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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 values for similar ...
The left graph shows a green function G that is phase-shifted relative to function F by a time displacement of 𝜏. The middle graph shows the function F and the phase-shifted G represented together as a Lissajous curve. Integrating F multiplied by the phase-shifted G produces the right graph, the cross-correlation across all values of 𝜏.
This property means that simple models using a Poisson distribution are inaccurate, and networks designed without taking self-similarity into account are likely to function in unexpected ways. Similarly, stock market movements are described as displaying self-affinity, i.e. they appear self-similar when transformed via an appropriate affine ...
A graph is Hamiltonian if it contains a Hamiltonian cycle, and traceable if it contains a Hamiltonian path. haven A k-haven is a function that maps every set X of fewer than k vertices to one of its flaps, often satisfying additional consistency conditions.
The similarity is a function such that its value is greater when two points are closer (contrary to the distance, which is a measure of dissimilarity: the closer the points, the lesser the distance). The definition of the similarity can vary among authors, depending on which properties are desired. The basic common properties are Positive defined:
arcosech – inverse hyperbolic cosecant function. (Also written as arcsch.) arcosh – inverse hyperbolic cosine function. arcoth – inverse hyperbolic cotangent function. arcsch – inverse hyperbolic cosecant function. (Also written as arcosech.) arcsec – inverse secant function. arcsin – inverse sine function. arctan – inverse ...
Similarly, a sequence,, … is called superadditive if it satisfies the inequality + + for all and . The term "superadditive" is also applied to functions from a boolean algebra to the real numbers where P ( X ∨ Y ) ≥ P ( X ) + P ( Y ) , {\displaystyle P(X\lor Y)\geq P(X)+P(Y),} such as lower probabilities .
Similarly, the function has a global (or absolute) minimum point at x ∗, if f(x ∗) ≤ f(x) for all x in X. The value of the function at a maximum point is called the maximum value of the function, denoted max ( f ( x ) ) {\displaystyle \max(f(x))} , and the value of the function at a minimum point is called the minimum value of the ...