Related papers: Weighted distance transforms generalized to module…
We provide a simple method and relevant theoretical analysis for efficiently estimating higher-order lp distances. While the analysis mainly focuses on l4, our methodology extends naturally to p = 6,8,10..., (i.e., when p is even).…
We prove some weighted Fourier restriction estimates using polynomial partitioning and refined Strichartz estimates. As application we obtain improved spherical average decay rates of the Fourier transform of fractal measures, and therefore…
The original k-means clustering method works only if the exact vectors representing the data points are known. Therefore calculating the distances from the centroids needs vector operations, since the average of abstract data points is…
We consider the directed Hausdorff distance between point sets in the plane, where one or both point sets consist of imprecise points. An imprecise point is modelled by a disc given by its centre and a radius. The actual position of an…
Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…
A weighted pointed curve consists of a nodal curve and a sequence of marked smooth points, each assigned a number between zero and one. A subset of the marked points may coincide if the sum of the corresponding weights is no greater than…
We study the metric structure of walks on graphs, understood as Lipschitz sequences. To this end, a weighted metric is introduced to handle sequences, enabling the definition of distances between walks based on stepwise vertex distances and…
A generalized prefactorization of compact schemes aimed at reducing the stencil and improving the computational efficiency is proposed here in the framework of transport equations. By the prefactorization introduced here, the computational…
Function-correcting codes are designed to reduce redundancy of codes when protecting function values of information against errors. As generalizations of Hamming weights and Lee weights over $ \mathbb{Z}_{4} $, homogeneous weights are used…
Our work presents extensive empirical evidence that layer rotation, i.e. the evolution across training of the cosine distance between each layer's weight vector and its initialization, constitutes an impressively consistent indicator of…
This report presents a new, algorithmic approach to the distributions of the distance between two points distributed uniformly at random in various polygons, based on the extended Kinematic Measure (KM) from integral geometry. We first…
This short note establishes explicit and broadly applicable relationships between persistence-based distances computed locally and globally. In particular, we show that the bottleneck distance between two zigzag persistence modules…
The aim of this work is to give degree formulas for the generalized Hamming weights of evaluation codes and to show lower bounds for these weights. In particular, we give degree formulas for the generalized Hamming weights of…
This paper provides the theoretical foundation for the construction of lattice algorithms for multivariate $L_2$ approximation in the worst case setting, for functions in a periodic space with general weight parameters. Our construction…
Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in…
The measurement of distance between two objects is generalized to the case where the objects are no longer points but are one-dimensional. Additional concepts such as non-extensibility, curvature constraints, and non-crossing become central…
This work has the purpose of applying the concept of Geometric Calculus (Clifford Algebras) to the Fibre Bundle description of Quantum Mechanics. Thus, it is intended to generalize that formulation to curved spacetimes [the base space of…
Many modern data analysis algorithms either assume that or are considerably more efficient if the distances between the data points satisfy a metric. These algorithms include metric learning, clustering, and dimensionality reduction.…
Given two distributions $P$ and $S$ of equal total mass, the Earth Mover's Distance measures the cost of transforming one distribution into the other, where the cost of moving a unit of mass is equal to the distance over which it is moved.…
We define generalized distance-squared mappings, and we concentrate on the plane to plane case. We classify generalized distance-squared mappings of the plane into the plane in a recognizable way.