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The approximate distance found by this filtering process is the final value of , computed in the step before becomes empty. Each step removes all points whose closest neighbor is at distance d {\displaystyle d} or greater, at least half of the points in expectation, from which it follows that the total expected time for filtering is linear.
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]
For two objects and having descriptors, the similarity is defined as: = = =, where the w i j k {\displaystyle w_{ijk}} are non-negative weights usually set to 1 {\displaystyle 1} [ 2 ] and s i j k {\displaystyle s_{ijk}} is the similarity between the two objects regarding their k {\displaystyle k} -th variable.
In statistics, probability theory, and information theory, a statistical distance quantifies the distance between two statistical objects, which can be two random variables, or two probability distributions or samples, or the distance can be between an individual sample point and a population or a wider sample of points.
The Hausdorff distance is the longest distance someone can be forced to travel by an adversary who chooses a point in one of the two sets, from where they then must travel to the other set. In other words, it is the greatest of all the distances from a point in one set to the closest point in the other set.
The distance travelled by an object is the length of a specific path travelled between two points, [6] such as the distance walked while navigating a maze. This can even be a closed distance along a closed curve which starts and ends at the same point, such as a ball thrown straight up, or the Earth when it completes one orbit .
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the distance between the two lines is the distance between the two intersection points of these lines with the perpendicular line = /. This distance can be found by first solving the linear systems {= + = /, and {= + = /, to get the coordinates of the intersection points. The solutions to the linear systems are the points