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Count sketch is a type of dimensionality reduction that is particularly efficient in statistics, machine learning and algorithms. [1] [2] It was invented by Moses Charikar, Kevin Chen and Martin Farach-Colton [3] in an effort to speed up the AMS Sketch by Alon, Matias and Szegedy for approximating the frequency moments of streams [4] (these calculations require counting of the number of ...
The count–min sketch was invented in 2003 by Graham Cormode and S. Muthu Muthukrishnan [1] and described by them in a 2005 paper. [2] Count–min sketch is an alternative to count sketch and AMS sketch and can be considered an implementation of a counting Bloom filter (Fan et al., 1998 [3]) or multistage-filter. [1]
The HyperLogLog has three main operations: add to add a new element to the set, count to obtain the cardinality of the set and merge to obtain the union of two sets. Some derived operations can be computed using the inclusion–exclusion principle like the cardinality of the intersection or the cardinality of the difference between two HyperLogLogs combining the merge and count operations.
These algorithms are designed to operate with limited memory, generally logarithmic in the size of the stream and/or in the maximum value in the stream, and may also have limited processing time per item. As a result of these constraints, streaming algorithms often produce approximate answers based on a summary or "sketch" of the data stream.
In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. In one variable, the mean of a function f(x) over the interval (a,b) is defined by: [1] ¯ = ().
Unlike the typical Bloom filter, elements are hashed to a bit array through deterministic, fast and simple-to-calculate functions. The maximal set size for which false positives are completely avoided is a function of the universe size and is controlled by the amount of allocated memory.
In the mathematical theory of categories, a sketch is a category D, together with a set of cones intended to be limits and a set of cocones intended to be colimits. A model of the sketch in a category C is a functor: that takes each specified cone to a limit cone in C and each specified cocone to a colimit cocone in C
The arithmetic mean (or simply mean or average) of a list of numbers, is the sum of all of the numbers divided by their count.Similarly, the mean of a sample ,, …,, usually denoted by ¯, is the sum of the sampled values divided by the number of items in the sample.