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paper_draft-Apriori.lyx
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paper_draft-Apriori.lyx
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#LyX 2.3 created this file. For more info see http://www.lyx.org/
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\begin_document
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\begin_body
\begin_layout Title
Improvement in the Apriori algorithm to reduce execution time for association
rule mining
\end_layout
\begin_layout Author
Cem Samiloglu
\begin_inset Formula $^{\dagger}$
\end_inset
\end_layout
\begin_layout Address
\begin_inset ERT
status open
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\backslash
begin{center}
\backslash
em{}
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vspace{-3.5em}
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\begin_inset Formula $^{\dagger}$
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Department of Computer Systems, TalTech, Estonia
\begin_inset ERT
status open
\begin_layout Plain Layout
\backslash
end{center}
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\end_inset
\end_layout
\begin_layout Abstract ICS
In the current literature, several algorithms are proposed for the implementatio
n of association rule mining in the field of data science such as Apriori,
FP-growth, Eclat etc.
These algorithms are analyzed and compared based on their use cases and
their efficiency in terms of execution time.
Apriori algorithm stands out in terms of its straightforward implementation
but also it has major drawbacks when its being applied to the large datasets.
In this paper, previously presented research on improving Apriori will
be studied in detail and an optimized version of the existing work in the
literature will be proposed.
The newly proposed algorithm will be implemented and executed on a large
real-world dataset for comparison in terms of efficiency.
\end_layout
\begin_layout Abstract ICS
\begin_inset ERT
status open
\begin_layout Plain Layout
\backslash
thispagestyle{empty}
\end_layout
\end_inset
\end_layout
\begin_layout Keywords ICS
Apriori algorithm; Algorithm optimization; Association rule; Data mining;
Execution time reduction
\end_layout
\begin_layout Section
Introduction
\begin_inset CommandInset label
LatexCommand label
name "sec:Introduction"
\end_inset
\end_layout
\begin_layout Standard
Nowadays, the data production rate is faster than it has ever been.
The advancements in computer hardware and database systems enabled us to
store huge amounts of data at cheaper costs.
Alongside that, with the evolution of information technologies there is
a big growth of data in science, engineering, medicine, business and in
almost every field.
\end_layout
\begin_layout Standard
However, analyzing this data and extracting meaningful information becomes
a challenging task for humans since exponentially growing data is not possible
to be analyzed manually.
It simply exceedes our ability for comprehension.
As a result, dealing with this task in an automated manner is becoming
an important topic and gets more attention in the research field of data
mining
\begin_inset CommandInset citation
LatexCommand cite
key "Lakshmi2011conceptualoverviewdata"
literal "false"
\end_inset
.
\end_layout
\begin_layout Standard
Data mining is the extraction of unrevealed patterns and interesting knowledge.
It can play an important role in many organizations giving insight of patterns
in their data to make decisions, with the purpose of increasing revenue,
cutting costs etc.
It is also often referred as KDD (Knowledge Discovery in Databases) in
the literature.
There are many different techniques used in data mining such as anomaly
detection, clustering, classification, regression, association rule mining,
summarization etc.
\begin_inset CommandInset citation
LatexCommand cite
key "Fayyad1996DataMiningKnowledge"
literal "false"
\end_inset
.
\end_layout
\begin_layout Standard
Techniques used in data mining can be classified into two categories as
descriptive and predictive.
In descriptive data mining, what happened in the past is investigated by
analyzing past data.
Anomaly detection, clustering and association rule mining are some of the
descriptive data mining techniques.
Meanwhile, predictive data mining is used to identify what can happen in
the future based on the present data.
Classification, regression are some of the example techniques that belongs
to predictive data mining
\begin_inset CommandInset citation
LatexCommand cite
key "Prithiviraj2015ComparativeAnalysisAssociation"
literal "false"
\end_inset
.
