Apriori algorithm: Difference between revisions

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== 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. Besides, the Apriori algorithm was used to mine associations between various accidents and causative factors and explored the potential laws for reducing subway operation safety accidents. Among the 608 accident cases, operation delay accounted for about 72% of total accident cases, while stampede accidents accounted for only 0.5%<ref> Deng et al. Analyzing Subway Operation Accidents Causations: Apriori Algorithm and Network Approaches. Int. J. Environ. Res. Public Health 2023, 20, 3386. https://doi.org/10.3390/ijerph20043386.</ref>

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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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 ==