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That is (unlike road distance with one-way streets) the distance between two points does not depend on which of the two points is the start and which is the destination. [11] It is positive, meaning that the distance between every two distinct points is a positive number, while the distance from any point to itself is zero. [11]
The normalized angle, referred to as angular distance, between any two vectors and is a formal distance metric and can be calculated from the cosine similarity. [5] The complement of the angular distance metric can then be used to define angular similarity function bounded between 0 and 1, inclusive.
The Canberra distance is a numerical measure of the distance between pairs of points in a vector space, introduced in 1966 [1] and refined in 1967 [2] by Godfrey N. Lance and William T. Williams. It is a weighted version of L ₁ (Manhattan) distance . [ 3 ]
Similarity (philosophy) – Relation of resemblance between objects; Statistical distance – Distance between two statistical objects; String metric – Metric that measures the distance between two strings of text; Similarity search – Searching for similar items in a data set; tf–idf – Estimate of the importance of a word in a document
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 derived and expressed in several ways.
In information theory, the Hamming distance between two strings or vectors of equal length is the number of positions at which the corresponding symbols are different. In other words, it measures the minimum number of substitutions required to change one string into the other, or equivalently, the minimum number of errors that could have transformed one string into the other.
Angular distance or angular separation is the measure of the angle between the orientation of two straight lines, rays, or vectors in three-dimensional space, or the central angle subtended by the radii through two points on a sphere.
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 ℝ k, the elements of their Euclidean distance matrix A are given by squares of distances between them. That is