Related papers: A Distance Function for Comparing Straight-Edge Ge…
In this paper we focus on the linear functionals defining an approximate version of the gradient of a function. These functionals are often used when dealing with optimization problems where the computation of the gradient of the objective…
Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function.…
Very few studies involve how to construct the efficient RBFs by means of problem features. Recently the present author presented general solution RBF (GS-RBF) methodology to create operator-dependent RBFs successfully [1]. On the other…
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…
Modeling place functions from a computational perspective is a prevalent research topic. Trajectory embedding, as a neural-network-backed dimension reduction technology, allows the possibility to put places with similar social functions at…
The graph is one of the most widely used mathematical structures in engineering and science because of its representational power and inherent ability to demonstrate the relationship between objects. The objective of this work is to…
When matching parts of a surface to its whole, a fundamental question arises: Which points should be included in the matching process? The issue is intensified when using isometry to measure similarity, as it requires the validation of…
The purpose of this paper is to give a survey on the notions of distance between subsets either of a metric space or of a measure space, including definitions, a classification, and a discussion of the best-known distance functions, which…
The Escherization problem involves finding a closed figure that tiles the plane that is most similar to a given goal figure. In Koizumi and Sugihara's formulation of the Escherization problem, the tile and goal figures are represented as…
Distance plays a fundamental role in measuring similarity between objects. Various visualization techniques and learning tasks in statistics and machine learning such as shape matching, classification, dimension reduction and clustering…
Data consisting of a graph with a function mapping into $\mathbb{R}^d$ arise in many data applications, encompassing structures such as Reeb graphs, geometric graphs, and knot embeddings. As such, the ability to compare and cluster such…
For pattern recognition like image recognition, it has become clear that each machine-learning dictionary data actually became data in probability space belonging to Euclidean space. However, the distances in the Euclidean space and the…
This research work aims to explore the distortions in distance in equidistant cylindrical projection. The horizontal bending that occurs in the projection process can be assessed by performing a geometric analysis using Tissot's…
We introduce a differential visual similarity metric to train deep neural networks for 3D reconstruction, aimed at improving reconstruction quality. The metric compares two 3D shapes by measuring distances between multi-view images…
Neural networks that map 3D coordinates to signed distance function (SDF) or occupancy values have enabled high-fidelity implicit representations of object shape. This paper develops a new shape model that allows synthesizing novel distance…
The Straightness is a measure designed to characterize a pair of vertices in a spatial graph. It is defined as the ratio of the Euclidean distance to the graph distance between these vertices. It is often used as an average, for instance to…
The $\mathcal{G}_I^0$ distribution is able to characterize different regions in monopolarized SAR imagery. It is indexed by three parameters: the number of looks (which can be estimated in the whole image), a scale parameter and a texture…
Measuring visual similarity between two or more instances within a data distribution is a fundamental task in image retrieval. Theoretically, non-metric distances are able to generate a more complex and accurate similarity model than metric…
Finite differences have been widely used in mathematical theory as well as in scientific and engineering computations. These concepts are constantly mentioned in calculus. Most frequently-used difference formulas provide excellent…
We investigate two classes of transformations of cosine similarity and Pearson and Spearman correlations into metric distances, utilising the simple tool of metric-preserving functions. The first class puts anti-correlated objects maximally…