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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.
Analysis of similarities (ANOSIM) is a non-parametric statistical test widely used in the field of ecology. The test was first suggested by K. R. Clarke [1] as an ANOVA -like test, where instead of operating on raw data, operates on a ranked dissimilarity matrix. Given a matrix of rank dissimilarities between a set of samples, each belonging to ...
Dice-Sørensen coefficient. A statistic used for comparing the similarity of two samples. The Dice-Sørensen coefficient (see below for other names) is a statistic used to gauge the similarity of two samples. It was independently developed by the botanists Lee Raymond Dice [1] and Thorvald Sørensen, [2] who published in 1945 and 1948 respectively.
Similarity measure. In statistics and related fields, a similarity measure or similarity function or similarity metric is a real-valued function that quantifies the similarity between two objects. Although no single definition of a similarity exists, usually such measures are in some sense the inverse of distance metrics: they take on large ...
A diversity index is a method of measuring how many different types (e.g. species) there are in a dataset (e.g. a community). Some more sophisticated indices also account for the phylogenetic relatedness among the types. [1]
The simple matching coefficient (SMC) or Rand similarity coefficient is a statistic used for comparing the similarity and diversity of sample sets. [1][better source needed] Given two objects, A and B, each with n binary attributes, SMC is defined as: where. is the total number of attributes where A has value 1 and B has value 0. The simple ...
Matrix similarity. In linear algebra, two n -by- n matrices A and B are called similar if there exists an invertible n -by- n matrix P such that Similar matrices represent the same linear map under two (possibly) different bases, with P being the change-of-basis matrix. [1][2] A transformation A ↦ P−1AP is called a similarity transformation ...
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 ...