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Metric multidimensional scaling (mMDS) It is a superset of classical MDS that generalizes the optimization procedure to a variety of loss functions and input matrices of known distances with weights and so on. A useful loss function in this context is called stress, which is often minimized using a procedure called stress majorization.
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 ...
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.
Jaccard distance is commonly used to calculate an n × n matrix for clustering and multidimensional scaling of n sample sets. This distance is a metric on the collection of all finite sets. [8] [9] [10] There is also a version of the Jaccard distance for measures, including probability measures.
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 ...
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.
The index of dissimilarity is a demographic measure of the evenness with which two groups are distributed across component geographic areas that make up a larger area. A group is evenly distributed when each geographic unit has the same percentage of group members as the total population. The index score can also be interpreted as the ...
UniFrac, a shortened version of unique fraction metric, is a distance metric used for comparing biological communities.It differs from dissimilarity measures such as Bray-Curtis dissimilarity in that it incorporates information on the relative relatedness of community members by incorporating phylogenetic distances between observed organisms in the computation.