Related papers: Euclidean Distance Matrices: Essential Theory, Alg…

We introduce a rigorous, physically appealing, and practical way to measure distances between exchange-only correlations of interacting many-electron systems, which works regardless of their size and inhomogeneity. We show that this…

We consider the projected semi-definite and Euclidean distance cones onto a subset of the matrix entries. These two sets are precisely the input data defining feasible semi-definite and Euclidean distance completion problems. We classify…

Discrete Euclidian Spaces (DESs) are the beginning of a journey without return towards the discretization of mathematics. Important mathematical concepts- such as the idea of number or the systems of numeration, whose formal definition is…

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…

Estimating the location of N coordinates in a P dimensional Euclidean space from pairwise distances (or proximity measurements), is a principal challenge in a wide variety of fields. Conventionally, when localizing a static network of…

Deep metric learning employs deep neural networks to embed instances into a metric space such that distances between instances of the same class are small and distances between instances from different classes are large. In most existing…

Self-Organising Maps (SOM) are Artificial Neural Networks used in Pattern Recognition tasks. Their major advantage over other architectures is human readability of a model. However, they often gain poorer accuracy. Mostly used metric in SOM…

Classical multidimensional scaling only works well when the noisy distances observed in a high dimensional space can be faithfully represented by Euclidean distances in a low dimensional space. Advanced models such as Maximum Variance…

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on…

Electrocardiogram (ECG) is widely used in healthcare applications, such as arrhythmia detection and sleep monitoring, making accurate ECG analysis critically essential. Traditional deep learning models for ECG are task-specific, with…

Performance accuracy of the Euclidean Distance Discriminant rule (EDDR) is studied in the high-dimensional asymptotic framework which allows the dimensionality to exceed sample size. Under mild assumptions on the traces of the covariance…

We describe new approaches for distances between pairs of 2-dimensional surfaces (embedded in 3-dimensional space) that use local structures and global information contained in inter-structure geometric relationships. We present algorithms…

Single-cell omics enable the profiles of cells, which contain large numbers of biological features, to be quantified. Cluster analysis, a dimensionality reduction process, is used to reduce the dimensions of the data to make it…

Learning the distance metric between pairs of examples is of great importance for learning and visual recognition. With the remarkable success from the state of the art convolutional neural networks, recent works have shown promising…

This paper rigorously solves the challenging problem of recognizing periodic patterns under rigid motion in Euclidean geometry. The 3-dimensional case is practically important for justifying the novelty of solid crystalline materials…

The distance geometry problem asks to find a realization of a given simple edge-weighted graph in a Euclidean space of given dimension K, where the edges are realized as straight segments of lengths equal (or as close as possible) to the…

The EMD algorithm, first proposed in [11], made more robust as well as more versatile in [12], is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of…

Permanent electric dipole moments (EDMs) are sensitive probes of the symmetry structure of elementary particles, which in turn is closely tied to the baryon asymmetry in the universe. A meaningful interpretation framework for EDM…

Conventional ideal point models rely on Gaussian or quadratic utility functions that violate the triangle inequality, producing non-metric distances that complicate geometric interpretation and undermine clustering and dispersion-based…

Image similarity is a core concept in Image Analysis due to its extensive application in computer vision, image processing, and pattern recognition. The objective of our study is to evaluate Quasi-Euclidean metric as an image similarity…