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  • 1.
    Blöcker, Christopher
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Smiljanic, Jelena
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Scholtes, Ingo
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Similarity-based Link Prediction from Modular Compression of Network FlowsManuscript (preprint) (Other academic)
    Abstract [en]

    Node similarity scores constitute a foundation for machine learning in graphs. Besides clustering, node classification, and anomaly detection, they are a basis for link prediction with critical applications in biological systems, information networks, and recommender systems. Recent works on link prediction use vector space embeddings to calculate node similarities. While these methods can provide good performance in undirected networks, they have several disadvantages: limited interpretability, problem-specific hyperparameter tuning, manual model fitting through dimensionality reduction, and poor performance of symmetric similarities in directed link prediction. To address these issues, we propose MapSim, a novel information-theoretic approach to assess node similarities based on modular compression of network flows. Different from vector space embeddings, MapSim represents nodes in a discrete, non-metric space of communities and yields asymmetric similarities suitable to predict directed and undirected links in an unsupervised fashion. The resulting similarities can be explained based on a network's hierarchical modular organisation, facilitating interpretability. MapSim naturally accounts for Occam's razor, leading to parsimonious representations of clusters at multiple scales. Addressing unsupervised link prediction, we compare MapSim to popular embedding-based algorithms across 47 data sets of networks from a few hundred to hundreds of thousands of nodes and millions of links. Our analysis shows that MapSim's average performance across all networks is more than 7% higher than its closest competitor, outperforming all embedding methods in 14 of the 47 networks, and a more than 33% better worst-case performance. Our method demonstrates the potential of compression-based approaches in graph representation learning, with promising applications in other graph learning tasks.

  • 2.
    Blöcker, Christopher
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Smiljanic, Jelena
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Scholtes, Ingo
    Center for Artificial Intelligence and Data Science, University of Würzburg, Germany.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Similarity-based link prediction from modular compression of network flows2022In: Proceedings of the First Learning on Graphs Conference, ML Research Press , 2022, p. 52:1-52:18Conference paper (Refereed)
    Abstract [en]

    Node similarity scores are a foundation for machine learning in graphs for clustering, node classification, anomaly detection, and link prediction with applications in biological systems, information networks, and recommender systems. Recent works on link prediction use vector space embeddings to calculate node similarities in undirected networks with good performance. Still, they have several disadvantages: limited interpretability, need for hyperparameter tuning, manual model fitting through dimensionality reduction, and poor performance from symmetric similarities in directed link prediction. We propose MapSim, an information-theoretic measure to assess node similarities based on modular compression of network flows. Unlike vector space embeddings, MapSim represents nodes in a discrete, non-metric space of communities and yields asymmetric similarities in an unsupervised fashion. We compare MapSim on a link prediction task to popular embedding-based algorithms across 47 networks and find that MapSim's average performance across all networks is more than 7% higher than its closest competitor, outperforming all embedding methods in 11 of the 47 networks. Our method demonstrates the potential of compression-based approaches in graph representation learning, with promising applications in other graph learning tasks.

  • 3.
    Edler, Daniel
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Smiljanić, Jelena
    Umeå University, Faculty of Science and Technology, Department of Physics. Institute of Physics, University of Belgrade, Belgrade, Serbia.
    Holmgren, Anton
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Antonelli, Alexandre
    Department of Biological and Environmental Sciences, University of Gothenburg, Gothenburg, Sweden; Gothenburg Global Biodiversity Centre, Department of Biological and Environmental Sciences, University of Gothenburg, Gothenburg, Sweden; Department of Plant Sciences, University of Oxford, Oxford, United Kingdom; Royal Botanic Gardens, Kew, Richmond, Surrey, United Kingdom.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Variable Markov dynamics as a multifocal lens to map multiscale complex networksManuscript (preprint) (Other academic)
  • 4.
    Smiljanic, Jelena
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics. Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade, Pregrevica 118, Belgrade, Serbia.
    Blöcker, Christopher
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Edler, Daniel
    Umeå University, Faculty of Science and Technology, Department of Physics. Gothenburg Global Biodiversity Centre, Box 461, Gothenburg, Sweden; Department of Biological and Environmental Sciences, University of Gothenburg, Carl Skottsbergs Gata 22B, Gothenburg, Sweden.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Mapping flows on weighted and directed networks with incomplete observations2021In: Journal of Complex Networks, ISSN 2051-1310, E-ISSN 2051-1329, Vol. 9, no 6, article id cnab044Article in journal (Refereed)
    Abstract [en]

