Related papers: A Set-to-Set Distance Measure in Hyperbolic Space
The two-dimensional hyperbolic plane, $\mathbb{H}^2$, is an unusual system in that dimensionality changes with scale: locally two-dimensional and planar at short distances, but effectively infinite-dimensional at large scales, it provides…
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…
Classification in the sense of similarity is an important issue. In this paper, we study similarity classification in Topological Data Analysis. We define a pseudometric $d_{S}^{(p)}$ to measure the distance between barcodes generated by…
Finding interesting symmetrical topological structures in high-dimensional systems is an important problem in statistical machine learning. Limited amount of available high-dimensional data and its sensitivity to noise pose computational…
Distance measures play an important role in shape classification and data analysis problems. Topological distances based on Reeb graphs and persistence diagrams have been employed to obtain effective algorithms in shape matching and scalar…
Deep distance metric learning (DDML), which is proposed to learn image similarity metrics in an end-to-end manner based on the convolution neural network, has achieved encouraging results in many computer vision tasks.$L2$-normalization in…
In recent years, networks with higher-order interactions have emerged as a powerful tool to model complex systems. Comparing these higher-order systems remains however a challenge. Traditional similarity measures designed for pairwise…
Recent studies have demonstrated the potential of hyperbolic geometry for capturing complex patterns from interaction data in recommender systems. In this work, we introduce a novel hyperbolic recommendation model that uses geometrical…
Hypergraphs have been becoming a popular choice to model complex, non-pairwise, and higher-order interactions for recommender system. However, compared with traditional graph-based methods, the constructed hypergraphs are usually much…
We show how to construct in linear time coresets of constant size for farthest point problems in fixed-dimensional hyperbolic space. Our coresets provide both an arbitrarily small relative error and additive error $\varepsilon$. More…
The notion of task similarity is at the core of various machine learning paradigms, such as domain adaptation and meta-learning. Current methods to quantify it are often heuristic, make strong assumptions on the label sets across the tasks,…
3D contrastive representation learning has exhibited remarkable efficacy across various downstream tasks. However, existing contrastive learning paradigms based on cosine similarity fail to deeply explore the potential intra-modal…
This paper introduces the induced matching distance, a novel topological metric designed to compare discrete structures represented by a symmetric non-negative function. We apply this notion to analyze agent trajectories over time. We use…
Visual environments are inherently hierarchical, as a panoramic view naturally encompasses and organizes multiple perspective views within its field. Capturing this hierarchy is crucial for effective perspective-to-equirectangular (P2E)…
This paper is one in a series that investigates topological measures on locally compact spaces. A topological measure is a set function which is finitely additive on the collection of open and compact sets, inner regular on open sets, and…
Autonomous robots are increasingly becoming a strong fixture in social environments. Effective crowd navigation requires not only safe yet fast planning, but should also enable interpretability and computational efficiency for working in…
The need to understand the structure of hierarchical or high-dimensional data is present in a variety of fields. Hyperbolic spaces have proven to be an important tool for embedding computations and analysis tasks as their non-linear nature…
The non-Euclidean geometry of hyperbolic spaces has recently garnered considerable attention in the realm of representation learning. Current endeavors in hyperbolic representation largely presuppose that the underlying hierarchies can be…
The aim of this work is to study a kind of refinement of the entropy conjecture, in the context of partially hyperbolic diffeomorphisms with one dimensional central direction, of d-dimensional torus. We start by establishing a connection…
Structuring latent representations in a hierarchical manner enables models to learn patterns at multiple levels of abstraction. However, most prevalent image understanding models focus on visual similarity, and learning visual hierarchies…