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...

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 x 1 , x 2 ,...

{\text{cosine distance}}=D_{C}(A,B):=1-S_{C}(A,B)\,.} It is important to note that, by virtue of being proportional to squared Euclidean distance, the cosine...

space of Euclidean geometry, but in modern mathematics there are Euclidean spaces of any positive integer dimension n, which are called Euclidean n-spaces...

Manhattan distance. Common metrics are: Euclidean distance Taxicab geometry, also known as City block distance or Manhattan distance. Chebyshev distance There...

Manhattan geometry is geometry where the familiar Euclidean distance is ignored, and the distance between two points is instead defined to be the sum...

meaning of distance in classical physics, including Newtonian mechanics. Straight-line distance is formalized mathematically as the Euclidean distance in two-...

transformations of that space that preserve the Euclidean distance between any two points (also called Euclidean transformations). The group depends only on...

Minkowski distance or Minkowski metric is a metric in a normed vector space which can be considered as a generalization of both the Euclidean distance and the...

squared Euclidean (which unlike Euclidean, does not have triangle inequality) distance at its core. The common learning goal is to minimize a distance metric...

TSPs for various metrics. In the Euclidean TSP (see below), the distance between two cities is the Euclidean distance between the corresponding points...

analogous to Euclidean geometry but without uniquely determined parallel lines Euclidean distance, the distance between pairs of points in Euclidean spaces...

called Euclidean transformation or Euclidean isometry) is a geometric transformation of a Euclidean space that preserves the Euclidean distance between...

variance, then the Mahalanobis distance corresponds to standard Euclidean distance in the transformed space. The Mahalanobis distance is thus unitless, scale-invariant...

particular, the Euclidean distance in a Euclidean space is defined by a norm on the associated Euclidean vector space, called the Euclidean norm, the 2-norm...

populations having the same allele Similar to Euclidean distance, Czekanowski distance involves calculated the distance between points of allele frequency that...

matching Damerau–Levenshtein distance diff Dynamic time warping Euclidean distance Homology of sequences in genetics Hamming distance Hunt–Szymanski algorithm...

include Euclidean distance, Manhattan distance, Minkowski distance, and Chebyshev distance. The Euclidean distance formula is used to find the distance between...

mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry...

matrix. A pre-distance matrix that can be embedded in a Euclidean space is called a Euclidean distance matrix. For mixed-type data that contain numerical as...

2 {\displaystyle n(n-1)/2} pairwise distance polynomials between n points in a real Euclidean space are Euclidean invariants that are associated via the...

thousands of years. When Euclidean space is represented by a Cartesian coordinate system in analytic geometry, Euclidean distance satisfies the Pythagorean...

clustering minimizes within-cluster variances (squared Euclidean distances), but not regular Euclidean distances, which would be the more difficult Weber problem:...

(involving the re-centering of Euclidean distance matrices) between two random vectors, and then compares this value to the distance correlations of many shuffles...

definitions make use of the Euclidean distance in a device-independent color space. As most definitions of color difference are distances within a color space...

interest while wanting to find a representative using some distance other than squared euclidean distance (for instance in movie-ratings). For some data sets...

Euclidean space, the isometry group (maps preserving the regular Euclidean distance) is the Euclidean group. It is generated by rotations, reflections and translations...

the quasar, galaxy, etc.). The distance measures discussed here all reduce to the common notion of Euclidean distance at low redshift. In accord with...

Damerau–Levenshtein distance Euclidean distance Gap-Hamming problem Gray code Jaccard index Jaro–Winkler distance Levenshtein distance Mahalanobis distance Mannheim...

3-dimensional Euclidean space with its usual notion of distance. Other well-known examples are a sphere equipped with the angular distance and the hyperbolic...