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...

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

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

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...

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...

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

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...

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

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

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

adjacency matrix, n = |V | the number of nodes and D the distance matrix. The basic idea to parallelize the algorithm is to partition the matrix and split...

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...

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

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...

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...

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

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

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...

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

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...

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...

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

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

of its input, when the input is provided in the form of an explicit distance matrix. The algorithm uses an amount of memory proportional to the number...

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

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