Related papers: Nearest Neighbor Search for Hyperbolic Embeddings

We explore a novel method to generate and characterize complex networks by means of their embedding on hyperbolic surfaces. Evolution through local elementary moves allows the exploration of the ensemble of networks which share common…

The problem of finding K-nearest neighbors in the given dataset for a given query point has been worked upon since several years. In very high dimensional spaces the K-nearest neighbor search (KNNS) suffers in terms of complexity in…

The complexity of nearest-neighbor search dominates the asymptotic running time of many sampling-based motion-planning algorithms. However, collision detection is often considered to be the computational bottleneck in practice. Examining…

We develop data structures for dynamic closest pair problems with arbitrary distance functions, that do not necessarily come from any geometric structure on the objects. Based on a technique previously used by the author for Euclidean…

Interactive exploration of large, multidimensional datasets plays a very important role in various scientific fields. It makes it possible not only to identify important structural features and forms, such as clusters of vertices and their…

Dense high dimensional vectors are becoming increasingly vital in fields such as computer vision, machine learning, and large language models (LLMs), serving as standard representations for multimodal data. Now the dimensionality of these…

Recently there was an increasing interest in applications of graph neural networks in non-Euclidean geometry; however, are non-Euclidean representations always useful for graph learning tasks? For different problems such as node…

The objective of ordinal embedding is to find a Euclidean representation of a set of abstract items, using only answers to triplet comparisons of the form "Is item $i$ closer to the item $j$ or item $k$?". In recent years, numerous…

Learning the embedding space, where semantically similar objects are located close together and dissimilar objects far apart, is a cornerstone of many computer vision applications. Existing approaches usually learn a single metric in the…

The issue of data sparsity poses a significant challenge to recommender systems. In response to this, algorithms that leverage side information such as review texts have been proposed. Furthermore, Cross-Domain Recommendation (CDR), which…

Embedding entities and relations into continuous vector spaces has attracted a surge of interest in recent years. Most embedding methods assume that all test entities are available during training, which makes it time-consuming to retrain…

Near neighbor problems are fundamental in algorithms for high-dimensional Euclidean spaces. While classical approaches suffer from the curse of dimensionality, locality sensitive hashing (LSH) can effectively solve a-approximate r-near…

Graph-based collaborative filtering is capable of capturing the essential and abundant collaborative signals from the high-order interactions, and thus received increasingly research interests. Conventionally, the embeddings of users and…

Graph embeddings have emerged as a powerful tool for representing complex network structures in a low-dimensional space, enabling the use of efficient methods that employ the metric structure in the embedding space as a proxy for the…

In many high-impact applications, it is important to ensure the quality of output of a machine learning algorithm as well as its reliability in comparison with the complexity of the algorithm used. In this paper, we have initiated a…

Neural embedding approaches have become a staple in the fields of computer vision, natural language processing, and more recently, graph analytics. Given the pervasive nature of these algorithms, the natural question becomes how to exploit…

Learning in hyperbolic spaces has attracted increasing attention due to its superior ability to model hierarchical structures of data. Most existing hyperbolic learning methods use fixed distance measures for all data, assuming a uniform…

In this work, we propose a fashion item recommendation model that incorporates hyperbolic geometry into user and item representations. Using hyperbolic space, our model aims to capture implicit hierarchies among items based on their visual…

Nearest neighbor search aims to obtain the samples in the database with the smallest distances from them to the queries, which is a basic task in a range of fields, including computer vision and data mining. Hashing is one of the most…

Hyperbolic geometry has recently garnered considerable attention in machine learning due to its capacity to embed hierarchical graph structures with low distortions for further downstream processing. This paper introduces a simple framework…