Download improving the efficiency of apriori algorithm in data mining

DATE OF ACCEPTANCE: JUNE 21, 2014
DATE OF PUBLICATION: JUNE 26, 2014
ISSN: 2348-4098
VOLUME 02 ISSUE 05 JUNE- 2014
IMPROVINGTHEEFFICIENCYOFAPRIORIALGORITHMIN
DATAMINING
GURNEETKAUR
Scholar,DepartmentofComputerScienceandApplications
KurukshetraUniversity,Kurukshetra
Email:[email protected]
ABSTRACT
Apriori algorithm is the classic algorithm of association rules, which finds the entire
frequent item, sets. When this algorithm is applied to dense data the algorithm
performancedeclinesduetothelargenumberoflongpatternsemerge.Inordertofind
more valuable rules, this paper proposes an improved algorithm of association rules,
the classical Apriori algorithm. Finally, the improved algorithm is verified, the results
showthattheimprovedalgorithmisreasonableandeffective,canextractmorevaluable
information.
KEYWORDS‐Associationrulemining,Apriori,Candidateitemsets,DataMining
1. INTRODUCTION
relational database, data warehouses
Dataminingisoneofthemostdynamic
emergingresearchesintoday’sdatabase
technology.Toextractthevaluabledata
from large databases, it is necessary to
explore the databases efficiently. It is
theanalysisstepoftheKDD(Knowledge
Discovery and Data Mining) process. It
is defined as the process of extracting
interesting
previously
(non‐trivial,
unknown
implicit,
and
useful)
information or patterns from large
information
repositories
such
as:
etc.Thegoalofthedataminingprocess
istoextractinformationfromadataset
andtransformitintoanunderstandable
structure for further use. The problem
of mining association rules from
transactional database was introduced
in[9].Theconceptaimstofindfrequent
patterns, interesting correlations, and
associations among sets of items in the
transaction databases or other data
repositories.Associationrulesarebeing
used widely in various areas such as
telecommunication
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networks,
drug
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VOLUME 02 ISSUE 05 JUNE- 2014
analysis, risk and market management,
Support(XY)/Total
inventorycontroletc.[2]
transactions.
Associationrulearethestatementsthat

confidence
parts “Antecedent” and “Consequent”.

Lift: is the ratio of the probability
that X and Y occur together to the
multiple of the two individual
which is found in the database, and
probabilities for X and Y. It is given
consequent is the item that is found in
antecedent[12].
=
Support(XUY)/Support(X).
consequent. Antecedent is that item
combination with the first i.e. the
Confidence:isdefinedaspercentage
X that also contain Y. It is given as:
any database. Association rule has two
breadistheantecedentandbutteristhe
of
oftransactionindatabasecontaining
find the relationship between data in
For example {bread} => {butter}. Here
number
as:lift=Pr(X,Y)/Pr(X).Pr(Y).

Conviction: Unlike lift, it measures
the effect of the right‐hand‐side not
Formal definition [3]: Let I = {i1,i2, …,
beingtrue.Itinvertstheratioandis
in} be a set of items. Let D be a set of
given as : conviction = Pr(X).Pr(not
task relevant data transactions where
Y)/Pr(X,Y).[11]
eachtransactionTisasetofitemssuch
that T ⊆ I. A unique TID is associated
2. APRIORIALGORITHM
with each transaction. Let A be a set of
items.AtransactionTissaidtocontain
Aprioriisthemostclassicalandfamous
A if and only if A ⊆ T. An association
algorithm for mining frequent patterns.
rule is implication of the form A ⇒ B,
Apriorialgorithmwasintroducedby[9].
whereA⊂I,B⊂I,andA∩B=null.
