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

Muscoloni, Alessandro; Thomas, Josephine Maria; Ciucci, Sara; Bianconi, Ginestra; Cannistraci, Carlo Vittorio

doi:10.1038/s41467-017-01825-5

Cited by 156 publications

(226 citation statements)

References 57 publications

(78 reference statements)

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“…If the agent navigates using hierarchical information, it will transition to the neighbour that is hierarchically closest to the target (top). We derive the navigation preference of each node (β parameter) as the source of information that maximizes recapitulation of shortest paths [45,46,54]. When β is valued close to 1, paths originating from the node are better recovered using spatial proximity compared to hierarchical proximity; the opposite is true when β is valued close 0.…”

Section: Temporal Evolution Of Communication Flowmentioning

confidence: 99%

Signal propagation via cortical hierarchies

Vázquez-Rodríguez

Liu

Hagmann

et al. 2020

Preprint

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†These authors contributed equally to this work.The wiring of the brain is organized around a putative unimodal-transmodal hierarchy. Here we investigate how this intrinsic hierarchical organization of the brain shapes the transmission of information among regions. The hierarchical positioning of individual regions was quantified by applying diffusion map embedding to resting state functional MRI networks. Structural networks were reconstructed from diffusion spectrum imaging and topological shortest paths among all brain regions were computed. Sequences of nodes encountered along a path were labelled by their hierarchical position, tracing out path motifs. We find that the cortical hierarchy guides communication in the network. Specifically, nodes are more likely to forward signals to nodes closer in the hierarchy and cover a range of unimodal and transmodal regions, potentially enriching or diversifying signals en route. We also find evidence of systematic detours, particularly in attention networks, where communication is rerouted. Altogether, the present work highlights how the cortical hierarchy shapes signal exchange and imparts behaviourally-relevant communication patterns in brain networks.

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Section: Temporal Evolution Of Communication Flowmentioning

confidence: 99%

Signal propagation via cortical hierarchies

Vázquez-Rodríguez

Liu

Hagmann

et al. 2020

Preprint

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“…Recently, Muscoloni et al [16] introduced coalescent embedding, a model-free topological-based machine learning class of algorithms that exploits nonlinear unsupervised dimensionality reduction to infer the node coordinates in the HS. The study also demonstrates that, exploiting the geometrical embedding information in order to weight the adjacency matrix in input to the community detection algorithms, the performance of the respective unweighted variants can be improved [16].…”

Section: Community Detection On Npso Network Using Network Embeddingmentioning

confidence: 99%

“…The investigation of hidden geometrical spaces behind complex network topologies has been a fervid topic in recent years and, currently, the hyperbolic space (HS) seems to be one of the most appropriate in order to explain many of the structural features observed in real networks [8][9][10][11][12][13][14][15][16][17][18][19]. The popularity-similarityoptimization (PSO) [12] is a generative model that grows random geometric graphs in the HS, reproducing networks that have realistic features such as clustering, small-worldness, scale-freeness and rich-clubness.…”

Section: Introductionmentioning

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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“…In recent years the study of hidden geometrical spaces behind complex network topologies has led to several developments and, currently, the hyperbolic space seems to be one of the most appropriate in order to explain many of the structural features observed in real networks [1][2][3][4][5][6][7][8][9][10][11][12]. In 2012 Papadopoulos et al [5] introduced the popularity-similarity-optimization (PSO) model in order to describe how random geometric graphs grow in the hyperbolic space optimizing a trade-off between popularity and similarity.…”

Section: Introductionmentioning

confidence: 99%

A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities

2018

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2 Brain bio-inspired computing (BBC) lab, IRCCS Centro Neurolesi 'Bonino Pulejo', Messina, Italy E-mail: kalokagathos.agon@gmail.com Keywords: network models, hyperbolic geometry, community structure Supplementary material for this article is available online AbstractThe investigation of the hidden metric space behind complex network topologies is a fervid topic in current network science and the hyperbolic space is one of the most studied, because it seems associated to the structural organization of many real complex systems. The popularity-similarityoptimization (PSO) model simulates how random geometric graphs grow in the hyperbolic space, generating realistic networks with clustering, small-worldness, scale-freeness and rich-clubness. However, it misses to reproduce an important feature of real complex networks, which is the community organization. The geometrical-preferential-attachment (GPA) model was recently developed in order to confer to the PSO also a soft community structure, which is obtained by forcing different angular regions of the hyperbolic disk to have a variable level of attractiveness. However, the number and size of the communities cannot be explicitly controlled in the GPA, which is a clear limitation for real applications. Here, we introduce the nonuniform PSO (nPSO) model. Differently from GPA, the nPSO generates synthetic networks in the hyperbolic space where heterogeneous angular node attractiveness is forced by sampling the angular coordinates from a tailored nonuniform probability distribution (for instance a mixture of Gaussians). The nPSO differs from GPA in other three aspects: it allows one to explicitly fix the number and size of communities; it allows one to tune their mixing property by means of the network temperature; it is efficient to generate networks with high clustering. Several tests on the detectability of the community structure in nPSO synthetic networks and wide investigations on their structural properties confirm that the nPSO is a valid and efficient model to generate realistic complex networks with communities.

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

Cited by 156 publications

References 57 publications

Signal propagation via cortical hierarchies

Signal propagation via cortical hierarchies

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

A nonuniform popularity-similarity optimization (nPSO) model to efficiently generate realistic complex networks with communities

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