Apriori algorithm: Difference between revisions

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{{Short description|Algorithm for frequent item set mining and association rule learning over transactional databases}}

'''Apriori'''<ref name=apriori>Rakesh Agrawal and Ramakrishnan Srikant .[http://www.vldb.org/conf/1994/P487.PDF Fast algorithms for mining association rules]. Proceedings of the 20th International Conference on Very Large Data Bases, VLDB, pages 487-499, Santiago, Chile, September 1994.</ref> is an [[algorithm]] for frequent item set mining and [[association rule learning]] over [[relational databases]]. It proceeds by identifying the frequent individual items in the database and extending them to larger and larger item sets as long as those item sets appear sufficiently often in the database. The frequent item sets determined by Apriori can be used to determine [[association rules]] which highlight general trends in the [[database]]: this has applications in domains such as [[market basket analysis]].

== Overview ==

The Apriori algorithm was proposed by Agrawal and Srikant in 1994. Apriori is designed to operate on [[database]]s containing transactions (for example, collections of items bought by customers, or details of a website frequentation or [[IP address]]es<ref>{{usurped|1=[https://web.archive.org/web/20210822191810/https://deductive.com/blogs/data-science-ip-matching/ The data science behind IP address matching]}} Published by deductive.com, September 6, 2018, retrieved September 7, 2018</ref>). Other algorithms are designed for finding association rules in data having no transactions ([[Winepi]] and Minepi), or having no timestamps ([[DNA sequencing]]). Each transaction is seen as a set of items (an ''itemset''). Given a threshold <math>C</math>, the Apriori algorithm identifies the item sets which are subsets of at least <math>C</math> transactions in the database.

Apriori uses a "bottom up" approach, where frequent subsets are extended one item at a time (a step known as ''candidate generation''), and groups of candidates are tested against the data. The algorithm terminates when no further successful extensions are found.

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'''Apriori'''(T, ε)

L₁ ← {large 1 -singleton itemsets}

k ← 2

'''while''' L_k−1 '''is not''' empty

C_k ← Apriori_genGenerate_candidates(L_k−1, k)

'''for''' transactions t '''in''' T

D_t ← {c in C_k : c ⊆ t}

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k ← k + 1

'''return''' Union(L_k) '''over all''' k

'''Apriori_genGenerate_candidates'''(L, k)

result ← listempty_set()

'''for all''' p ∈ L, q ∈ L '''where''' p₁ =and q₁, p₂differ =in q₂,exactly ...,one p_k-2 = q_k-2 and p_k-1 < q_k-1element

c =← p ∪ {q_k-1}

'''if''' u ∈ L '''for all''' u ⊆ c '''where''' |u| = k-1

result.add(c)

'''return''' result

== Examples ==

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{| class="wikitable"

|-

| &alpha; || &beta; || theta&epsilon;

|-

| &alpha; || &beta; || epsilon&theta;

|-

| &alpha; || &beta; || theta&epsilon;

|-

| &alpha ; || &beta; || epsilon&theta;

|-

| alpha|| beta || theta

|}

The association rules that can be determined from this database are the following:

# 100% of sets with &alpha; also contain &beta;

# 50% of sets with &alpha;, &beta; also have &epsilon;

# 50% of sets with &alpha;, &beta; also have &theta;

we can also illustrate this through a variety of examples.

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in the example, there are no frequent triplets. {2,3,4} is below the minimal threshold, and the other triplets were excluded because they were super sets of pairs that were already below the threshold.

We have thus determined the frequent sets of items in the database, and illustrated how some items were not counted because one of their subsets was already known to be below the threshold. James Coddington.

== Limitations ==

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Also, both the time and space complexity of this algorithm are very high: <math>O\left(2^{|D|}\right)</math>, thus exponential, where <math>|D|</math> is the horizontal width (the total number of items) present in the database.

Later algorithms such as [[Max-Miner]]<ref>{{cite journal|author=Bayardo Jr, Roberto J.|title=Efficiently mining long patterns from databases|journal=ACM SIGMOD Record |volume=27|issue=2|year=1998|pages=85–93 |doi=10.1145/276305.276313 |url=http://www.cs.sfu.ca/CourseCentral/741/jpei/readings/baya98.pdf}}</ref> try to identify the maximal frequent item sets without enumerating their subsets, and perform "jumps" in the search space rather than a purely bottom-up approach.

== References ==