The algorithm works on categorical
attributes and employs bottom up
The ARM technique is based on several
threshold values which are explained
below:

Support:
strategy. It is based on the Apriori
property which is useful for trimming
irrelevantdata.Itstatesthatanysubset
is
defined
as
the
offrequentitem‐setsmustbefrequent.
percentage/fraction of records that
2.1 DESCRIPTION OF THE TYPICAL
contain XUY to the total number of
APRIORIALGORITHM
records in the database. It is given
as:
Support(XUY)=
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Apriori employs an iterative approach,
sets are members of Ck. A scan of the
where k‐item sets are used to explore
database is required to determine the
(k+1)‐itemsets.First,thesetoffrequent
countofeachcandidateinCk.Thescan
1‐itemsets is found by scanning the
of the database result in the formation
database to count the occurrences for
of Lk i.e. it contains all candidates
each item, and then collecting those
having a count no less than the
items that satisfy minimum support
minimumsupportcountarefrequentby
defined. The result set obtained is
definition, and therefore belong to Lk.
denoted as L1. Now, L1 is used to find
The Apriori property is used to reduce
thesetoffrequent2‐itemsets,L2andso
thesizeofCk,asfollows.Any(K‐1)‐item
on, until no more frequent k‐item sets
set that is not frequent cannot be a
can be found. Thus the finding of each
subsetofafrequentk‐itemset.Hence,if
frequent k‐item set requires one full
any(K‐1)‐subsetofthecandidatek‐item
scan of the database. To improve the
set is not in Lk‐1, then the candidate
efficiency of frequent item sets level‐
item cannot be frequent either and so
wise generation, an important property
canbedeletedfromCk[5].
called the Apriori property, is used. It
reduces the search space. Apriori
property states that “All nonempty
3. RELATEDWORK
subsetsofafrequentitemsetmustalso
Rehab H. Alwa and Anasuya V. Patil
be frequent”. Thus it is divided into a
(2013) [1] described a novel approach
two‐step process which is used to find
to improve the Apriori algorithm
the frequent item sets: join and prune
throughthecreationofMatrix‐File.For
actions.
thispurposeMATLABisused,wherethe
A)THEJOINSTEP
database transactions are saved. Thus
repeated scanning is avoided and
A set of candidate k‐item set is
particularrows&columnsareextracted
generated by joining Lk‐1 with itself.
and perform a function on that rather
ThissetofcandidatesisdenotedasCk.
than scanning entire database. The
B)THEPRUNESTEP
results are visualize using graphical
form display and then interpreted. The
The members of Ck may or may not be
novel approach showed a very good
frequent, but all of the frequent k‐item
result in comparison to the traditional
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Apriori algorithm because there is a
that is not frequent. The improved
pruning process to those columns
algorithm not only optimizes the
whoseitemcountislessthanthevalue
algorithm by reducing the size of the
of minimum support. Hence the size of
candidate set of k‐item‐sets, Ck, but it
the Matrix reduces which saves a lot of
also reduces the amount of I / O
time, and an improvement in the speed
spending by cutting down transaction
is noticed by reducing the redundant
records
scanningofthedatabase.
performance of Apriori algorithm is
Jaio Yabing (2013) [4] proposed an
improvedalgorithmofassociationrules,
the classical Apriori algorithm. The
in
the
database.
The
optimized so that we can mine
association information from massive
datafasterandbetter.
improvedalgorithmisimplementedand
Jose L. Balcazar (2013) [6] proposed a
the results show that the improved
measure to the confidence boost of a
algorithm is reasonable and effective,
rule. Acting as a balance to confidence
can extract more value information.
andsupport,ithelpstoobtainsmalland
Although this process can decline the
crispsetsofminedassociationrulesand
numberofcandidateitemsetsinCkand
solves the well‐known problem such as
reduce time cost of data mining, the
rules of negative correlation may pass
price of it is pruning frequent item set,
the confidence bound. He analyzed the
whichcouldcostcertaintime.Fordense
propertiesoftwoversionsofthenotion
databases,
this
ofconfidenceboost,onebeinganatural
algorithm is higher than Apriori
generalization of the other. They
algorithm.
