Related papers: Hypergraph Random Walks, Laplacians, and Clusterin…

Large datasets with interactions between objects are common to numerous scientific fields (i.e. social science, internet, biology...). The interactions naturally define a graph and a common way to explore or summarize such dataset is graph…

We consider a decentralized learning setting in which data is distributed over nodes in a graph. The goal is to learn a global model on the distributed data without involving any central entity that needs to be trusted. While gossip-based…

Being cognizant of the abundance of multi-body interactions in various complex systems, here we investigate a possible way to incorporate multi-body interactions in dynamical networks. Adopting hypergraph as the underlying architecture aids…

Agglomerative hierarchical clustering based on Ordered Weighted Averaging (OWA) operators not only generalises the single, complete, and average linkages, but also includes intercluster distances based on a few nearest or farthest…

Convex clustering is a recent stable alternative to hierarchical clustering. It formulates the recovery of progressively coalescing clusters as a regularized convex problem. While convex clustering was originally designed for handling…

There are few known exponential speedups for quantum algorithms and these tend to fall into even fewer families. One speedup that has mostly resisted generalization is the use of quantum walks to traverse the welded-tree graph, due to…

The rapid growth in feature dimension may introduce implicit associations between features and labels in multi-label datasets, making the relationships between features and labels increasingly complex. Moreover, existing methods often adopt…

The structure of many complex networks includes edge directionality and weights on top of their topology. Network analysis that can seamlessly consider combination of these properties are desirable. In this paper, we study two important…

Empirical networks possess considerable heterogeneity of node connections, resulting in a small portion of nodes playing crucial roles in network structure and function. Yet, how to characterize nodes' influence and identify vital nodes is…

Observational data usually comes with a multimodal nature, which means that it can be naturally represented by a multi-layer graph whose layers share the same set of vertices (users) with different edges (pairwise relationships). In this…

In this paper, we study the fundamental problem of random walk for network embedding. We propose to use non-Markovian random walk, variants of vertex-reinforced random walk (VRRW), to fully use the history of a random walk path. To solve…

Here we study the problem of matched record clustering in unsupervised entity resolution. We build upon a state-of-the-art probabilistic framework named the Data Washing Machine (DWM). We introduce a graph-based hierarchical 2-step record…

Random walks have been intensively studied on regular and complex networks, which are used to represent pairwise interactions. Nonetheless, recent works have demonstrated that many real-world processes are better captured by higher-order…

Graph clustering aims to partition nodes into distinct clusters based on their similarity, thereby revealing relationships among nodes. Nevertheless, most existing methods do not fully utilize these edge weights. Leveraging edge weights in…

We extend the notion of nonbacktracking walks from unweighted graphs to graphs whose edges have a nonnegative weight. Here the weight associated with a walk is taken to be the product over the weights along the individual edges. We give two…

Random walks over directed graphs are used to model activities in many domains, such as social networks, influence propagation, and Bayesian graphical models. They are often used to compute the importance or centrality of individual nodes…

Full synchronization of dynamical elements coupled via hypergraphs can be analyzed with the hypergraph projection onto dyadic matrices, but this is not sufficient for analyzing cluster synchronization. Here we develop the necessary…

Many complex systems exhibit interactions that depend not only on pairwise connections, but also group structures and memory effects. To capture such effects, we develop a unified tensor framework for modeling higher-order Markov chains…

Clustering is a data analysis method for extracting knowledge by discovering groups of data called clusters. Among these methods, state-of-the-art density-based clustering methods have proven to be effective for arbitrary-shaped clusters.…

When forming a team or group of individuals, we often seek a balance of expertise in a particular task while at the same time maintaining diversity of skills within each group. Here, we view the problem of finding diverse and experienced…