science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements...

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 , …...

Computing the Levenshtein distance is based on the observation that if we reserve a matrix to hold the Levenshtein distances between all prefixes of the...

of the distance between each pair of taxa (e.g., species or sequences) to create the phylogenetic tree. Neighbor joining takes a distance matrix, which...

0)-adjacency matrix. This matrix is used in studying strongly regular graphs and two-graphs. The distance matrix has in position (i, j) the distance between...

inferring the supporting tree from one distance matrix and then for adding reticulation branches using another distance matrix. Such an algorithm can be useful...

information contained in a distance matrix. It is a form of non-linear dimensionality reduction. Given a distance matrix with the distances between each pair of...

{T}}} and positive semi-definite covariance matrix Σ {\displaystyle \mathbf {\Sigma } } , the Mahalanobis distance of a point x → = ( x 1 , x 2 , x 3 , … ...

squared distance. The collection of all squared distances between pairs of points from a finite set may be stored in a Euclidean distance matrix, and is...

similarity matrix (or a dissimilarity matrix). At each step, the nearest two clusters are combined into a higher-level cluster. The distance between any...

(mathematics) Distance geometry problem Dijkstra's algorithm Distance matrix Distance set Engineering tolerance Multiplicative distance Optical path length...

determining if any real symmetric matrix is a Euclidean distance matrix for some n + 1 points in the field of distance geometry. Karl Menger was a young...

Distance matrices are used in phylogeny as non-parametric distance methods and were originally applied to phenetic data using a matrix of pairwise distances...

else u {\displaystyle u} is a pseudo-peripheral vertex. Distance matrix Resistance distance Betweenness centrality Centrality Closeness Degree diameter...

Min-plus matrix multiplication, also known as distance product, is an operation on matrices. Given two n × n {\displaystyle n\times n} matrices A = (...

dendrogram) First distance matrix update We then proceed to update the initial proximity matrix D 1 {\displaystyle D_{1}} into a new proximity matrix D 2 {\displaystyle...

an example. Each axis on a PCA plot is an eigenvector of the covariance matrix of shape variables. The first axis accounts for maximum variation in the...

dendrogram) First distance matrix update We then proceed to update the initial proximity matrix D 1 {\displaystyle D_{1}} into a new proximity matrix D 2 {\displaystyle...

Dissimilarity (which is 1 - the Jaccard Index). This distance matrix is used to calculate the distance between two points on a one-dimensional graph.[citation...

The U-matrix (unified distance matrix) is a representation of a self-organizing map (SOM) where the Euclidean distance between the codebook vectors of...

matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries...

may be analyzed at once. Distance-matrix methods of phylogenetic analysis explicitly rely on a measure of "genetic distance" between the sequences being...

such norms are referred to as matrix norms. Matrix norms differ from vector norms in that they must also interact with matrix multiplication. Given a field...

Dijkstra's algorithm, for example). The top n eigenvectors of the geodesic distance matrix, represent the coordinates in the new n-dimensional Euclidean space...

a divide-and-conquer approach. Slightly faster algorithms based on distance matrix multiplication have been proposed by Tamaki & Tokuyama (1998) and by...

each program) that are available in the package include parsimony, distance matrix, and likelihood methods, including bootstrapping and consensus trees...

solve the traveling salesman problem (TSP), in which the input is a distance matrix between a set of cities, and the goal is to find a minimum-length tour...

skew-symmetric matrix. Other examples are the adjacency matrix of a finite simple graph, and a distance matrix or Euclidean distance matrix. In other words...

defined by Ward's method, in time proportional to the size of the input distance matrix and space linear in the number of points being clustered. Ward's minimum...

matrix is a graphical representation of similar sequences in a data series. Similarity can be explained by different measures, like spatial distance (distance...