Over the past two decades, there has been a tremendous increase in the growth of representation learning methods for graphs, with numerous applications across various fields, including bioinformatics, chemistry, and the social sciences. However, current dynamic network approaches focus on discrete-time networks or treat links in continuous-time networks as instantaneous events. Therefore, these approaches have limitations in capturing the persistence or absence of links that continuously emerge and disappear over time for particular durations. To address this, we propose a novel stochastic process relying on survival functions to model the durations of links and their absences over time. This forms a generic new likelihood specification explicitly accounting for intermittent edge-persistent networks, namely GraSSP: Graph Representation with Sequential Survival Process. We apply the developed framework to a recent continuous time dynamic latent distance model characterizing network dynamics in terms of a sequence of piecewise linear movements of nodes in latent space. We quantitatively assess the developed framework in various downstream tasks, such as link prediction and network completion, demonstrating that the developed modeling framework accounting for link persistence and absence well tracks the intrinsic trajectories of nodes in a latent space and captures the underlying characteristics of evolving network structure.

Understanding the structure and dynamics of scientific research, i.e., the science of science (SciSci), has become an important area of research in order to address imminent questions including how scholars interact to advance science, how disciplines are related and evolve, and how research impact can be quantified and predicted. Central to the study of SciSci has been the analysis of citation networks. Here, two prominent modeling methodologies have been employed: one is to assess the citation impact dynamics of papers using parametric distributions, and the other is to embed the citation networks in a latent space optimal for characterizing the static relations between papers in terms of their citations. Interestingly, citation networks are a prominent example of single-event dynamic networks, i.e., networks for which each dyad only has a single event (i.e., the point in time of citation). We presently propose a novel likelihood function for the characterization of such single-event networks. Using this likelihood, we propose the Dynamic Impact Single-Event Embedding model (DISEE). The DISEE model characterizes the scientific interactions in terms of a latent distance model in which random effects account for citation heterogeneity while the time-varying impact is characterized using existing parametric representations for assessment of dynamic impact. We highlight the proposed approach on several real citation networks finding that DISEE well reconciles static latent distance network embedding approaches with classical dynamic impact assessments.

Obtaining effective representations of DNA sequences is crucial for genome analysis. Metagenomic binning, for instance, relies on genome representations to cluster complex mixtures of DNA fragments from biological samples with the aim of determining their microbial compositions. In this paper, we revisit k-mer-based representations of genomes and provide a theoretical analysis of their use in representation learning. Based on the analysis, we propose a lightweight and scalable model for performing metagenomic binning at the genome read level, relying only on the k-mer compositions of the DNA fragments. We compare the model to recent genome foundation models and demonstrate that while the models are comparable in performance, the proposed model is significantly more effective in terms of scalability, a crucial aspect for performing metagenomic binning of real-world data sets.

Graph Representation Learning (GRL) has become central for characterizing structures of complex networks and performing tasks such as link prediction, node classification, network reconstruction, and community detection. Whereas numerous generative GRL models have been proposed, many approaches have prohibitive computational requirements hampering large-scale network analysis, fewer are able to explicitly account for structure emerging at multiple scales, and only a few explicitly respect important network properties such as homophily and transitivity. This paper proposes a novel scalable graph representation learning method named the Hierarchical Block Distance Model (HBDM). The HBDM imposes a multiscale block structure akin to stochastic block modeling (SBM) and accounts for homophily and transitivity by accurately approximating the latent distance model (LDM) throughout the inferred hierarchy. The HBDM naturally accommodates unipartite, directed, and bipartite networks whereas the hierarchy is designed to ensure linearithmic time and space complexity enabling the analysis of very large-scale networks. We evaluate the performance of the HBDM on massive networks consisting of millions of nodes. Importantly, we find that the proposed HBDM framework significantly outperforms recent scalable approaches in all considered downstream tasks. Surprisingly, we observe superior performance even imposing ultra-low two-dimensional embeddings facilitating accurate direct and hierarchical-aware network visualization and interpretation.