developed algorithms to filter rules
the
efficiency
of
JaishreeSinghetal(2013)[5]proposed
an Improved Apriori algorithm which
reduces the scanning time by cutting
down not required transaction records
as well as reduce the redundant
generation of sub‐items during pruning
thecandidateitem‐sets,whichcanform
directly the set of frequent item‐sets
andeliminatecandidatehavingasubset
accordingtotheirconfidenceboost,and
compared the given concept to some
similar notions in the literature, and
described
the
results
of
experimentation employing the new
notions
on
standard
benchmark
datasets. He also described an open
source association mining tool that
embodies one of our variants of
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confidenceboostinsuchawaythatthe
mostly improved Apriori algorithms
data mining process does not require
aimstogeneratelesscandidatesetsand
the user to select any value for any
yet get all frequent items. They
parameter.
concludedthatmanyimprovementsare
Mohammed Al‐ Maolegi and Bassam
Arkok
(2013)
[8]
indicated
the
needed basically on pruning in Apriori
toimproveefficiencyofalgorithm.
limitation of the original Apriori
Apriori Algorithm is the classical
algorithm of wasting time for scanning
algorithm for association rule mining.
the whole database searching on the
From the above reviews it has been
frequent item‐sets, and presented an
found that Apriori Algorithm is simple
improvement on Apriori by reducing
and easy to implement but still it has
thatwastedtimedependingonscanning
several drawbacks such as it requires
onlysometransactions.Theyperformed
multiplescanofthedatabase.Moreover
experiments with several groups of
for candidate generation process it
transactions, and with severalvalues of
takesmorememoryspaceandtime.The
minimum support applied on the
rules generated consist of items which
original Apriori and the improved
areirrelevant.Incaseoflargedatabases
Apriori,andtheresultsshowedthatthe
redundant
improved Apriori reduces the time
Moreover the Apriori Algorithm works
consumed by 67.38% in comparison
onlyonasinglevalueofconfidenceand
withtheoriginalApriori,andmakesthe
supportthroughoutthealgorithm.Thus
improved Apriori algorithm more
it is not suitable for dense databases.
efficientandlesstimeconsuming.
[13]
RinaRavaletal(2013)[10]performeda
survey
on
few
good
improved
approachesofApriorialgorithmsuchas
rules
are
generated.
4. PROPOSEDALGORITHM
A. THEORYOFALGORITHM
RecordFilterandIntersectionapproach,
Classical Apriori algorithm generates
Improvement
size
large number of candidate sets if
frequency and trade list, Improvement
database is large. And due to large
by reducing candidate set and memory
numberofrecordsindatabaseresultsin
utilization, Improvement based on
much more I/O cost. In this project, we
frequency of items etc. They found that
proposed an optimized method for
based
on
set
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Apriori algorithm which reduces the
sizeofdatabasealongwithreducingthe
number
of
candidate
item
sets
generated.Inourproposedmethod,we
introduced
an
attribute
named
SizeOfTransaction (SOT), containing
number
of
items
in
individual
transaction in database. The deletion
process of transaction in database will
made according to the value of K.
Depending on the value of K, algorithm
1)L1=find_frequent_1‐itemsets(D);
2)For(k=2;Lk‐1≠∅;k++){
3)Prune1(Lk‐1)
4)Ck=apriori_gen(Lk‐1,min_sup);
5)foreachtransactiont∈D{
6)Ct=subset(Ck,t);
7)foreachcandidatec∈Ct
8)c.count++;
searches the same value for SOT in
database. If value of SOT matches with
9)}
value of K then those transactions are
10)Lk={c∈Ck|c.count≥min_sup};
deletedfromthedatabase.Forreducing
the size of the candidate item sets
11)if(k>=2){
formed before the candidate item sets
12)delete_datavalue(D,Lk,Lk‐1);
Ck are generated, further prune Lk‐1,
count the timesofallitemsoccurredin
Lk‐1, delete item sets with this number
less than k‐1 in Lk‐1. In this way, the
number of connecting items sets and
the size of the database to be scanned
willbedecreased,sothatthenumberof
candidateitemswilldecline.
