H2TNE: Temporal Heterogeneous Information Network Embedding in Hyperbolic Spaces

Temporal heterogeneous information network (temporal HIN) embedding, aiming to represent various types of nodes of different timestamps into low dimensional spaces while preserving structural and semantic information, is of vital importance in diverse real-life tasks. Researchers have made great efforts on temporal HIN embedding in Euclidean spaces and got some considerable achievements. However, there is always a fundamental conflict that many real-world networks show hierarchical property and power-law distribution, and are not isometric of Euclidean spaces. Recently, representation learning in hyperbolic spaces has been proved to be valid for data with hierarchical and power-law structure. Inspired by this character, we propose a hyperbolic heterogeneous temporal network embedding (H2TNE) model for temporal HINs. Specifically, we leverage a temporally and heterogeneously double-constrained random walk strategy to capture the structural and semantic information, and then calculate the embedding by exploiting hyperbolic distance in proximity measurement. Experimental results show that our method has superior performance on temporal link prediction and node classification compared with SOTA models.Comment: arXiv admin note: text overlap with arXiv:1705.08039 by other author

Uncovering the functional organization of molecular interaction networks using network embeddings based on graphlet topology

[eng] For this purpose, Spatial Analysis of Functional Enrichment (SAFE) framework was proposed to uncover functional regions in a network by embedding it in 2-dimensions (2D) using the Spring embedding algorithm. However, biological networks often have a heterogeneous degree distribution, i.e., nodes in the network have varying numbers of neighbours. In this case, the Spring embedding sometimes provides uninformative, densely packed embeddings best described as a ‘hairball’. On the other hand, hyperbolic embeddings, such as the Coalescent embedding, maps a network onto a disk, so that nodes of high topological importance (i.e., of high node degree) are placed closer to the center of such disk. Additionally, these embedding methods only capture node connectivity information (i.e., which nodes are connected) but does not consider network structure (i.e., wiring or topology), which captures complementary information. The state-of-the-art methods to capture network structure are based on graphlets, which are small, connected, non-isomorphic, induced sub-graphs (e.g., triangles, paths). To better capture the functional organization of networks with heterogeneous degree distributions, taking into account different types of graphlet-based wiring patterns, in this work we introduce the graphlet-based Spring (GraSpring) and the graphlet-based Coalescent (GraCoal) embeddings. Furthermore, we extend the popular SAFE framework to take as input these two newly proposed embedding methods and we use SAFE to evaluate their performance on three types of molecular interaction networks (genetic interaction, protein-protein interaction and co-expression) of various model organisms. We show that the performance in terms of functional information uncovered by each of the embedding algorithms varies depending on the type of network considered and also the model organism considered. For instance, we show that GraCoals better capture the functional and spatial organization of the genetic interaction networks of four species (fruit fly, budding yeast, fission yeast and E. coli ). Moreover, we discover that GraCoals capture different topology-function relationships depending on the species. We show that triangle-based GraCoals capture functional redundancy in GI networks of species whose genome is characterised by high counts of duplicated genes

Navigability of temporal networks in hyperbolic space

Information routing is one of the main tasks in many complex networks with a communication function. Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation strategies. However, only static maps have been considered so far, while navigation in more realistic situations, where the network structure may vary in time, remain largely unexplored. Here, we analyze the navigability of real networks by using greedy routing in hyperbolic space, where the nodes are subject to a stochastic activation-inactivation dynamics. We find that such dynamics enhances navigability with respect to the static case. Interestingly, there exists an optimal intermediate activation value, which ensures the best trade-off between the increase in the number of successful paths and a limited growth of their length. Contrary to expectations, the enhanced navigability is robust even when the most connected nodes inactivate with very high probability. Finally, our results indicate that some real networks are ultranavigable and remain highly navigable even if the network structure is extremely unsteady. These findings have important implications for the design and evaluation of efficient routing protocols that account for the temporal nature of real complex networks.Comment: 10 pages, 4 figures. Includes Supplemental Informatio

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