Related papers: Community detection, pattern recognition, and hype…
The application of network techniques to the analysis of neural data has greatly improved our ability to quantify and describe these rich interacting systems. Among many important contributions, networks have proven useful in identifying…
Embedding a network in hyperbolic space can reveal interesting features for the network structure, especially in terms of self-similar characteristics. The hidden metric space, which can be thought of as the underlying structure of the…
Topological data analysis can reveal higher-order structure beyond pairwise connections between vertices in complex networks. We present a new method based on discrete Morse theory to study topological properties of unweighted and…
A network can be analyzed at different topological scales, ranging from single nodes to motifs, communities, up to the complete structure. We propose a novel intermediate-level topological analysis that considers non-overlapping subgraphs…
Community is a common characteristic of networks including social networks, biological networks, computer and information networks, to name a few. Community detection is a basic step for exploring and analysing these network data.…
We introduce and explore a new method for inferring hidden geometric coordinates of nodes in complex networks based on the number of common neighbors between the nodes. We compare this approach to the HyperMap method, which is based only on…
The study of complex networks has significantly advanced our understanding of community structures which serves as a crucial feature of real-world graphs. Detecting communities in graphs is a challenging problem with applications in…
Many real world systems or web services can be represented as a network such as social networks and transportation networks. In the past decade, many algorithms have been developed to detect the communities in a network using connections…
Many community detection algorithms require the introduction of a measure on the set of nodes. Previously, a lot of efforts have been made to find the top-performing measures. In most cases, experiments were conducted on several datasets or…
In topological data analysis, persistent homology is used to study the "shape of data". Persistent homology computations are completely characterized by a set of intervals called a bar code. It is often said that the long intervals…
Topological properties of networks are widely applied to study the link-prediction problem recently. Common Neighbors, for example, is a natural yet efficient framework. Many variants of Common Neighbors have been thus proposed to further…
Despite the tremendous success of graph-based learning systems in handling structural data, it has been widely investigated that they are fragile to adversarial attacks on homophilic graph data, where adversaries maliciously modify the…
Persistent homology is a technique recently developed in algebraic and computational topology well-suited to analysing structure in complex, high-dimensional data. In this paper, we exposit the theory of persistent homology from first…
Community detection refers to the problem of clustering the nodes of a network (either graph or hypergrah) into groups. Various algorithms are available for community detection and all these methods apply to uncensored networks. In…
With the emergence of graph databases, the task of frequent subgraph discovery has been extensively addressed. Although the proposed approaches in the literature have made this task feasible, the number of discovered frequent subgraphs is…
In a world abundant with diverse data arising from complex acquisition techniques, there is a growing need for new data analysis methods. In this paper we focus on high-dimensional data that are organized into several hierarchical datasets.…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
In this paper, we propose a method that extends the persistence-based topological data analysis (TDA) that is typically used for characterizing shapes to general networks. We introduce the concept of the community tree, a tree structure…
Understanding the structure of high-dimensional data is fundamental to neuroscience and other data-intensive scientific fields. While persistent homology effectively identifies basic topological features such as "holes," it lacks the…
Hypergraphs are mathematical models for many problems in data sciences. In recent decades, the topological properties of hypergraphs have been studied and various kinds of (co)homologies have been constructed (cf. [3, 4, 12]). In this…