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Square matrix containing the distances between elements in a set
science and especially graph theory, a distance matrix is a square matrix (two-dimensional array) containing the distances, taken pairwise, between the elements
Distance_matrix
Type of 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 x 1 , x 2 , …
Euclidean_distance_matrix
Formula for the "volume" of an n-simplex
ultimately, in the field of distance geometry, determining whether any real symmetric matrix is a Euclidean distance matrix for some n + 1 {\displaystyle
Cayley–Menger_determinant
Computer science metric for string similarity
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
Levenshtein_distance
Length of shortest path between two nodes of a graph
theory, distances between nodes can be represented computationally by using a distance matrix (also called the all-pairs shortest-path matrix). This is
Distance_(graph_theory)
Bottom-up clustering method for creating phylogenetic trees
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
Neighbor_joining
Square matrix used to represent a graph or network
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
Adjacency_matrix
Separation between two points
(mathematics) Distance geometry problem Dijkstra's algorithm Distance matrix Distance set Engineering tolerance Multiplicative distance Optical path length
Distance
Statistical distance measure
{T}}} and positive semi-definite covariance matrix Σ {\displaystyle \mathbf {\Sigma } } , the Mahalanobis distance of a point x → = ( x 1 , x 2 , x 3 , …
Mahalanobis_distance
Norm on a vector space of matrices
such norms are referred to as matrix norms. Matrix norms behave in certain ways like the distance from the zero matrix. They are distinguished from the
Matrix_norm
Software for analyzing phylogenic trees
inferring the supporting tree from one distance matrix and then for adding reticulation branches using another distance matrix. Such an algorithm can be useful
T-REX_(web_server)
Length of a line segment
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
Euclidean_distance
Set of related ordination techniques used in information visualization
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
Multidimensional_scaling
Several types of mathematical matrix containing zeroes
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
Hollow_matrix
matrix is a graphical representation of similar sequences in a data series. Similarity can be explained by different measures, like spatial distance (distance
Self-similarity_matrix
Mathematical operation on matrices
Min-plus matrix multiplication, also known as distance product, is an operation on matrices. Given two n × n {\displaystyle n\times n} matrices A = (
Min-plus matrix multiplication
Min-plus_matrix_multiplication
Clustering algorithm minimizing the sum of distances to k representatives
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
K-medoids
Agglomerative hierarchical clustering method
similarity matrix (or a dissimilarity matrix). At each step, the nearest two clusters are combined into a higher-level cluster. The distance between any
UPGMA
Agglomerative hierarchical clustering method
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
Single-linkage_clustering
Self-organizing map
The U-matrix (unified distance matrix) is a representation of a self-organizing map (SOM) where the Euclidean distance between the codebook vectors of
U-matrix
Agglomerative hierarchical clustering method
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
Complete-linkage_clustering
Matrices used in construction of phylogenetic trees
Distance matrices are used in phylogeny as non-parametric distance methods and were originally applied to phenetic data using a matrix of pairwise distances
Distance matrices in phylogeny
Distance_matrices_in_phylogeny
Nonlinear dimensionality reduction method
Dijkstra's algorithm, for example). The top n eigenvectors of the geodesic distance matrix, represent the coordinates in the new n-dimensional Euclidean space
Isomap
Quantitative study of size and shape
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
Morphometrics
Solution of the traveling salesman problem
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
Held–Karp_algorithm
Application of computational algorithms, methods and programs to phylogenetic analyses
may be analyzed at once. Distance-matrix methods of phylogenetic analysis explicitly rely on a measure of "genetic distance" between the sequences being
Computational_phylogenetics
matrices used in mathematics, science and engineering. A matrix (plural matrices, or less commonly matrixes) is a rectangular array of numbers called entries
List_of_named_matrices
Problem in computer science
a divide-and-conquer approach. Slightly faster algorithms based on distance matrix multiplication have been proposed by Tamaki & Tokuyama (1998) and by
Maximum_subarray_problem
