Link prediction based on hyperbolic mapping with community structure for complex networks

Wang, Zuxi; Wu, Yao; Li, Qingguang; Jin, Fengdong; Xiong, Wei

doi:10.1016/j.physa.2016.01.010

Cited by 56 publications

(42 citation statements)

References 32 publications

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“…The plots report the average correlation over the 100 synthetic networks that have been generated for each different PSO model parameter combination. It is evident that the coalescent embedding techniques pre-weighted with RA and adjusted according to EA are outperforming HyperMap 29 , HyperMap-CN 30 , and LPCS 31 that are the state-of-the-art, and this is the second key discovery of our study. RA performed similarly to EBC, and in general both the pre-weighting strategies are effective (Supplementary Figs.…”

Section: Resultsmentioning

confidence: 53%

“…Link prediction with community structure (LPCS) 31 is a hyperbolic embedding technique that consists of the following steps: (1) Detect the hierarchical organization of communities. (2) Order the top-level communities starting from the one that has the largest number of nodes and using the community intimacy index, which takes into account the proportion of edges within and between communities.…”

Section: Methodsmentioning

confidence: 99%

See 1 more Smart Citation

Machine learning meets complex networks via coalescent embedding in the hyperbolic space

Muscoloni¹,

Thomas²,

Ciucci³

et al. 2017

Nat Commun

164

225

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Physicists recently observed that realistic complex networks emerge as discrete samples from a continuous hyperbolic geometry enclosed in a circle: the radius represents the node centrality and the angular displacement between two nodes resembles their topological proximity. The hyperbolic circle aims to become a universal space of representation and analysis of many real networks. Yet, inferring the angular coordinates to map a real network back to its latent geometry remains a challenging inverse problem. Here, we show that intelligent machines for unsupervised recognition and visualization of similarities in big data can also infer the network angular coordinates of the hyperbolic model according to a geometrical organization that we term “angular coalescence.” Based on this phenomenon, we propose a class of algorithms that offers fast and accurate “coalescent embedding” in the hyperbolic circle even for large networks. This computational solution to an inverse problem in physics of complex systems favors the application of network latent geometry techniques in disciplines dealing with big network data analysis including biology, medicine, and social science.

show abstract

Section: Resultsmentioning

confidence: 53%

Section: Methodsmentioning

confidence: 99%

Machine learning meets complex networks via coalescent embedding in the hyperbolic space

Muscoloni¹,

Thomas²,

Ciucci³

et al. 2017

Nat Commun

164

225

View full text Add to dashboard Cite

show abstract

“…LPCS [47] is a hyperbolic embedding technique that consists of the following steps: (1) detect the hierarchical organization of communities. (2) Order the top-level communities starting from the one that has the largest number of nodes and using the community intimacy index, which takes into account the proportion of edges within and between communities.…”

Section: Lpcsmentioning

confidence: 99%

Leveraging the nonuniform PSO network model as a benchmark for performance evaluation in community detection and link prediction

Muscoloni

Vittorio

2018

New J. Phys.

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Advances in network geometry pointed out that structural properties observed in networks derived from real complex systems can emerge in the hyperbolic space (HS). The nonuniform popularitysimilarity-optimization (nPSO) is a generative model recently introduced in order to grow random geometric graphs in the HS, reproducing networks that have realistic features such as high clustering, small-worldness, scale-freeness and rich-clubness, with the additional possibility to control the community organization. Generative models allowing to tune the structural properties of 'realistic' synthetic networks are fundamental, because they offer a ground truth to investigate how predictive algorithms react to controlled topological variations. Here, we discuss how to leverage the nPSO model as a synthetic benchmark to compare the performance of methods for community detection and link prediction; and we prove that the nPSO offers a reliable and realistic testing framework which can complement other existing benchmarks not based on latent geometry. Furthermore, we confirm that network embedding information can improve community detection, whereas boosting link prediction in HS still needs further investigations. Indeed, we find that the presence of communities in nPSO significantly modifies the performance of link predictors and is fundamental for the reproducibility of results observed on real networks. The nPSO can trigger valuable insights to understand the intrinsic rules of link-growth and self-organization that connect topology to geometry and that are encoded in link prediction algorithms differentiating their performance.

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“…erefore, some more interesting properties of the network can be captured through detecting communities. In addition, community detection can help to facilitate many downstream studies, such as prevention of epidemic propagation [4], disease detection [5], link prediction [6], and influence maximization [7]. Overall, the problem of community detection has attracted many researchers from different fields in the last decade.…”

Section: Introductionmentioning

confidence: 99%

A Seed-Expanding Method Based on TOPSIS for Community Detection in Complex Networks

et al. 2020

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The centrality plays an important role in many community-detection algorithms, which depend on various kinds of centralities to identify seed vertices of communities first and then expand each of communities based on the seeds to get the resulting community structure. The traditional algorithms always use a single centrality measure to recognize seed vertices from the network, but each centrality measure has both pros and cons when being used in this circumstance; hence seed vertices identified using a single centrality measure might not be the best ones. In this paper, we propose a framework which integrates advantages of various centrality measures to identify the seed vertices from the network based on the TOPSIS (Technique for Order of Preference by Similarity to Ideal Solution) multiattribute decision-making technology. We take each of the centrality measures involved as an attribute, rank vertices according to the scores which are calculated for them using TOPSIS, and then take vertices with top ranks as the seeds. To put this framework into practice, we concretize it in this paper by considering four centrality measures as attributes to identify the seed vertices of communities first, then expanding communities by iteratively inserting one unclassified vertex into the community to which its most similar neighbor belongs, and the similarity between them is the largest among all pairs of vertices. After that, we obtain the initial community structure. However, the amount of communities might be much more than they should be, and some communities might be too small to make sense. Therefore, we finally consider a postprocessing procedure to merge some initial communities into larger ones to acquire the resulting community structure. To test the effectiveness of the proposed framework and method, we have performed extensive experiments on both some synthetic networks and some real-world networks; the experimental results show that the proposed method can get better results, and the quality of the detected community structure is much higher than those of competitors.

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Link prediction based on hyperbolic mapping with community structure for complex networks

Cited by 56 publications

References 32 publications

Machine learning meets complex networks via coalescent embedding in the hyperbolic space

Machine learning meets complex networks via coalescent embedding in the hyperbolic space

Leveraging the nonuniform PSO network model as a benchmark for performance evaluation in community detection and link prediction

A Seed-Expanding Method Based on TOPSIS for Community Detection in Complex Networks

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