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Distributed stochastic optimization algorithms can simultaneously process large-scale datasets, significantly accelerating model training. However, their effectiveness is often hindered by the sparsity of distributed networks and data…

In this paper, we develop a novel method for fast geodesic distance queries. The key idea is to embed the mesh into a high-dimensional space, such that the Euclidean distance in the high-dimensional space can induce the geodesic distance in…

Euclidean distance matrix optimization with ordinal constraints (EDMOC) has found important applications in sensor network localization and molecular conformation. It can also be viewed as a matrix formulation of multidimensional scaling,…

Qualifying the discrepancy between 3D geometric models, which could be represented with either point clouds or triangle meshes, is a pivotal issue with board applications. Existing methods mainly focus on directly establishing the…

The Earth Mover's Distance (EMD) is a state-of-the art metric for comparing discrete probability distributions, but its high distinguishability comes at a high cost in computational complexity. Even though linear-complexity approximation…

Random walk based node embedding algorithms learn vector representations of nodes by optimizing an objective function of node embedding vectors and skip-bigram statistics computed from random walks on the network. They have been applied to…

The distance metric plays an important role in nearest neighbor (NN) classification. Usually the Euclidean distance metric is assumed or a Mahalanobis distance metric is optimized to improve the NN performance. In this paper, we study the…

Most previous bounding-box-based segmentation methods assume the bounding box tightly covers the object of interest. However it is common that a rectangle input could be too large or too small. In this paper, we propose a novel segmentation…

Distance Geometry Problem (DGP) and Nonlinear Mapping (NLM) are two well established questions: Distance Geometry Problem is about finding a Euclidean realization of an incomplete set of distances in a Euclidean space, whereas Nonlinear…

We present a new numerical method for the isometric embedding of 2-geometries specified by their 2-metrics in three dimensional Euclidean space. Our approach is to directly solve the fundamental embedding equation supplemented by six…

We present a novel two-view geometry estimation framework which is based on a differentiable robust loss function fitting. We propose to treat the robust fundamental matrix estimation as an implicit layer, which allows us to avoid…

We introduce the Equilibrated Averaging Residual Method (EARM), a unified equilibrated flux-recovery framework for elliptic interface problems that applies to a broad class of finite element discretizations. The method is applicable in both…

This paper presents a novel method for modeling the shape of a continuum robot as a Neural Configuration Euclidean Distance Function (N-CEDF). By learning separate distance fields for each link and combining them through the kinematics…

We present a framework for embedding graph structured data into a vector space, taking into account node features and topology of a graph into the optimal transport (OT) problem. Then we propose a novel distance between two graphs, named…

This paper proposes two algorithms for estimating square Wasserstein distance matrices from a small number of entries. These matrices are used to compute manifold learning embeddings like multidimensional scaling (MDS) or Isomap, but…

The Earth movers distance (EMD) is a measure of distance between probability distributions which is at the heart of mass transportation theory. Recent research has shown that the EMD plays a crucial role in studying the potential impact of…

Point cloud registration is a central theme in computer vision, with alignment algorithms continuously improving for greater robustness. Commonly used methods evaluate Euclidean distances between point clouds and minimize an objective…

Pairwise Euclidean distance calculation is a fundamental step in many machine learning and data analysis algorithms. In real-world applications, however, these distances are frequently distorted by heteroskedastic noise$\unicode{x2014}$a…

In the era of foundation models and Large Language Models (LLMs), Euclidean space has been the de facto geometric setting for machine learning architectures. However, recent literature has demonstrated that this choice comes with…

We present a new approach to approximate nearest-neighbor queries in fixed dimension under a variety of non-Euclidean distances. We are given a set $S$ of $n$ points in $\mathbb{R}^d$, an approximation parameter $\varepsilon > 0$, and a…