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Apriori Algorithm

, 10 Aug 2012 CPOL 233K 9.5K 145
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Implementation of the Apriori algorithm in C#.


In data mining, Apriori is a classic algorithm for learning association rules. Apriori is designed to operate on databases containing transactions (for example, collections of items bought by customers, or details of a website frequentation).

Other algorithms are designed for finding association rules in data having no transactions (Winepi and Minepi), or having no timestamps (DNA sequencing).


The whole point of the algorithm (and data mining, in general) is to extract useful information from large amounts of data. For example, the information that a customer who purchases a keyboard also tends to buy a mouse at the same time is acquired from the association rule below:

Support: The percentage of task-relevant data transactions for which the pattern is true.

Support (Keyboard -> Mouse) = AprioriAlgorithm/eq_1.JPG

Confidence: The measure of certainty or trustworthiness associated with each discovered pattern.

Confidence (Keyboard -> Mouse) = AprioriAlgorithm/eq_2.JPG

The algorithm aims to find the rules which satisfy both a minimum support threshold and a minimum confidence threshold (Strong Rules).

  • Item: article in the basket.
  • Itemset: a group of items purchased together in a single transaction.

How Apriori Works

  1. Find all frequent itemsets:
    • Get frequent items:
      • Items whose occurrence in database is greater than or equal to the threshold.
    • Get frequent itemsets:
      • Generate candidates from frequent items.
      • Prune the results to find the frequent itemsets.
  2. Generate strong association rules from frequent itemsets
    • Rules which satisfy the and min.confidence threshold.

High Level Design


Low Level Design



A database has five transactions. Let the min sup = 50% and min con f = 80%.



Step 1: Find all Frequent Itemsets


Frequent Itemsets

{A}   {B}   {C}   {E}   {A C}   {B C}   {B E}   {C E}   {B C E}

Step 2: Generate strong association rules from the frequent itemsets



Closed Itemset: support of all parents are not equal to the support of the itemset.

Maximal Itemset: all parents of that itemset must be infrequent.

Keep in mind:



Itemset {c} is closed as support of parents (supersets) {A C}:2, {B C}:2, {C D}:1, {C E}:2 not equal support of {c}:3.

And the same for {A C}, {B E} & {B C E}.

Itemset {A C} is maximal as all parents (supersets) {A B C}, {A C D}, {A C E} are infrequent.

And the same for {B C E}.


This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)


About the Author

Omar Gameel Salem
Software Developer
Australia Australia
Enthusiastic programmer/researcher, passionate to learn new technologies, interested in problem solving, data structures, algorithms, AI, machine learning and nlp.

Amateur guitarist/ keyboardist, squash player.

If you have a question\suggestion about one of my articles, or you want an algorithm implemented in C#, feel free to contact me.

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Comments and Discussions

QuestionEfficient Data Mining Software Pin
Member 1051770411-Jul-15 2:21
memberMember 1051770411-Jul-15 2:21 
Questionrequest for your Aprori java code Pin
Member 1175977411-Jun-15 11:00
memberMember 1175977411-Jun-15 11:00 
Questionrequest for apriori code in php Pin
Member 117461826-Jun-15 0:23
memberMember 117461826-Jun-15 0:23 
QuestionThanks Pin
Jon_adam1-May-15 0:40
memberJon_adam1-May-15 0:40 
QuestionRegarding apriori algorithm Pin
Member 1138385413-Apr-15 2:31
memberMember 1138385413-Apr-15 2:31 
QuestionQuery regarding extension of this code for strings Pin
Member 112361666-Apr-15 7:58
memberMember 112361666-Apr-15 7:58 
Generalthanks Pin
hope_amal28-Mar-15 10:16
memberhope_amal28-Mar-15 10:16 
QuestionRequest for Aprori code in java Pin
Member 114197271-Feb-15 21:02
memberMember 114197271-Feb-15 21:02 
AnswerRe: Request for Aprori code in java Pin
Member 1156231327-Mar-15 23:23
memberMember 1156231327-Mar-15 23:23 
GeneralNeed code for Closed and maximal frequent item set Pin
Member 1141126828-Jan-15 22:45
memberMember 1141126828-Jan-15 22:45 
Questionplease send me the apriori algorith code Pin
Member 1125434324-Dec-14 19:59
memberMember 1125434324-Dec-14 19:59 
Questionplease send me the apriori algorith code Pin
Member 111309425-Oct-14 8:34
memberMember 111309425-Oct-14 8:34 
AnswerRe: please send me the apriori algorith code Pin
Member 1030011418-Oct-14 0:00
professionalMember 1030011418-Oct-14 0:00 
QuestionCan I have the C# code Pin
Member 1087192112-Jun-14 3:53
memberMember 1087192112-Jun-14 3:53 
AnswerRe: Can I have the C# code Pin
Omar Gameel Salem12-Jun-14 16:24
memberOmar Gameel Salem12-Jun-14 16:24 
QuestionHelp me Pin
Member 107997886-May-14 14:04
memberMember 107997886-May-14 14:04 
QuestionMMAC algorithm Pin
Xuan Dung Phu Yen16-Mar-14 19:15
memberXuan Dung Phu Yen16-Mar-14 19:15 
Questiondo you know? high-utility rule mining? Pin
hothi_vuong14-Mar-14 4:23
memberhothi_vuong14-Mar-14 4:23 
QuestionApriory Algo Implementation Pin
Member 106110551-Mar-14 0:56
memberMember 106110551-Mar-14 0:56 
Questionlimit to your code Pin
yogeshwarmisal27-Feb-14 19:32
memberyogeshwarmisal27-Feb-14 19:32 
AnswerRe: limit to your code Pin
Omar Gameel Salem27-Feb-14 21:11
memberOmar Gameel Salem27-Feb-14 21:11 
Questionhow this algo will take my sql server table rows as transaction? Pin
Mona198618-Jan-14 9:29
groupMona198618-Jan-14 9:29 
QuestionApriori Pin
Member 1022814823-Aug-13 6:42
memberMember 1022814823-Aug-13 6:42 
Questionhelp Pin
milad199130-Jun-13 22:14
membermilad199130-Jun-13 22:14 
QuestionApriori variations Pin
Saira1119-Mar-13 3:27
memberSaira1119-Mar-13 3:27 

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