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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.
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 ...
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.
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.
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 ...
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]
In data analysis, the self-similarity matrix is a graphical representation of similar sequences in a data series. Similarity can be explained by different measures, like spatial distance (distance matrix), correlation, or comparison of local histograms or spectral properties (e.g. IXEGRAM [1]). A similarity plot can be the starting point for ...