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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.
The first moment is simply the sum of the frequencies (i.e., the total count). The second moment F 2 {\displaystyle F_{2}} is useful for computing statistical properties of the data, such as the Gini coefficient of variation.
In statistics, machine learning and algorithms, a tensor sketch is a type of dimensionality reduction that is particularly efficient when applied to vectors that have tensor structure. [ 1 ] [ 2 ] Such a sketch can be used to speed up explicit kernel methods , bilinear pooling in neural networks and is a cornerstone in many numerical linear ...
The Flajolet–Martin algorithm is an algorithm for approximating the number of distinct elements in a stream with a single pass and space-consumption logarithmic in the maximal number of possible distinct elements in the stream (the count-distinct problem).
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There are other estimation techniques other than min/max sketches. The first paper on count-distinct estimation [7] describes the Flajolet–Martin algorithm, a bit pattern sketch. In this case, the elements are hashed into a bit vector and the sketch holds the logical OR of all hashed values.