each program) that are available in the package include parsimony, distance matrix, and likelihood methods, including bootstrapping and consensus trees
PHYLIP
neighbor joining algorithm. Like neighbor joining, the method takes a distance matrix as input, and works by agglomerating clusters. However, the NeighborNet
Neighbor-net
is O(L^2) where L is the sequence. Distance Matrix – Using the calculated pairwise alignments, a distance matrix calculation is done to evaluate the
MAFFT
Statistical method in data analysis
valid measure of distance can be used. In fact, the observations themselves are not required: all that is used is a matrix of distances. On the other hand
Hierarchical_clustering
Array of numbers
In mathematics, a matrix (pl.: matrices) is a rectangular array of numbers or other mathematical objects with elements or entries arranged in rows and
Matrix_(mathematics)
Criterion applied in hierarchical cluster analysis
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
Ward's_method
Software for inferring bioinformatics split graphs
graphs, from various types of data such as a sequence alignment, a distance matrix or a set of trees. SplitsTree implements published methods such as
SplitsTree
Software for sequence alignment
by computing the k-mer distance for every pair of input sequences to create a distance matrix. UPGMA clusters the distance matrix to produce a binary tree
MUSCLE_(alignment_software)
Topological index of a molecule
topological indexes of chemical graphs, based on information in the distance matrix of the graph, have been developed subsequently to Wiener's work. The
Wiener_index
Evolution (ME) is a phylogenetic tree building method. It uses a pairwise distance matrix, calculated from a multiple sequence alignment, to generate a phylogenetic
Minimum_evolution
Stack-based method for clustering
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
Nearest-neighbor chain algorithm
Nearest-neighbor_chain_algorithm
Map that depicts the area accessible from a point within a time threshold
"QGIS Isochrones & Distance Matrix | QGIS TravelTime Plugin". "TravelTime ArcGIS plugin | Isochrones | Travel Time Distance Matrix". "Isochrone API -
Isochrone_map
Machine learning framework for portfolio construction
secondary distance matrix D ~ = d ~ i , j {\displaystyle {\tilde {D}}={{\tilde {d}}_{i,j}}} is computed, where each entry measures the Euclidean distance between
Hierarchical_Risk_Parity
Topics referred to by the same term
modeling Enterprise decision management Entity Data Model Euclidean distance matrix Experiment-directed metadynamics Edmonton, Alberta, Canada Edmonds
EDM
Compilation of software used to produce phylogenetic trees
(UPGMA), Bayesian phylogenetic inference, maximum likelihood, and distance matrix methods. List of phylogenetic tree visualization software Patterson
List of phylogenetics software
List_of_phylogenetics_software
Measure of the influence of a data point in regression analysis
Cook's distance is in the metric of an F distribution with p {\displaystyle p} and n − p {\displaystyle n-p} (as defined for the design matrix X {\displaystyle
Cook's_distance
taxa. The edit distances between sequences are calculated for each of the tree's internal vertices, such that the sum of all edit distances within the tree
Tree_alignment
shapeDNA include singular values of Geodesic Distance Matrix (SD-GDM) and Reduced BiHarmonic Distance Matrix (R-BiHDM). However, the eigenvalues are global
Spectral_shape_analysis
Computational phylogenetics program
version 4.0 (when the program became known as PAUP*) it also supports distance matrix and likelihood methods. Version 3.0 ran on Macintosh computers and
PAUP*
Measure of covariance of components of a random vector
covariance matrix (also known as auto-covariance matrix, dispersion matrix, variance matrix, or variance–covariance matrix) is a square matrix giving the
Covariance_matrix
context in which they studied the matrix. A Euclidean distance matrix is a particular example of Euclidean random matrix with either f(ri - rj) = |ri - rj|2
Euclidean_random_matrix
Agglomerative hierarchical clustering method
(dendrogram) that reflects the structure present in a pairwise distance matrix (or a similarity matrix). At each step, the nearest two clusters, say i {\displaystyle
WPGMA
Area of discrete mathematics
theorem on the number of spanning trees of a graph. The distance matrix, like the adjacency matrix, has both its rows and columns indexed by vertices, but
Graph_theory
symmetric matrix. A Supnick matrix is a square Monge array that is symmetric around the main diagonal. An n-by-n matrix is a Supnick matrix if, for all
Supnick_matrix
Filling in missing entries of a matrix
Matrix completion is the task of filling in the missing entries of a partially observed matrix, which is equivalent to performing data imputation in statistics
Matrix_completion
Statistical measure
grand mean of the distance matrix of the X sample. The notation is similar for the b values. (In the matrices of centered distances (Aj, k) and (Bj,k)
