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A comprehensive step-by-step tutorial with an explanation of the theoretical foundations of Approximate Entropy is available. [8] The algorithm is: Step 1 Assume a time series of data (), (), …, (). These are raw data values from measurements equally spaced in time. Step 2
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 distance between sets A and B is the infimum of the distances between any two of their respective points: (,) =, (,). This does not define a metric on the set of such subsets: the distance between overlapping sets is zero, and this distance does not satisfy the triangle inequality for any metric space with two or more points (consider the ...
This result generalises the earlier example of the Wasserstein distance between two point masses (at least in the case =), since a point mass can be regarded as a normal distribution with covariance matrix equal to zero, in which case the trace term disappears and only the term involving the Euclidean distance between the means remains.
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 (,) = ().
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.
Dynamic time warping between two piecewise linear functions. The dotted line illustrates the time-warp relation. Notice that several points in the lower function are mapped to one point in the upper function, and vice versa. Two repetitions of a walking sequence recorded using a motion-capture system.
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