Link prediction with hyperbolic geometry

Kitsak, Maksim; Voitalov, Ivan; Krioukov, Dmitri

doi:10.48550/arxiv.1903.08810

Cited by 2 publications

(5 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Cross-geometric representations can be obtained by repurposing any existing MLE-based geometric embedding methods, e.g., Refs. [11,17,58,59]. MLE-based embedders aim to find node coordinates maximizing the likelihood L that the network of interest was generated as the latent space model.…”

Section: Appendix D: Embedding Complementarity-driven Networkmentioning

confidence: 99%

“…( 1). In our work repurpose the HyperLink Embedder (HL) [11] and refer to the resulting complementarity-based embedder as the Complementarity-based HyperLink (CHL) embedder, see Appendix D.…”

Section: Appendix D: Embedding Complementarity-driven Networkmentioning

confidence: 99%

“…Latent-geometric distances are often interpreted as generalized measures of node similarities [1]: the closer the two nodes in the latent space the more similar they are and the more likely they are to be connected in the network of interest. It is the similarity interpretation of latent distances that lies at the origin of many applications of network embeddings, including link prediction [2][3][4][5][6][7][8][9][10][11][12], soft community detection and clustering [13][14][15][16], network navigation [17][18][19][20], and search [21][22][23].…”

mentioning

confidence: 99%

“…where k H (r) is the expected degree of a node with radial coordinate r in the RHG: All experiments correspond to the 1 − q = 0.5 fraction of removed links. Considered link prediction methods are the (CHL) Complementarity HyperLink (our method), the L3 method [27], the Structural Perturbation Method (SPM) [28], Katz index [29] with parameter β = 0.1 (Katz01) and β = 0.9 (Katz09), Preferential Attachment (PA) [30], Hyperlink (HL) [11], Cannistraci Resource Allocation (CRA) [31], Resource Allocation (RA) [32], Adamic Adar (AA) [33], Jaccard Index (JACC) [34], and the number of common neighbors (CN) [35].…”

mentioning

confidence: 99%

See 3 more Smart Citations

Latent geometry of bipartite networks

2017

Self Cite

View full text Add to dashboard Cite

Despite the abundance of bipartite networked systems, their organizing principles are less studied, compared to unipartite networks. Bipartite networks are often analyzed after projecting them onto one of the two sets of nodes. As a result of the projection, nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network. Even though these projections allow one to study bipartite networks using tools developed for unipartite networks, one-mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs. Here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure: network nodes are points in a latent metric space, while connections are more likely to form between nodes separated by shorter distances. This approach has been developed for unipartite networks, and relatively little is known about its applicability to bipartite systems. Here, we fully analyze a simple latent-geometric model of bipartite networks, and show that this model explains the peculiar structural properties of many real bipartite systems, including the distributions of common neighbors and bipartite clustering. We also analyze the geometric information loss in one-mode projections in this model, and propose an efficient method to infer the latent pairwise distances between nodes. Uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains, ranging from constructing efficient recommender systems to understanding cell metabolism.

show abstract

Section: Appendix D: Embedding Complementarity-driven Networkmentioning

confidence: 99%

Section: Appendix D: Embedding Complementarity-driven Networkmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

Latent geometry of bipartite networks

2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…Beyond being a formal theoretical framework to explain the topology of real networks, network geometry can be used to develop practical applications for real systems, including routing of information in the Internet [9], community detection [9,14,15], prediction of missing links [3,16,17], a precise definition of hierarchy in networks [15], and downscaled network replicas [10], to name a few. However, applications require faithful embeddings of real-world networks into the hidden metric space using only the information contained in their topology.…”

Section: Introductionmentioning

confidence: 99%

Mercator: uncovering faithful hyperbolic embeddings of complex networks

et al. 2019

View full text Add to dashboard Cite

We introduce Mercator, a reliable embedding method to map real complex networks into their hyperbolic latent geometry. The method assumes that the structure of networks is well described by the popularity× similarity   1 2 static geometric network model, which can accommodate arbitrary degree distributions and reproduces many pivotal properties of real networks, including self-similarity patterns. The algorithm mixes machine learning and maximum likelihood (ML) approaches to infer the coordinates of the nodes in the underlying hyperbolic disk with the best matching between the observed network topology and the geometric model. In its fast mode, Mercator uses a model-adjusted machine learning technique performing dimensional reduction to produce a fast and accurate map, whose quality already outperforms other embedding algorithms in the literature. In the refined Mercator mode, the fast mode embedding result is taken as an initial condition in a ML estimation, which significantly improves the quality of the final embedding. Apart from its accuracy as an embedding tool, Mercator has the clear advantage of systematically inferring not only node orderings, or angular positions, but also the hidden degrees and global model parameters, and has the ability to embed networks with arbitrary degree distributions. Overall, our results suggest that mixing machine learning and ML techniques in a model-dependent framework can boost the meaningful mapping of complex networks.The code will be available at https://github.com/networkgeometry/mercator upon publication. 10 Notice that in thermodynamic limit the curvature of the circle vanishes and the model is effectively defined on  1 .

show abstract

Link prediction with hyperbolic geometry

Cited by 2 publications

References 46 publications

Latent geometry of bipartite networks

Latent geometry of bipartite networks

Mercator: uncovering faithful hyperbolic embeddings of complex networks

Contact Info

Product

Resources

About