Distance_correlation
Aligning molecular sequences using sequence and structural information
the DALI, or Distance-matrix ALIgnment method, which breaks the input structures into hexapeptide fragments and calculates a distance matrix by evaluating
Structural_alignment
the distance matrix used in determining the solvability of the traveling salesman problem. These conditions apply to a special kind of cost matrix, the
Kalmanson combinatorial conditions
Kalmanson_combinatorial_conditions
Density-based data clustering algorithm
triangle of the distance matrix can be materialized to avoid distance recomputations, but this needs O(n²) memory, whereas a non-matrix based implementation
DBSCAN
Open source software analysis package
characters Phylogenetic discrete character methods Phylogeny distance matrix Phylogenetic distance matrix methods Phylogeny gene frequencies Phylogenetic gene
EMBOSS
Matrix representation of a graph
theory, the Laplacian matrix, also called the graph Laplacian, admittance matrix, Kirchhoff matrix, or discrete Laplacian, is a matrix representation of a
Laplacian_matrix
Matrix of partial derivatives of a vector-valued function
vector calculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order partial
Jacobian matrix and determinant
Jacobian_matrix_and_determinant
Computational problem of graph theory
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
Parallel all-pairs shortest path algorithm
Parallel_all-pairs_shortest_path_algorithm
Fictional character
bullets, running at high speeds, jumping great distances, and physically possessing people in the Matrix. If killed, they simply find a new host to overcome
Neo_(The_Matrix)
Bioinformatics computer program
UPGMA/neighbor-joining method to generate a distance matrix. A guide tree is calculated from the scores of the sequences in the matrix, then subsequently used to build
Clustal
Matrix equal to its conjugate-transpose
In mathematics, a Hermitian matrix (or self-adjoint matrix) is a square matrix with complex-valued entries that is equal to its own conjugate transpose
Hermitian_matrix
Graph metric of electrical resistance between nodes
J.; Lukovits, I.; Nikolic, S.; Trinajstic, N. (2002). "Resistance-distance matrix: a computational algorithm and its application". Int. J. Quantum Chem
Resistance_distance
Topics referred to by the same term
protocol for lighting control released 1990s and specified in IEC 62386 Distance-matrix alignment algorithm used in the FSSP database on structurally similar
Dali
2021 video game and technology demonstration
The Matrix Awakens is a 2021 action-adventure game and technology demonstration developed by Epic Games using Unreal Engine 5 in partnership with Warner
The_Matrix_Awakens
Real-valued function that quantifies similarity between two objects
matrix for a set of n points, where the entry ( i , j ) {\displaystyle (i,j)} in the matrix can be simply the (reciprocal of the) Euclidean distance between
Similarity_measure
Projection of data onto lower-dimensional manifolds
data is presented to the algorithm in the form of a similarity matrix or a distance matrix. These methods all fall under the broader class of metric multidimensional
Nonlinear dimensionality reduction
Nonlinear_dimensionality_reduction
clustering consists of two separate phases. Initially, a distance matrix containing all the pairwise distances between the genes is calculated. Pearson's correlation
Microarray analysis techniques
Microarray_analysis_techniques
Graph used to visualize evolutionary relationships, including reticulation events
from a set of splits, optimal realizations and reticulograms from a distance matrix), or restrictions to get computationally tractable problems (galled
Phylogenetic_network
Algorithmic library developed by Intel
another. Cosine distance matrix: Measuring pairwise distance using cosine distance. Correlation distance matrix: Measuring pairwise distance between items
Data_Analytics_Library
Branching diagram of evolutionary relationships between organisms
computational phylogenetics methods. Distance-matrix methods such as neighbor-joining or UPGMA, which calculate genetic distance from multiple sequence alignments
Phylogenetic_tree
Technique in information theory
Markov transition matrix method and this has some mathematical synergy with the bottleneck method itself. The arbitrarily increasing distance metric f {\displaystyle
Information_bottleneck_method
Technique in numerical linear algebra
given matrix by a matrix of lower rank. More precisely, it is a minimization problem, in which the cost function measures the fit between a given matrix (the
Low-rank_approximation
Probability distribution
model among-sites rate variation when maximum likelihood, Bayesian, or distance matrix methods are used to estimate phylogenetic trees. Phylogenetic analyzes
Gamma_distribution