B. PSEUDOCODEOFTHE
ALGORITHM
Input:D:Databaseoftransactions;
min_sup:minimumsupportthreshold
Output:L:frequentitemsetsinD
13)delete_datarow(D,Lk);}
14)}
15)returnL=UkLk;
Procedureapriori_gen(Lk‐
1:frequent(k‐1)‐itemsets)
1)foreachitemsetl1∈Lk‐1{
2)foreachitemsetl2∈Lk‐1{
3)if(l1[1]=l2[1])∧(l1[2]=l2[2])
∧…∧(l1[k‐2]=l2[k‐2])∧(l1[k‐1]<l2
[k‐1])then{
Method:
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4)c=l1∞l2;
6)deletedatarow;}
5)foreachitemsetl1∈Lk‐1{
7)}
6)foreachcandidatec∈Ck{
ProcedurePrune1(Lk‐1)
7)ifl1isthesubsetofcthen
1)forallitemsetsL1∈Lk‐1
8)c.num++;}}}}}
2)ifcount(L1)≤k‐1
9)C'k={c∈Ck|c.num=k};
3)thendeleteallLjfromLk‐1
10)returnC'k;
4)returnL'k‐1//gobackanddelete
Proceduredelete_datavalue
itemsetswiththis
(D:Database;Lk:frequent(k)‐itemsets;
numberlessthank‐1.
Lk‐1:frequent(k‐1)‐itemsets)
1)foreachitemseti∈Lk‐1andi∉Lk{
2)foreachtransactiont∈D{
C. EXAMPLEOFTHEALGORITHM
Let us consider a transaction database
asshownintable1.
TABLEI:Transactiondatabase
3)foreachdatavalue∈t{
4)if(datavalue=i)
TID
ITEMS
SOT
5)updatedatavalue=null;
T1
A,B,D
3
6)}}
T2
A,B,C,D
4
Proceduredelete_datarow(D:
T3
A,B,E
3
DatabaseLk:frequent(k)‐itemsets)
T4
B,E,F
3
1)foreachtransactiont∈D{
T5
A,B,D,F
4
2)foreachdatavalue∈t{
T6
A,E
2
3)if(datavalue!=nullanddatavalue!=0
T7
C
1
T8
E,F
2
){
4)datarow.count++;}}
5)if(datarow.count<k){
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Suppose the minimum support count
Step1:Firstly,theSOTcolumnisadded
min_sup=2. The algorithm proceeds as
tothedatabase.
follows(fig1):
Step2:Inthefirstiteration,eachitemis
a member of candidate 1‐itemsets,C1.
The
algorithm
simply
scans
the
database to count the occurrences of
eachitem.
Step 3: This algorithm will then
generate number of items in each
transaction. We called this Size_Of
_Transaction(SOT).
Step4:Becauseofmin_sup=2,thesetof
frequent
1‐itemset,
L1
can
be
determined. It consistsofthecandidate
1‐itemset, satisfying the minimum
supportthreshold.
Step 5: As there are no items with
support less than 2 nothing is deleted.
Inaddition,whenL1isgenerated,now,
thevalueofkis2,deletethoserecords
of transaction having SOT=1 in D. And
there won’t exist any elements of C2 in
the records we find there is only one
data in the T7. Thus after deleting the
transaction we obtain transaction
databaseD1.
Step 6: To discover the set of frequent
Figure1:Exampleofproposedalgorithm
2‐itemsets, L2, the algorithm uses the
joinL1∞L1togenerateacandidateset
of2‐itemsets,C2.
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Step 7: The transactions in D1 are
Step 12: The transactions in D2 are
scannedandthesupportcountandSOT
scanned and the support count of each
of each candidate item‐set in C2 is
candidateitemsetinC3isaccumulated.
accumulated.
