Related papers: Hyperbolic Geometry in Computer Vision: A Survey

Modern machine learning increasingly leverages the insight that high-dimensional data often lie near low-dimensional, non-linear manifolds, an idea known as the manifold hypothesis. By explicitly modeling the geometric structure of data…

The class of coarsely convex spaces is a coarse geometric analogue of the class of nonpositively curved Riemannian manifolds. It includes Gromov hyperbolic spaces, CAT(0) spaces, proper injective metric spaces and systolic complexes. It is…

Electroencephalography (EEG)-based brain-computer interfaces facilitate direct communication with a computer, enabling promising applications in human-computer interactions. However, their utility is currently limited because EEG decoding…

Originally designed for applications in computer graphics, visual computing (VC) methods synthesize information about physical and virtual worlds, using prescribed algorithms optimized for spatial computing. VC is used to analyze geometry,…

We develop a geometric framework to study the structure and function of complex networks. We assume that hyperbolic geometry underlies these networks, and we show that with this assumption, heterogeneous degree distributions and strong…

Visual geolocalization, the task of predicting where an image was taken, remains challenging due to global scale, visual ambiguity, and the inherently hierarchical structure of geography. Existing paradigms rely on either large-scale…

We investigate the problem of finding smooth hypersurfaces of constant mean curvature in hyperbolic space, which can be represented as radial graphs over a subdomain of the upper hemisphere. Our approach is variational and our main results…

Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical material and to work with it. This approach lends itself…

Object detection, for the most part, has been formulated in the euclidean space, where euclidean or spherical geodesic distances measure the similarity of an image region to an object class prototype. In this work, we study whether a…

Hyperbolic spaces allow for more efficient modeling of complex, hierarchical structures, which is particularly beneficial in tasks involving multi-modal data. Although hyperbolic geometries have been proven effective for language-image…

Learning graph representations via low-dimensional embeddings that preserve relevant network properties is an important class of problems in machine learning. We here present a novel method to embed directed acyclic graphs. Following prior…

Multi-view clustering (MVC) aims to uncover the latent structure of multi-view data by learning view-common and view-specific information. Although recent studies have explored hyperbolic representations for better tackling the…

Probabilistic Latent Variable Models (LVMs) excel at modeling complex, high-dimensional data through lower-dimensional representations. Recent advances show that equipping these latent representations with a Riemannian metric unlocks…

Hyperbolic geometry is an effective geometry for embedding hierarchical data structures. Hyperbolic learning has therefore become increasingly prominent in machine learning applications where data is hierarchically organized or governed by…

We present a large scale hyperbolic recommender system. We discuss why hyperbolic geometry is a more suitable underlying geometry for many recommendation systems and cover the fundamental milestones and insights that we have gained from its…

Many scientific fields study data with an underlying structure that is a non-Euclidean space. Some examples include social networks in computational social sciences, sensor networks in communications, functional networks in brain imaging,…

Image analysis in the euclidean space through linear hyperspaces is well studied. However, in the quest for more effective image representations, we turn to hyperbolic manifolds. They provide a compelling alternative to capture complex…

Most previous heterogeneous graph embedding models represent elements in a heterogeneous graph as vector representations in a low-dimensional Euclidean space. However, because heterogeneous graphs inherently possess complex structures, such…

Hyperbolic machine learning is an emerging field aimed at representing data with a hierarchical structure. However, there is a lack of tools for evaluation and analysis of the resulting hyperbolic data representations. To this end, we…

Functional magnetic resonance imaging (fMRI) reveals complex brain functional networks with hierarchical topologies crucial for cognitive processing. Standard Euclidean Graph Neural Networks (GNNs) often struggle to represent these…