\end_layout
\begin_layout Standard
Association rule mining is used to find frequent patterns, correlations
in a transactional database
\begin_inset CommandInset citation
LatexCommand cite
key "Solanki2015SurveyAssociationRule"
literal "false"
\end_inset
.
The aim of this paper is to propose an improved version of Apriori algorithm
- one of the well-known algorithms used in association rule mining, to
reduce its execution time when being applied to a large dataset.
\end_layout
\begin_layout Standard
In order to have a clear understanding of association rule mining at algorithms
used for this purpose, one should study some preliminary concepts presented
at Section 1.1.
\end_layout
\begin_layout Subsection
Background
\begin_inset CommandInset label
LatexCommand label
name "sec:Background"
\end_inset
\end_layout
\begin_layout Standard
Let us define the following:
\end_layout
\begin_layout Itemize
π· = {π
\begin_inset script subscript
\begin_layout Plain Layout
1
\end_layout
\end_inset
, π
\begin_inset script subscript
\begin_layout Plain Layout
2
\end_layout
\end_inset
,\SpecialChar ldots
, π
\begin_inset script subscript
\begin_layout Plain Layout
m
\end_layout
\end_inset
}, a database contains a set of transactions where each transaction denoted
as π.
Each transaction is also associated with a unique identifier called its
ππΌπ·.
\end_layout
\begin_layout Itemize
πΌ = {π
\begin_inset script subscript
\begin_layout Plain Layout
1
\end_layout
\end_inset
, π
\begin_inset script subscript
\begin_layout Plain Layout
2
\end_layout
\end_inset
,\SpecialChar ldots
, π
\begin_inset script subscript
\begin_layout Plain Layout
m
\end_layout
\end_inset
}, a set of items where each item is denoted as π.
Each transaction π is a nonempty itemset such that π β πΌ.
\end_layout
\begin_layout Standard
Then we can say if π β π is true; transaction π contains X, a subset of
πΌ.
\end_layout
\begin_layout Standard
Association rules are if/then statements that uncover relationships of items
in a database
\begin_inset CommandInset citation
LatexCommand cite
key "Kumbhare2014OverviewAssociationRule"
literal "false"
\end_inset
.
We can define an association rule as π βπ, meaning that whenever π occurs,
there is a strong correlation of π occuring.
Here π and π denotes the set of items that are included in transaction
π.
\end_layout
\begin_layout Itemize
π βπ, where π β πΌ, π β πΌ and π β© π = {}, an empty set.
\end_layout
\begin_layout Standard
There are two main interestingness measures used in association rule mining;
support and confidence.
\end_layout
\begin_layout Itemize
\emph on
support
\emph default
(π βπ) =
\emph on
P
\emph default
(π βͺ π) =
\begin_inset Formula $\frac{Count\:of\:transactions\:containing\:items\:(πβͺπ)}{Total\:number\:of\:transactions\:in\:π}$
\end_inset
, , is the percentage of transactions in π· that contains the union of sets
π and π.
\end_layout
\begin_layout Itemize
\emph on
confidence
\emph default
(π βπ) =
\emph on
P
\emph default
(π | π) =
\begin_inset Formula $\frac{support(πβͺπ)}{support(π)}$
\end_inset
, is the percentage of transactions in π· containing π that also contains
π.
\end_layout
\begin_layout Standard
Additionally, following two definitions are useful to comprehend the steps
of the algorithms that will be explained later on.
\end_layout
\begin_layout Itemize
Frequent itemset, denoted as πΏ
\begin_inset script subscript
\begin_layout Plain Layout
π
\end_layout
\end_inset
can be described as the large k-itemsets that satisfies a support value.
\end_layout
\begin_layout Itemize
Candidate itemset, denoted as πΆ
\begin_inset script subscript
\begin_layout Plain Layout
π
\end_layout
\end_inset
can be described as is any valid itemset that are potentially frequent
itemsets.
