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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.
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 Euclidean distance formula is used to find the distance between two points on a plane, which is visualized in the image below. Manhattan distance is commonly used in GPS applications, as it can be used to find the shortest route between two addresses. [citation needed] When you generalize the Euclidean distance formula and Manhattan ...
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 ]
The Minkowski distance can also be viewed as a multiple of the power mean of the component-wise differences between and . The following figure shows unit circles (the level set of the distance function where all points are at the unit distance from the center) with various values of :
Candidate documents from the corpus can be retrieved and ranked using a variety of methods. Relevance rankings of documents in a keyword search can be calculated, using the assumptions of document similarities theory, by comparing the deviation of angles between each document vector and the original query vector where the query is represented as a vector with same dimension as the vectors that ...
If vectors u and v have direction cosines (α u, β u, γ u) and (α v, β v, γ v) respectively, with an angle θ between them, their units vectors are ^ = + + (+ +) = + + ^ = + + (+ +) = + +. Taking the dot product of these two unit vectors yield, ^ ^ = + + = , where θ is the angle between the two unit vectors, and is also the angle between u and v.
Wasserstein metrics measure the distance between two measures on the same metric space. The Wasserstein distance between two measures is, roughly speaking, the cost of transporting one to the other. The set of all m by n matrices over some field is a metric space with respect to the rank distance (,) = ().