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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.
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 ...
Distance from a point to a line. The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be ...
Euclidean distance. In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance. These names come from the ancient Greek ...
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.
Inverse distance weighting (IDW) is a type of deterministic method for multivariate interpolation with a known scattered set of points. The assigned values to unknown points are calculated with a weighted average of the values available at the known points. This method can also be used to create spatial weights matrices in spatial ...
Neighbor joining takes a distance matrix, which specifies the distance between each pair of taxa, as input. The algorithm starts with a completely unresolved tree, whose topology corresponds to that of a star network, and iterates over the following steps, until the tree is completely resolved, and all branch lengths are known:
Leverage (statistics) In statistics and in particular in regression analysis, leverage is a measure of how far away the independent variable values of an observation are from those of the other observations. High-leverage points, if any, are outliers with respect to the independent variables. That is, high-leverage points have no neighboring ...