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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 ...
The Levenshtein distance between two words is the minimum number of single-character edits (insertions, deletions or substitutions) required to change one word into the other. It is named after Soviet mathematician Vladimir Levenshtein, who defined the metric in 1965. [1] Levenshtein distance may also be referred to as edit distance, although ...
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 .
Euclidean distance. In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance . These names come from the ancient Greek ...
Distance matrices are used in phylogeny as non-parametric distance methods and were originally applied to phenetic data using a matrix of pairwise distances. These distances are then reconciled to produce a tree (a phylogram, with informative branch lengths). The distance matrix can come from a number of different sources, including measured ...
Neighbor joining takes a distance matrix, which specifies the distance between each pair of taxa, as input. The algorithm starts with a completely unresolved tree, whose topology corresponds to that of a star network, and iterates over the following steps, until the tree is completely resolved, and all branch lengths are known: Based on the ...
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.
Jaccard distance is commonly used to calculate an n × n matrix for clustering and multidimensional scaling of n sample sets. This distance is a metric on the collection of all finite sets. [8] [9] [10] There is also a version of the Jaccard distance for measures, including probability measures.