Graph representation learning has become a prominent tool for the characterization and understanding of the structure of networks in general and social networks in particular. Typically, these representation learning approaches embed the networks into a low-dimensional space in which the role of each individual can be characterized in terms of their latent position. A major current concern in social networks is the emergence of polarization and filter bubbles promoting a mindset of ”us-versus-them” that may be defined by extreme positions believed to ultimately lead to political violence and the erosion of democracy. Such polarized networks are typically characterized in terms of signed links reflecting likes and dislikes. We propose the Signed Latent Distance Model (SLDM) utilizing for the first time the Skellam distribution as a likelihood function for signed networks. We further extend the modeling to the characterization of distinct extreme positions by constraining the embedding space to polytopes, forming the Signed Latent Relational Distance Model (SLIM). On four real social signed networks of polarization, we demonstrate that the models extract low-dimensional characterizations that well predict friendships and animosity while SLIM provides interpretable visualizations defined by extreme positions when restricting the embedding space to polytopes.

Learning representations of nodes in a low dimensional space is a crucial task with numerous interesting applications in network analysis, including link prediction, node classification, and visualization. Two popular approaches for this problem are \textit{matrix factorization} and \textit{random walk}-based models. In this paper, we aim to bring together the best of both worlds, towards learning node representations. In particular, we propose a weighted matrix factorization model that encodes random walk-based information about nodes of the network. The benefit of this novel formulation is that it enables us to utilize kernel functions without realizing the exact proximity matrix so that it enhances the expressiveness of existing matrix decomposition methods with kernels and alleviate their computational complexities. We extend the approach with a multiple kernel learning formulation that provides the flexibility of learning the kernel as the linear combination of a dictionary of kernels in data-driven fashion. We perform an empirical evaluation on real-world networks, showing that the proposed model outperforms baseline node embedding algorithms in downstream machine learning tasks.

Graph Representation Learning (GRL) has become a key paradigm in network analysis, with a plethora of interdis-ciplinary applications. As the scale of networks increases, most of the widely used learning-based graph representation models also face computational challenges. While there is a recent effort toward designing algorithms that solely deal with scalability issues, most of them behave poorly in terms of accuracy on downstream tasks. In this paper, we aim to study models that balance the trade-off between efficiency and accuracy. In particular, we propose Nodesig, a scalable model that computes binary node representations. Nodesig exploits random walk diffusion probabilities via stable random projections towards efficiently computing embeddings in the Hamming space. Our extensive experimental evaluation on various networks has demonstrated that the proposed model achieves a good balance between accuracy and efficiency compared to well-known baseline models on the node classification and link prediction tasks.

MOTIVATION: The cellular system of a living organism is composed of interacting bio-molecules that control cellular processes at multiple levels. Their correspondences are represented by tightly regulated molecular networks. The increase of omics technologies has favored the generation of large-scale disparate data and the consequent demand for simultaneously using molecular and functional interaction networks: gene co-expression, protein-protein interaction (PPI), genetic interaction and metabolic networks. They are rich sources of information at different molecular levels, and their effective integration is essential to understand cell functioning and their building blocks (proteins). Therefore, it is necessary to obtain informative representations of proteins and their proximity, that are not fully captured by features extracted directly from a single informational level. We propose BraneMF, a novel random walk-based matrix factorization method for learning node representation in a multilayer network, with application to omics data integration. RESULTS: We test BraneMF with PPI networks of Saccharomyces cerevisiae, a well-studied yeast model organism. We demonstrate the applicability of the learned features for essential multi-omics inference tasks: clustering, function and PPI prediction. We compare it to the state-of-the-art integration methods for multilayer networks. BraneMF outperforms baseline methods by achieving high prediction scores for a variety of downstream tasks. The robustness of results is assessed by an extensive parameter sensitivity analysis. AVAILABILITY AND IMPLEMENTATION: BraneMF's code is freely available at: https://github.com/Surabhivj/BraneMF, along with datasets, embeddings and result files. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Representing networks in a low dimensional latent space is a crucial task with many interesting applications in graph learning problems, such as link prediction and node classification. A widely applied network representation learning paradigm is based on the combination of random walks for sampling context nodes and the traditional Skip-Gram model to capture center-context node relationships. In this paper, we emphasize on exponential family distributions to capture rich interaction patterns between nodes in random walk sequences. We introduce the generic exponential family graph embedding model, that generalizes random walk-based network representation learning techniques to exponential family conditional distributions. We study three particular instances of this model, analyzing their properties and showing their relationship to existing unsupervised learning models. Our experimental evaluation on real-world datasets demonstrates that the proposed techniques outperform well-known baseline methods in two downstream machine learning tasks.