\end_layout
\begin_layout Section
Literature Review
\begin_inset CommandInset label
LatexCommand label
name "sec:Literature Review"
\end_inset
\end_layout
\begin_layout Standard
Association rule mining can be overviewed as a two-step approach as first,
discovering all frequent itemsets that have support value above the minimum
support treshold and second, use these frequent itemsets to generate associatio
n rules that satisfy a minumum confidence treshold
\begin_inset CommandInset citation
LatexCommand cite
key "Agrawal1993Miningassociationrules"
literal "false"
\end_inset
.
Throughout the years, many different algoritms are presented in the literature
to handle the task of association rule mining.
However, improvements are still needed in performance perspective because
of long execution time and heavy overload on memory of these algorithms.
Because the second step is much less costly than the first one, performance
of the algorithm is mainly dependent on the first step
\begin_inset CommandInset citation
LatexCommand cite
key "Chee2018Algorithmsfrequentitemset"
literal "false"
\end_inset
.
\end_layout
\begin_layout Standard
Many researchers have put effort into developing efficient algorithms for
association rule mining since the beginning of 1990's.
The key algorithms in the literature are examined in the following section.
\end_layout
\begin_layout Subsection
AIS and SETM Algorithms
\begin_inset CommandInset label
LatexCommand label
name "sec:AIS and SETM Algorithms"
\end_inset
\end_layout
\begin_layout Standard
AIS
\begin_inset CommandInset citation
LatexCommand cite
key "Agrawal1993Miningassociationrules"
literal "false"
\end_inset
is the first algorithm presented in the literature followed by SETM
\begin_inset CommandInset citation
LatexCommand cite
key "HoutsmaSetorientedmining"
literal "false"
\end_inset
, which was motivated by the aim of using SQL.
Candidate generation in both of these algorithms are on-the-fly during
passing over the database as the data is being read.
Then candidate itemsets are generated by extending frequent itemsets with
all other items in the transaction.
\end_layout
\begin_layout Standard
Because of this specific attribute, they generate so many non-essential
candidate itemsets that eventually turned out to to not satisfying the
minimum support level
\begin_inset CommandInset citation
LatexCommand cite
key "Prithiviraj2015ComparativeAnalysisAssociation"
literal "false"
\end_inset
.
AIS and SETM algorithms are not very popular nowadays due to their limitations
but they paved a foundation for the next algorithms to be developed in
the literature.
\end_layout
\begin_layout Subsection
Apriori Algorithm
\begin_inset CommandInset label
LatexCommand label
name "sec:Apriori Algorithm"
\end_inset
\end_layout
\begin_layout Standard
Following that, in 1994 Agrawal and Srikant proposed a more efficient algorithm
alternative to AIS and STEM, called Apriori
\begin_inset CommandInset citation
LatexCommand cite
key "Agrawal1994FastAlgorithmsMining"
literal "false"
\end_inset
.
Main difference of Apriori compared to AIS and SETM was that in Apriori,
candidate itemsets are generated in a pass over the itemsets found frequent
in previous passing, without passing over all the transactions in the database.
This is because of the assumption that any subset of a frequent itemset
must be frequent.
Therefore, any subset of a non-frequent itemset is also not frequent.
Using this property, Apriori prunes the items which is not a subset of
a frequent itemset, resulting in a smaller number of candidate itemsets.
\end_layout
\begin_layout Standard
Apriori employs an iterative approach known as a level-wise search, where
(π-1)-itemsets are used to explore π-itemsets.
First passing over the database counts the frequency of each item and determine
s frequent 1-itemsets.
The following passes, denoted as pass π, generates candidate itemsets πΆ
\begin_inset script subscript
\begin_layout Plain Layout
π
\end_layout
\end_inset
by finding the frequent itemsets πΏ
\begin_inset script subscript
\begin_layout Plain Layout
π-1
\end_layout
\end_inset
during the (π-1)th passing.
Then database is scanned again to count frequency of each candidate in
πΆ
\begin_inset script subscript
\begin_layout Plain Layout
π
\end_layout
\end_inset
.
