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Distance matrix. In mathematics, computer science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements of a set. [1] Depending upon the application involved, the distance being used to define this matrix may or may not be a metric. If there are N ...
GraphHopper is an open-source routing library and server written in Java and provides a routing API over HTTP. [1] It runs on the server, desktop, Android, iOS or Raspberry Pi. [2][3] By default OpenStreetMap data for the road network and elevation data from the Shuttle Radar Topography Mission is used. The front-end is open-source too and ...
Euclidean distance matrix. In mathematics, a Euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in Euclidean space. For points in k -dimensional space ℝk, the elements of their Euclidean distance matrix A are given by squares of distances between them. That is. where denotes the Euclidean norm on ℝk.
Distance is often defined as the fraction of mismatches at aligned positions, with gaps either ignored or counted as mismatches. [1] Distance-matrix methods are frequently used as the basis for progressive and iterative types of multiple sequence alignment. The main disadvantage of distance-matrix methods is their inability to efficiently use ...
The Mahalanobis distance is a measure of the distance between a point and a distribution , introduced by P. C. Mahalanobis in 1936. [1] The mathematical details of Mahalanobis distance has appeared in the Journal of The Asiatic Society of Bengal. [2] Mahalanobis's definition was prompted by the problem of identifying the similarities of skulls ...
DO for general metric spaces. The oracle is built of a decreasing collection of k +1 sets of vertices: For every : contains each element of , independently, with probability . Note that the expected size of is . The elements of are called i-centers. For every node v, calculate its distance from each of these sets: For every : and .
Distance correlation. In statistics and in probability theory, distance correlation or distance covariance is a measure of dependence between two paired random vectors of arbitrary, not necessarily equal, dimension. The population distance correlation coefficient is zero if and only if the random vectors are independent.
In mathematics and its applications, the signed distance function or signed distance field (SDF) is the orthogonal distance of a given point x to the boundary of a set Ω in a metric space (such as the surface of a geometric shape), with the sign determined by whether or not x is in the interior of Ω. The function has positive values at points ...