while the lower half will contain the rating-reason code. distance matrix correlation matrix Groover, M. P. (2007). Work Systems: The Methods, Measurement
Activity_relationship_chart
Quality measure in cluster analysis
clusters. This algorithm needs pairwise distances and is typically implemented with a pairwise distance matrix. The O ( N 2 ) {\displaystyle {\mathcal
Silhouette_(clustering)
based on biostatistics that include but are not limited to: parsimony, distance matrix, likelihood methods, and Bayesian probability. Some examples of genomically
Patrocladogram
Geospatial methods for analyzing distance
the aggregate distance to another set of points (e.g., customer locations). A commonly used example is Lloyd's algorithm. Distance matrix, an array containing
Proximity_analysis
Central object in linear algebra; mapping vectors to vectors
represented using a 2×2 transformation matrix. A stretch in the xy-plane is a linear transformation which enlarges all distances in a particular direction by a
Transformation_matrix
Map that displays roads and transport links
state or province. Often a distance matrix is included showing the distance between pairs of cities. Since it is a symmetric matrix, only the upper triangle
Road_map
Methods in computational biology
given sequence. Cosine distance function is then used to compute pairwise distance between CVs of sequences. The distance matrix thus obtained can be used
Alignment-free sequence analysis
Alignment-free_sequence_analysis
Feature inherited from common ancestor
reconciliation Probabilistic methods Maximum likelihood Bayesian inference Distance-matrix methods Neighbor-joining UPGMA Least squares Three-taxon analysis Current
Primitive_(phylogenetics)
Set of distances defined from a set of points
under division by integers. Distance sets have also been used as a shape descriptor in computer vision. Distance matrix Arutyunyants, G.; Iosevich, A
Distance_set
Branch of mathematics
between the sensors. Euclidean distance matrix Multidimensional scaling (a statistical technique used when distances are measured with random errors)
Distance_geometry
DNA profiling tool
used for AFLP) and neighbor joining, a distance matrix is required. There are several ideas on how a distance matrix can be made: Hill et al. (1996) uses
Amplified fragment length polymorphism
Amplified_fragment_length_polymorphism
Family of linear error-correcting codes
any other code word is three) and block length 2r − 1. The parity-check matrix of a Hamming code is constructed by listing all columns of length r that
Hamming_code
Matrix representing a Euclidean rotation
rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix R = [
Rotation_matrix
system based on the matrix factorization model. Network coordinate (NC) systems are an efficient mechanism for internet distance (round-trip latency)
Phoenix_network_coordinates
2005 massively multiplayer online role-playing game
The Matrix Online (abbreviated as MxO) is a discontinued massively multiplayer online role-playing game (MMORPG) initially developed by Monolith Productions
The_Matrix_Online
NP-hard problem in combinatorial optimization
into a standard TSP with the same number of cities, but a modified distance matrix. The sequential ordering problem deals with the problem of visiting
Travelling_salesman_problem
Mathematics concept
In mathematics, a Hadamard matrix, named after the French mathematician Jacques Hadamard, is a square matrix whose entries are either +1 or −1 and whose
Hadamard_matrix
Existence of a graph with a degree sequence
Yichuan; Krislock, Nathan (2008), "Sensor Network Localization, Euclidean Distance Matrix Completions, and Graph Realization", Proceedings of the First ACM International
Graph_realization_problem
Type of geometric transformation
a shear matrix or transvection, an elementary matrix that represents the addition of a multiple of one row or column to another. Such a matrix may be derived
Shear_mapping
Indo-European language
Matasovic, Ranko (2018). Page 35. Orel 2000, p. 191. "Excel File_Lexical-Distance-Matrix". Alternative Transport. 19 November 2016. "How much does language
Albanian_language
Open source routing engine
an offering of the GraphHopper GmbH and includes a Geocoding API, a Distance Matrix API, a Map Matching API, an Isochrone API, a Cluster API, a Profiles
GraphHopper
normalized distance from some subsequence of t is: // input is placed in observation s[1..n], template t[1..m], // and [[distance matrix]] d[1..n,1.
Iterative_Viterbi_decoding
Real square matrix whose columns and rows are orthogonal unit vectors
In linear algebra, an orthogonal matrix or orthonormal matrix Q, is a real-valued square matrix whose columns and rows are orthonormal vectors. One way
Orthogonal_matrix
geometry Non-Euclidean geometry Euclid's formula Euclidean distance Euclidean distance matrix Euclidean space Pseudo-Euclidean space Euclidean vector Euclidean
List of things named after Euclid
List_of_things_named_after_Euclid
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