pseudometric


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pseudometric

[¦süd·ə¦me·trik]
(mathematics)
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To calculate the distance between the fuzzy numbers, we will use Kelley's definition[8] as a basis to delimit a distance or pseudometric of a set X as the function d of the Cartesian product X x X in the non-negative real numbers, such that for every element x, y, z [member of] X, is verified:
In order to improve the accuracy of classification, we can also employ metric learning methods using the label information to learn a new metric or pseudometric such as neighborhood components analysis and large margin nearest neighbor.
One of the spaces in literature that generalises the metric and pseudometric spaces is the uniform space.
Note that [DELTA] does satisfy the requirement for a pseudometric space.
There have been a number of generalizations of metric spaces such as vector valued metric spaces, G-metric spaces, pseudometric spaces, fuzzy metric spaces, D-metric spaces, cone metric spaces, and modular metric spaces.
Then ([[bar.M].sub.r], d) is an internal pseudometric space.
There are some online metric learning methods in the literatures, including pseudometric online learning algorithm (POLA) [12], online ITML algorithm [7], and Logdet exact gradient online metric learning algorithm (LEGO) [13].
According to [15], this metric is equivalent to the pseudometric; that is,
The distance between sets defined above is a pseudometric to K (X) since dist (A, B) - 0 if and only if A [subset or equal to] B, not necessarily equal value.
By a pseudometric over M we shall mean any map d : M x M [right arrow] [R.sub.+].
In FRS, the true factor structure cannot be known because the original data have been altered by the aggregation of raw ordinal ratings into pseudometric means.
(The degeneracy locus of the Kobayashi pseudometric was studied by Adachi and Suzuki in [1], [2]).