    Detecting significant community structure in networks with incomplete observations is challenging because the evidence for specific solutions fades away with missing data. For example, recent research shows that flow-based community detection methods can highlight spurious communities in sparse undirected and unweighted networks with missing links. Current Bayesian approaches developed to overcome this problem do not work for incomplete observations in weighted and directed networks that describe network flows. To overcome this gap, we extend the idea behind the Bayesian estimate of the map equation for unweighted and undirected networks to enable more robust community detection in weighted and directed networks. We derive an empirical Bayes estimate of the transitions rates that can incorporate metadata information and show how an efficient implementation in the community-detection method Infomap provides more reliable communities even with a significant fraction of data missing.

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  • 5.
    Smiljanic, Jelena
    et al.
    Umeå University, Faculty of Science and Technology, Department of Physics. Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics, University of Belgrade, Serbia.
    Edler, Daniel
    Umeå University, Faculty of Science and Technology, Department of Physics. Gothenburg Global Biodiversity Centre, Gothenburg, Sweden; Department of Biological and Environmental Sciences, University of Gothenburg, Sweden.
    Rosvall, Martin
    Umeå University, Faculty of Science and Technology, Department of Physics.
    Mapping flows on sparse networks with missing links2020In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 102, no 1, article id 012302Article in journal (Refereed)
    Abstract [en]

    Unreliable network data can cause community-detection methods to overfit and highlight spurious structures with misleading information about the organization and function of complex systems. Here we show how to detect significant flow-based communities in sparse networks with missing links using the map equation. Since the map equation builds on Shannon entropy estimation, it assumes complete data such that analyzing undersampled networks can lead to overfitting. To overcome this problem, we incorporate a Bayesian approach with assumptions about network uncertainties into the map equation framework. Results in both synthetic and real-world networks show that the Bayesian estimate of the map equation provides a principled approach to revealing significant structures in undersampled networks.

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  • 6.
    Vranić, Ana
    et al.
    Institute of Physics Belgrade, University of Belgrade, Belgrade, Serbia.
    Smiljanic, Jelena
    Umeå University, Faculty of Science and Technology, Department of Physics. Institute of Physics Belgrade, University of Belgrade, Belgrade, Serbia.
    Dankulov, Marija Mitrović
    Institute of Physics Belgrade, University of Belgrade, Belgrade, Serbia.
    Universal growth of social groups: empirical analysis and modeling2022In: Journal of Statistical Mechanics: Theory and Experiment, ISSN 1742-5468, E-ISSN 1742-5468, Vol. 2022, no 12, article id 123402Article in journal (Refereed)
    Abstract [en]

    Social groups are fundamental elements of any social system. Their emergence and evolution are closely related to the structure and dynamics of a social system. Research on social groups was primarily focused on the growth and the structure of the interaction networks of social system members and how members’ group affiliation influences the evolution of these networks. The distribution of groups’ size and how members join groups has not been investigated in detail. Here we combine statistical physics and complex network theory tools to analyze the distribution of group sizes in three data sets, Meetup groups based in London and New York and Reddit. We show that all three distributions exhibit log-normal behavior that indicates universal growth patterns in these systems. We propose a theoretical model that combines social and random diffusion of members between groups to simulate the roles of social interactions and members’ interest in the growth of social groups. The simulation results show that our model reproduces growth patterns observed in empirical data. Moreover, our analysis shows that social interactions are more critical for the diffusion of members in online groups, such as Reddit, than in offline groups, such as Meetup. This work shows that social groups follow universal growth mechanisms that need to be considered in modeling the evolution of social systems.

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