相关论文: Hyper-distance Oracles in Hypergraphs
This paper aims for set-to-hypergraph prediction, where the goal is to infer the set of relations for a given set of entities. This is a common abstraction for applications in particle physics, biological systems, and combinatorial…
Do higher-order network structures aid graph semi-supervised learning? Given a graph and a few labeled vertices, labeling the remaining vertices is a high-impact problem with applications in several tasks, such as recommender systems, fraud…
Despite the prevalence of hypergraphs in a variety of high-impact applications, there are relatively few works on hypergraph representation learning, most of which primarily focus on hyperlink prediction, often restricted to the…
Network embedding has recently attracted lots of attentions in data mining. Existing network embedding methods mainly focus on networks with pairwise relationships. In real world, however, the relationships among data points could go beyond…
Many important real-world applications-such as social networks or distributed data bases-can be modeled as hypergraphs. In such a model, vertices represent entities-such as users or data records-whereas hyperedges model a group membership…
We present a scheme, based on Gilbert's algorithm for quadratic minimization [SIAM J. Contrl., vol. 4, pp. 61-80, 1966], to prove separation between a point and an arbitrary convex set $S\subset\mathbb{R}^{n}$ via calls to an oracle able to…
The microscopic organization of dynamical systems coupled via higher-order interactions plays a pivotal role in understanding their collective behavior. In this paper, we introduce a framework for systematically investigating the impact of…
Graphs are widely used to model data in many application domains. Thanks to the wide spread use of GPS-enabled devices, many applications assign a spatial attribute to graph vertices (e.g., geo-tagged social media). Users may issue a…
Modern deep learning models capture the semantics of complex data by transforming them into high-dimensional embedding vectors. Emerging applications, such as retrieval-augmented generation, use approximate nearest neighbor (ANN) search in…
A hypergraph is a useful combinatorial object to model ternary or higher-order relations among entities. Clustering hypergraphs is a fundamental task in network analysis. In this study, we develop two clustering algorithms based on…
Given a hypergraph $\mathcal{H}$, we introduce a new class of evaluation toric codes called edge codes derived from $\mathcal{H}$. We analyze these codes, focusing on determining their basic parameters. We provide estimations for the…
We introduce a novel measure for quantifying the error in input predictions. The error is based on a minimum-cost hyperedge cover in a suitably defined hypergraph and provides a general template which we apply to online graph problems. The…
Superpixels have become very popular in many computer vision applications. Nevertheless, they remain underexploited since the superpixel decomposition may produce irregular and non stable segmentation results due to the dependency to the…
How efficiently can we find an unknown graph using distance or shortest path queries between its vertices? Let $G = (V,E)$ be an unweighted, connected graph of bounded degree. The edge set $E$ is initially unknown, and the graph can be…
Visual recognition relies on understanding the semantics of image tokens and their complex interactions. Mainstream self-attention methods, while effective at modeling global pair-wise relations, fail to capture high-order associations…
We study the problem of designing \emph{sublinear spectral clustering oracles} for well-clusterable graphs. Such an oracle is an algorithm that, given query access to the adjacency list of a graph $G$, first constructs a compact data…
Groups with complex set intersection relations are a natural way to model a wide array of data, from the formation of social groups to the complex protein interactions which form the basis of biological life. One approach to representing…
We show how to assign labels of size $\tilde O(1)$ to the vertices of a directed planar graph $G$, such that from the labels of any three vertices $s,t,f$ we can deduce in $\tilde O(1)$ time whether $t$ is reachable from $s$ in the graph…
In this paper, we propose a simple and effective {geometric} model fitting method to fit and segment multi-structure data even in the presence of severe outliers. We cast the task of geometric model fitting as a representative mode-seeking…
Many real-world systems involve higher-order interactions and thus demand complex models such as hypergraphs. For instance, a research article could have multiple collaborating authors, and therefore the co-authorship network is best…