Related papers: Representing higher-order dependencies in networks

Complex systems are often driven by higher-order interactions among multiple units, naturally represented as hypergraphs. Understanding dependency structures within these hypergraphs is crucial for understanding and predicting the behavior…

Representations of multivariate functions with low-dimensional functions that depend on subsets of original coordinates (corresponding of different orders of coupling) are useful in quantum dynamics and other applications, especially where…

Graph Nerual Networks (GNNs) are effective models in graph embedding. It extracts shallow features and neighborhood information by aggregating neighbor information to learn the embedding representation of different nodes. However, the local…

Users form information trails as they browse the web, checkin with a geolocation, rate items, or consume media. A common problem is to predict what a user might do next for the purposes of guidance, recommendation, or prefetching.…

Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for…

Higher-order networks effectively represent complex systems with group interactions. Existing methods usually overlook the relative contribution of group interactions (hyperlinks) of different sizes to the overall network structure. Yet,…

We consider the problem of flexible modeling of higher order hidden Markov models when the number of latent states and the nature of the serial dependence, including the true order, are unknown. We propose Bayesian nonparametric methodology…

Graph neural network models have been extensively used to learn node representations for graph structured data in an end-to-end setting. These models often rely on localized first order approximations of spectral graph convolutions and…

Assortativity was first introduced by Newman and has been extensively studied and applied to many real world networked systems since then. Assortativity is a graph metrics and describes the tendency of high degree nodes to be directly…

Networks are models representing relationships between entities. Often these relationships are explicitly given, or we must learn a representation which generalizes and predicts observed behavior in underlying individual data (e.g.…

Identifying patterns of relations among the units of a complex system from measurements of their activities in time is a fundamental problem with many practical applications. Here, we introduce a method that detects dependencies of any…

Unsupervised homogeneous network embedding (NE) represents every vertex of networks into a low-dimensional vector and meanwhile preserves the network information. Adjacency matrices retain most of the network information, and directly…

Random walks on networks is the standard tool for modelling spreading processes in social and biological systems. This first-order Markov approach is used in conventional community detection, ranking, and spreading analysis although it…

Network structure evolves with time in the real world, and the discovery of changing communities in dynamic networks is an important research topic that poses challenging tasks. Most existing methods assume that no significant change in the…

Graph Neural Networks (GNNs) are a popular approach for predicting graph structured data. As GNNs tightly entangle the input graph into the neural network structure, common explainable AI approaches are not applicable. To a large extent,…

In contrast to regular (simple) networks, hyper networks possess the ability to depict more complex relationships among nodes and store extensive information. Such networks are commonly found in real-world applications, such as in social…

Many real-world systems, from social networks to protein-protein interactions and species distributions, exhibit overlapping flow-based communities that reflect their functional organisation. However, reliably identifying such overlapping…

In this paper, we study ordered representations of data in which different dimensions have different degrees of importance. To learn these representations we introduce nested dropout, a procedure for stochastically removing coherent nested…

With the rise of deep learning technology in practical applications, Convolutional Neural Networks (CNNs) have been able to assist humans in solving many real-world problems. To enhance the performance of CNNs, numerous network…

To better understand the flows of ideas or information through social and biological systems, researchers develop maps that reveal important patterns in network flows. In practice, network flow models have implied memoryless first-order…