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

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-Similarity-Optimization (PSO) model simulates how random geometric graphs grow in the hyperbolic space, reproducing strong clustering and scale-free degree distribution, 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 to confer to the PSO also a community structure, which is obtained by forcing different angular regions of the hyperbolic disk to have 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 that, differently from GPA, forces heterogeneous angular node attractiveness 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 to explicitly fix the number and size of communities; it allows to tune their mixing property through the network temperature; it is efficient to generate networks with high clustering. After several tests we propose the nPSO as a valid and efficient model to generate networks with communities in the hyperbolic space, which can be adopted as a realistic benchmark for different tasks such as community detection and link prediction

Latent Geometry Inspired Graph Dissimilarities Enhance Affinity Propagation Community Detection in Complex Networks

Affinity propagation is one of the most effective unsupervised pattern recognition algorithms for data clustering in high-dimensional feature space. However, the numerous attempts to test its performance for community detection in complex networks have been attaining results very far from the state of the art methods such as Infomap and Louvain. Yet, all these studies agreed that the crucial problem is to convert the unweighted network topology in a 'smart-enough' node dissimilarity matrix that is able to properly address the message passing procedure behind affinity propagation clustering. Here we introduce a conceptual innovation and we discuss how to leverage network latent geometry notions in order to design dissimilarity matrices for affinity propagation community detection. Our results demonstrate that the latent geometry inspired dissimilarity measures we design bring affinity propagation to equal or outperform current state of the art methods for community detection. These findings are solidly proven considering both synthetic 'realistic' networks (with known ground-truth communities) and real networks (with community metadata), even when the data structure is corrupted by noise artificially induced by missing or spurious connectivity

Machine intelligence and network science for complex systems big data analysis

I will present our research at the Center for Complex Network Intelligence (CCNI) that I recently established in the Tsinghua Laboratory of Brain and Intelligence at the Tsinghua University in Beijing. We adopt a transdisciplinary approach integrating information theory, machine learning and network science to investigate the physics of adaptive complex networked systems at different scales, from molecules to ecological and social systems, with a particular attention to biology and medicine, and a new emerging interest for the analysis of complex big data in social and economic science. Our theoretical effort is to translate advanced mathematical paradigms typically adopted in theoretical physics (such as topology, network and manifold theory) to characterize many-body interactions in complex systems. We apply the theoretical frameworks we invent in the mission to develop computational tools for machine intelligent systems and network analysis. We deal with: prediction of wiring in networks, sparse deep learning, network geometry and multiscale-combinatorial marker design for quantification of topological modifications in complex networks. This talk will focus on two main theoretical innovation. Firstly, the development of machine learning and computational solutions for network geometry, topological estimation of nonlinear relations in high-dimensional data (or in complex networks) and its relevance for applications in big data, with a emphasis on brain connectome analysis. Secondly, we will discuss the Local Community Paradigm (LCP) and its recent extension to the Cannistraci-Hebb network automata, which are braininspired theories proposed to model local-topology-dependent link-growth in complex networks and therefore are useful to devise topological methods for link prediction in sparse deep learning, or monopartite and bipartite networks, such as molecular drugtarget interactions and product-consumer networks.Book of abstract: 4th Belgrade Bioinformatics Conference, June 19-23, 202