017, Dai et al, 2018, Mossel and Xu, 2019. In this paper, we introduced a global MNA algorithm, as a new member of the PGM class.…”

Section: Why Does Multiplepercolation Work?mentioning

confidence: 99%

MPGM: Scalable and Accurate Multiple Network Alignment

Kazemi

Grossglauser

2020

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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Protein-protein interaction (PPI) network alignment is a canonical operation to transfer biological knowledge among species. The alignment of PPI-networks has many applications, such as the prediction of protein function, detection of conserved network motifs, and the reconstruction of species' phylogenetic relationships. A good multiple-network alignment (MNA), by considering the data related to several species, provides a deep understanding of biological networks and system-level cellular processes. With the massive amounts of available PPI data and the increasing number of known PPI networks, the problem of MNA is gaining more attention in the systems-biology studies.In this paper, we introduce a new scalable and accurate algorithm, called MPGM, for aligning multiple networks. The MPGM algorithm has two main steps: (i) SEEDGENERA-TION and (ii) MULTIPLEPERCOLATION. In the first step, to generate an initial set of seed tuples, the SEEDGENERATION algorithm uses only protein sequence similarities. In the second step, to align remaining unmatched nodes, the MULTIPLEPERCOLATION algorithm uses network structures and the seed tuples generated from the first step. We show that, with respect to different evaluation criteria, MPGM outperforms the other state-of-the-art algorithms. In addition, we guarantee the performance of MPGM under certain classes of network models. We introduce a sampling-based stochastic model for generating k correlated networks. We prove that for this model if a sufficient number of seed tuples are available, the MULTIPLEPERCOLATION algorithm correctly aligns almost all the nodes. Our theoretical results are supported by experimental evaluations over synthetic networks.

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Section: Why Does Multiplepercolation Work?mentioning

confidence: 99%

MPGM: Scalable and Accurate Multiple Network Alignment

Kazemi

Grossglauser

2020

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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“…If there is more than one k-core alignment, it makes an arbitrary choice. (0, 7) (1, 5) Figure 1: The matching µ = {(0, 7), (1,5), (2,6), (3,9)} is a 2-core alignment of G a and G b : δ(G a ∧ µ G b ) = 2 and extending µ with (4, 8) leads to a minimum degree of 0.…”

Section: K-cores and K-core Alignmentsmentioning

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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“…The problem of matching nonidentical pairs of correlated Erdös-Rényi graphs have been studied in [6]- [12]. Furthermore, graphs with community structure have been considered in [13]- [16]. Seeded versions ?…”

Section: Introductionmentioning

confidence: 99%

Typicality Matching for Pairs of Correlated Graphs

Shirani

Garg

Erkip

2018

2018 IEEE International Symposium on Information Theory (ISIT)

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In this paper, the problem of matching pairs of correlated random graphs with multi-valued edge attributes is considered. Graph matching problems of this nature arise in several settings of practical interest including social network deanonymization, study of biological data, web graphs, etc. An achievable region for successful matching is derived by analyzing a new matching algorithm that we refer to as typicality matching. The algorithm operates by investigating the joint typicality of the adjacency matrices of the two correlated graphs. Our main result shows that the achievable region depends on the mutual information between the variables corresponding to the edge probabilities of the two graphs. The result is based on bounds on the typicality of permutations of sequences of random variables that might be of independent interest.

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When can two unlabeled networks be aligned under partial overlap?

Cited by 41 publications

References 26 publications

MPGM: Scalable and Accurate Multiple Network Alignment

MPGM: Scalable and Accurate Multiple Network Alignment

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

Typicality Matching for Pairs of Correlated Graphs

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