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Apriori Algorithm

, 10 Aug 2012 CPOL
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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

Questiondo you know? high-utility rule mining? Pin
hothi_vuong14-Mar-14 5:23
memberhothi_vuong14-Mar-14 5:23 
QuestionApriory Algo Implementation Pin
Member 106110551-Mar-14 1:56
memberMember 106110551-Mar-14 1:56 
Questionlimit to your code Pin
yogeshwarmisal27-Feb-14 20:32
memberyogeshwarmisal27-Feb-14 20:32 
AnswerRe: limit to your code Pin
Omar Gameel Salem27-Feb-14 22:11
memberOmar Gameel Salem27-Feb-14 22:11 
Questionhow this algo will take my sql server table rows as transaction? Pin
Mona198618-Jan-14 10:29
groupMona198618-Jan-14 10:29 
QuestionApriori Pin
Member 1022814823-Aug-13 7:42
memberMember 1022814823-Aug-13 7:42 
Questionhelp Pin
milad199130-Jun-13 23:14
membermilad199130-Jun-13 23:14 
QuestionApriori variations Pin
Saira1119-Mar-13 4:27
memberSaira1119-Mar-13 4:27 

I am doing my Masters research in Apriori Algorithm innovation. Kindly suggest me few approaches.
QuestionApriori algorithm Pin
Member 987030028-Feb-13 5:24
memberMember 987030028-Feb-13 5:24 
AnswerRe: Apriori algorithm Pin
aspround18-Apr-13 6:49
memberaspround18-Apr-13 6:49 
GeneralRe: Apriori algorithm Pin
Member 1065266925-Feb-15 21:22
memberMember 1065266925-Feb-15 21:22 
Questionplease need help Pin
azizhai12-Jan-13 19:24
memberazizhai12-Jan-13 19:24 
QuestionYou should add rate. Pin
jingjingtr9-Dec-12 3:40
memberjingjingtr9-Dec-12 3:40 
QuestionNew Version is only changed the UI? Pin
jingjingtr5-Dec-12 22:47
memberjingjingtr5-Dec-12 22:47 
AnswerRe: New Version is only changed the UI? Pin
Omar Gamil5-Dec-12 22:53
memberOmar Gamil5-Dec-12 22:53 
GeneralRe: New Version is only changed the UI? Pin
jingjingtr6-Dec-12 0:29
memberjingjingtr6-Dec-12 0:29 
GeneralRe: New Version is only changed the UI? Pin
friday250f19-Dec-12 14:16
memberfriday250f19-Dec-12 14:16 
QuestionError Pin
jingjingtr2-Dec-12 21:33
memberjingjingtr2-Dec-12 21:33 
AnswerRe: Error Pin
Omar Gamil2-Dec-12 22:00
memberOmar Gamil2-Dec-12 22:00 
GeneralRe: Error Pin
jingjingtr3-Dec-12 15:51
memberjingjingtr3-Dec-12 15:51 
QuestionHow can i add many items? Pin
jingjingtr2-Dec-12 21:27
memberjingjingtr2-Dec-12 21:27 
AnswerRe: How can i add many items? Pin
Omar Gamil2-Dec-12 22:33
memberOmar Gamil2-Dec-12 22:33 
QuestioncSPADE algorithm Pin
Marwa M. Ghareeb26-Nov-12 7:42
memberMarwa M. Ghareeb26-Nov-12 7:42 
AnswerRe: cSPADE algorithm Pin
Omar Gamil26-Nov-12 7:54
memberOmar Gamil26-Nov-12 7:54 
GeneralRe: cSPADE algorithm Pin
Marwa M. Ghareeb26-Nov-12 8:43
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