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Hypergraphs, a generalization of graphs, naturally represent groupwise relationships among multiple individuals or objects, which are common in many application areas, including web, bioinformatics, and social networks. The flexibility in the number of nodes in each hyperedge, which provides the expressiveness of hypergraphs, brings about structural differences between graphs and hypergraphs. Especially, the overlaps of hyperedges lead to complex high-order relations beyond pairwise relations, r

Hypergraphs, which belong to the family of higher-order networks, are a natural and powerful choice for modeling group interactions in the real world. For example, when modeling collaboration networks, which may involve not just two but three or more people, the use of hypergraphs allows us to explore beyond pairwise (dyadic) patterns and capture groupwise (polyadic) patterns. The mathematical complexity of hypergraphs offers both opportunities and challenges for hypergraph mining. The goal of h

Group interactions arise in our daily lives (email communications, on-demand ride sharing, comment interactions on online communities, to name a few), and they together form hypergraphs that evolve over time. Given such temporal hypergraphs, how can we describe their underlying design principles? If their sizes and time spans are considerably different, how can we compare their structural and temporal characteristics? In this work, we define 96 temporal hypergraph motifs (TH-motifs), and propose

Sequences of group interactions, such as emails, online discussions, and co-authorships, are ubiquitous; and they are naturally represented as a stream of hyperedges (i.e., sets of nodes). Despite its broad potential applications, anomaly detection in hypergraphs (i.e., sets of hyperedges) has received surprisingly little attention, compared to anomaly detection in graphs. While it is tempting to reduce hypergraphs to graphs and apply existing graph-based methods, according to our experiments, t

Graph Neural Networks (GNNs) have emerged as effective tools in recommender systems. Among various GNN models, LightGCN is distinguished by its simplicity and outstanding performance. Its efficiency has led to widespread adoption across different domains, including social, bundle, and multimedia recommendations. In this paper, we thoroughly examine the mechanisms of LightGCN, focusing on its strategies for scaling embeddings, aggregating neighbors, and pooling embeddings across layers. Our analy

We formally define a hyperlink classification problem in web search by classifying hyperlinks into three classes based on their roles: navigation, suggestion, and action. Real-world web graph datasets are generated for this task. We approach the hyperlink classification problem from a structured graph embedding perspective, and show that we can solve the problem by modifying the recently proposed knowledge graph embedding techniques. The key idea of our modification is to introduce a relation pe

Hypergraphs naturally represent group interactions, which are omnipresent in many domains: collaborations of researchers, co-purchases of items, joint interactions of proteins, to name a few. In this work, we propose tools for answering the following questions in a systematic manner: (Q1) what are structural design principles of real-world hypergraphs? (Q2) how can we compare local structures of hypergraphs of different sizes? (Q3) how can we identify domains which hypergraphs are from? We first

Item popularity in real-world data follows a long-tail distribution, where a few items attract most of the attention, while the majority receive much less. This disparity results in high-quality embeddings for popular (head) items, but lower-quality embeddings for unpopular (tail) items, leading to less accurate recommendations for the latter. Our observations confirm that embeddings of tail items often exhibit (1) magnitudes (i.e., norms) that are less reflective of actual popularity and (2) di

Group interactions are prevalent in various complex systems (e.g., collaborations of researchers and group discussions on online Q&A sites), and they are commonly modeled as hypergraphs. Hyperedges, which compose a hypergraph, are non-empty subsets of any number of nodes, and thus each hyperedge naturally represents a group interaction among entities. The higher-order nature of hypergraphs brings about unique structural properties that have not been considered in ordinary pairwise graphs. In thi

Given a sequence of epidemic events, can a single epidemic model capture its dynamics during the entire period? How should we divide the sequence into segments to better capture the dynamics? Throughout human history, infectious diseases (e.g., the Black Death and COVID-19) have been serious threats. Consequently, understanding and forecasting the evolving patterns of epidemic events are critical for prevention and decision making. To this end, epidemic models based on ordinary differential equa

Sets have been used for modeling various types of objects, and measuring similarity between them has been a key building block of a wide range of applications. However, as sets have grown in numbers and sizes, the computational cost and storage required for set similarity computation have become substantial. In this work, we propose SET2Box, which represents sets as boxes to precisely capture overlaps of sets and thus accurately estimate various similarity measures. Additionally, based on the pr

Group interactions are prevalent in various complex systems (e.g., collaborations of researchers and group discussions on online Q&A sites), and they are commonly modeled as hypergraphs. Hyperedges, which compose a hypergraph, are non-empty subsets of any number of nodes, and thus each hyperedge naturally represents a group interaction among entities. The higher-order nature of hypergraphs brings about unique structural properties that have not been considered in ordinary pairwise graphs.