en>Trappist the monk: /* References */replace mr template with mr parameter in CS1 templates; using AWB

2014-09-24T14:35:51Z

References: replace mr template with mr parameter in CS1 templates; using AWB

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	~~The '''Count–min sketch''' (or '''CM sketch''')~~ is a [[Randomized algorithm\|probabilistic]] [[Complexity class\|sub-linear space]] [[streaming algorithm]] which can be used to summarize a data stream in many different ways. The algorithm was invented in 2003 by [[Graham Cormode]] and [[S. Muthu Muthukrishnan]].<~~ref~~>~~{{cite journal\|last=Cormode\|first=Graham\|coauthors=S. Muthukrishnan\|title=An Improved Data Stream Summary~~: ~~The Count-Min Sketch and its Applications\|journal=J~~. ~~Algorithms\|year=2004\|volume=55\|pages=29–38\|accessdate=14 October 2011}}~~<~~/ref~~>		Hello! My name is Homer. <br>It is a little about myself: I live in Sweden, my city of Ilsbo. <br>It's called often Northern or cultural capital of . I've married 1 years ago.<br>I have two children - a son (Marta) and the daughter (Kathy). We all like Fishing.<br><br>My webpage; [http://www.taxiforsure.com/bangalore-to-mysore/ bangalore to mysore car rental]

	~~Count–min sketches are somewhat similar to [[Bloom filter]]~~s~~; the main distinction is that Bloom filters represent sets, while CM sketches represent [[multiset]]s and [[Frequency (statistics)\|frequency tables]].~~

	~~== Algorithm ==~~

	~~=== Setup ===~~
	~~The data structure is parameterized by the constants <math>w</math> and <math>d</math> which determine the time and space needs and the probability~~ of ~~error of the queries~~. ~~The algorithm needs a [[Array_data_structure#Two-dimensional_arrays\|two dimensional array]], called here~~ ''count'', with <math>w</math> columns and <math>d</math> rows. A series of <math>d</math> hash functions must be randomly drawn from a [[Pairwise independence\|pairwise independent]] [[hash function]] family, each associated with a row in the array.

	~~For later convenience we assign <math>w = \lceil e/\epsilon \rceil</math> and <math> d = \lceil \ln{~~1~~/\delta} \rceil</math>, where the error in answering a query is within a factor of <math>\epsilon</math> with probability <math>\delta</math>~~.

	~~=== Update ===~~
	~~When a new value~~ <~~math~~>a~~</math> arrives we update as follows: <math>\forall j : 1 \leq j \leq d</math>, <math> count[j,h_j~~(a)~~] \leftarrow count[j,h_j(a)]%d + 1 </math>. That is, for each row we take the corresponding hash function, apply it to the newly received value~~ and ~~add one to the column corresponding to the hash value.~~

	~~=== Query ===~~
	The array can then be used to estimate any of several different statistics at any point. If we want to estimate, for instance, the number of times <math> a_i</math> for a specific value <math>i</math> appeared so far in the ~~stream we would compute <math>\hat a_i=\min_j count[j,h_j~~(i)~~]</math> (this assume~~ all ~~added values are positive)~~. ~~This estimate has the guarantee that~~ <~~math~~>~~\hat a_i \leq a_i + \epsilon \|a\|~~ <~~/math~~> ~~with probability <math>1-\delta</math>.~~

	~~Small modifications to the data structure can be used to sketch other different stream statistics.~~

	~~== External links ==~~
	* [http://www.~~corelab~~.~~ece.ntua.gr/courses~~/~~ds.grad/count~~-~~min.ppt Powerpoint presentation on the algorithm]~~
	* [https://sites.google.com/site/countminsketch/home/faq Count–min FAQ]

	~~==See also==~~
	* [[Bloom filter]]
	* [[Feature hashing]]
	* [[Locality-~~sensitive hashing]]~~
	* [[MinHash]]

	~~== References ==~~
	~~<references~~ />

	~~{{DEFAULTSORT:Count-min sketch}}~~
	~~[[Category:Hashing]]~~
	~~[[Category:Probabilistic data structures]~~]

en>Bibcode Bot: Adding 0 arxiv eprint(s), 1 bibcode(s) and 1 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot

2012-08-30T18:00:05Z

Adding 0 arxiv eprint(s), 1 bibcode(s) and 1 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot

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The '''Count–min sketch''' (or '''CM sketch''') is a [[Randomized algorithm|probabilistic]] [[Complexity class|sub-linear space]] [[streaming algorithm]] which can be used to summarize a data stream in many different ways. The algorithm was invented in 2003 by [[Graham Cormode]] and [[S. Muthu Muthukrishnan]].<ref>{{cite journal|last=Cormode|first=Graham|coauthors=S. Muthukrishnan|title=An Improved Data Stream Summary: The Count-Min Sketch and its Applications|journal=J. Algorithms|year=2004|volume=55|pages=29–38|accessdate=14 October 2011}}</ref>

Count–min sketches are somewhat similar to [[Bloom filter]]s; the main distinction is that Bloom filters represent sets, while CM sketches represent [[multiset]]s and [[Frequency (statistics)|frequency tables]].

== Algorithm ==

=== Setup ===
The data structure is parameterized by the constants <math>w</math> and <math>d</math> which determine the time and space needs and the probability of error of the queries. The algorithm needs a [[Array_data_structure#Two-dimensional_arrays|two dimensional array]], called here ''count'', with <math>w</math> columns and <math>d</math> rows. A series of <math>d</math> hash functions must be randomly drawn from a [[Pairwise independence|pairwise independent]] [[hash function]] family, each associated with a row in the array.

For later convenience we assign <math>w = \lceil e/\epsilon \rceil</math> and <math> d = \lceil \ln{1/\delta} \rceil</math>, where the error in answering a query is within a factor of <math>\epsilon</math> with probability <math>\delta</math>.

=== Update ===
When a new value <math>a</math> arrives we update as follows: <math>\forall j : 1 \leq j \leq d</math>, <math> count[j,h_j(a)] \leftarrow count[j,h_j(a)]%d + 1 </math>. That is, for each row we take the corresponding hash function, apply it to the newly received value and add one to the column corresponding to the hash value.

=== Query ===
The array can then be used to estimate any of several different statistics at any point. If we want to estimate, for instance, the number of times <math> a_i</math> for a specific value <math>i</math> appeared so far in the stream we would compute <math>\hat a_i=\min_j count[j,h_j(i)]</math> (this assume all added values are positive). This estimate has the guarantee that <math>\hat a_i \leq a_i + \epsilon |a| </math> with probability <math>1-\delta</math>.

Small modifications to the data structure can be used to sketch other different stream statistics.

== External links ==
* [http://www.corelab.ece.ntua.gr/courses/ds.grad/count-min.ppt Powerpoint presentation on the algorithm]
* [https://sites.google.com/site/countminsketch/home/faq Count–min FAQ]

==See also==
* [[Bloom filter]]
* [[Feature hashing]]
* [[Locality-sensitive hashing]]
* [[MinHash]]

== References ==
<references />

{{DEFAULTSORT:Count-min sketch}}
[[Category:Hashing]]
[[Category:Probabilistic data structures]]

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en>Trappist the monk: /* References */replace mr template with mr parameter in CS1 templates; using AWB

en>Bibcode Bot: Adding 0 arxiv eprint(s), 1 bibcode(s) and 1 doi(s). Did it miss something? Report bugs, errors, and suggestions at User talk:Bibcode Bot