\end_layout
\begin_layout Standard
\begin_inset Float algorithm
wide false
sideways false
status open
\begin_layout Plain Layout
\begin_inset ERT
status open
\begin_layout Plain Layout
\backslash
begin{algorithmic}[1]
\end_layout
\begin_layout Plain Layout
\backslash
State{$L_{1}$ = {frequent 1-itemsets}}
\end_layout
\begin_layout Plain Layout
\backslash
For{$k=2$; $L_{k-1}$!= emptyset; $k++$}
\end_layout
\begin_layout Plain Layout
\backslash
State{$C_{k}$ = apriori-gen$(L_{k-1})$}
\end_layout
\begin_layout Plain Layout
\backslash
For{all transactions $t$ in $D$}
\end_layout
\begin_layout Plain Layout
\backslash
State{$C_{t}$ = subset$(C_{k},t)$}
\end_layout
\begin_layout Plain Layout
\backslash
For{all candidates $c$ in $C_{t}$}
\end_layout
\begin_layout Plain Layout
\backslash
State{$c$.count++}
\end_layout
\begin_layout Plain Layout
\backslash
EndFor
\end_layout
\begin_layout Plain Layout
\backslash
EndFor
\end_layout
\begin_layout Plain Layout
\backslash
State{$L_{k}$ = (c in $C_{k}$| $c$.count >= minsup)}
\end_layout
\begin_layout Plain Layout
\backslash
EndFor
\end_layout
\begin_layout Plain Layout
\backslash
end{algorithmic}
\end_layout
\end_inset
\end_layout
\begin_layout Plain Layout
\begin_inset Caption Standard
\begin_layout Plain Layout
Apriori Algorithm
\end_layout
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Standard
The candidate generation of Apriori, called apriori-gen returns a superset
of all frequent π-itemsets from frequent (π-1)-itemsets.
It consists of two steps, join and prune.
In the join step, basically frequent (π-1)-itemsets are joined with each
other, πΏ
\begin_inset script subscript
\begin_layout Plain Layout
π-1
\end_layout
\end_inset
β πΏ
\begin_inset script subscript
\begin_layout Plain Layout
π-1
\end_layout
\end_inset
.
\end_layout
\begin_layout Standard
\begin_inset Float algorithm
wide false
sideways false
status open
\begin_layout Plain Layout
\begin_inset ERT
status open
\begin_layout Plain Layout
\backslash
begin{algorithmic}[1]
\end_layout
\begin_layout Plain Layout
\backslash
State{insert into $C_{k}$}
\end_layout
\begin_layout Plain Layout
\backslash
State{select $p$.$item_{1}$, $p$.$item_{2}$, ..., $p$.$item_{k-1}$, $q$.$item_{k-1}$}
\end_layout
\begin_layout Plain Layout
\backslash
State{from $L_{k-1}$ $p$, $L_{k-1}$ $q$}
\end_layout
\begin_layout Plain Layout
\backslash
State{where $p$.$item_{1}$ = $q$.$item_{1}$}, ..., $p$.$item_{k-2}$ = $q$.$item_{k-2}$,
$p$.$item_{k-1}$ < $q$.$item_{k-1}$
\end_layout
\begin_layout Plain Layout
\end_layout
\begin_layout Plain Layout
\backslash
end{algorithmic}
\end_layout
\end_inset
\end_layout
\begin_layout Plain Layout
\begin_inset Caption Standard
\begin_layout Plain Layout
Join step of apriori-gen
\end_layout
\end_inset
\end_layout
\end_inset
\end_layout
\begin_layout Standard
Then in the prune step, all itemsets π present in candidate itemsets πΆ
\begin_inset script subscript
\begin_layout Plain Layout
π
\end_layout
\end_inset
, is removed if (π-1)-subset of π is not present in πΏ
\begin_inset script subscript
\begin_layout Plain Layout
π-1
\end_layout
\end_inset
.
By doing so, the final output of πΆ
\begin_inset script subscript