UseC3togenerateL3.
Step 8: L2, the set of frequent 2‐
Step13:L3hasonlyone3‐itemsetsso
itemsets is now then determined,
that C4 =null. The algorithm will stop
consistingofthosecandidate2‐itemsets
andgiveoutallthefrequentitemsets.
in C2 having minimum support greater
orequaltothespecifiedvalue.
Step 14: Algorithm will be generated
forCkuntilCk+1becomesempty.
Step 9: Now L2 is pruned by deleting
the
5. ANALYTICAL ANALYSIS OF
item
sets
with
number
of
occurrences in Lk‐1 less than k‐1 to
before candidate item sets occur i.e.
itemsets {B,F}, {A,E}, {B,E}, {E,F} are
deleted.
THEPROPOSEDALGORITHM
The basic thought of this proposed
algorithm is similar with the existing
apirori algorithm, that is it gets the
Step10:AfterL2ispruned,wefindthat
frequentitemsetL1whichhassupport
the transactions T6 and T8 consists of
level larger than or equal to the given
onlytwoitems.Now,thevalueofkis2,
level of the users support via scan the
delete the transactions having SOT=2.
databaseD.Theniteratetheprocessand
And there won’t exist any elements of
getL2，L3……Lk..Butstilltheproposed
C3 in the records. Therefore, these
algorithm differs from the existing
records can be deleted and we obtain
algorithm.
transactiondatabaseD2.
The size of the database is reduced by
Step11:Todiscoverthesetoffrequent
cutting
the
database
using
3‐itemsets, L3, the algorithm uses the
SizeofTransaction
joinL2’∞L2’togenerateacandidateset
optimizedalgorithmprunesLk‐1before
of3‐itemsetsC3.Thereareanumberof
Ck is generated. In other words,
elements in C3. According to the
frequentitemsetinLk‐1whichisgoing
propertyofApriorialgorithm,C3needs
toconnectarecounted.Accordingtothe
ispruned.
result obtained item sets with number
attribute.
the
The
less than k‐1 in Lk‐1 are deleted to
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decrease the number of the connecting
frequent item‐set. The typical Apriori
itemsetandremovalofsomeelements
algorithm has performance bottleneck
that does not satisfy the conditions.
in the large data processing so that we
Next the transactions whose value of
need to optimize the existing algorithm
SOT is less than k‐1 are removed from
with variety of methods. Thus the
the database. This decreases the
optimizedalgorithmprunesLk‐1before
possibility
thus
we generate Ck. Thus decreasing the
declining the number of candidate item
number of connecting item sets and
sets in Ck, and reduces the number of
removing the item‐sets which does not
times to repeat the process and the
satisfies the conditions. The improved
number of transactions that need to be
algorithm proposed optimizes the
scanned from iterations. For large
algorithm by reducing the size of the
database, this algorithm can thus save
candidate set Ck and also reducing the
time and increase the efficiency of data
I/O spend by cutting down transaction
mining. This is what Apriori algorithm
records in the database. The proposed
doesnothave.
algorithm also reduces the time to
of
combination,
Although this process can decline the
numberofcandidateitemsetsinCkand
reduce time cost of data mining, the
price of it is pruning frequent item set,
whichcouldcostcertaintime.Fordense
database such as, telecom, population,
multinationalcompanies,census,etc.as
repeat the process. For large database,
this algorithm can save time cost and
increase the efficiency of data mining.
Thus the performance of Apriori
algorithm is optimized so that we can
mine association information from
massivedatafasterandbetter.
they consist of large amounts of long
Although this improved algorithm has
forms,theefficiencyofthisalgorithmis
optimized the existing algorithm and is
higherthanApriori.
more efficient but it has overhead to
6. CONCLUSION
manage the new database after every
generationofLk.Tus,thereshouldexist
some approach which requires less
In this paper, Apriori algorithm is
number of scans of database. Another
improved based on the properties of
solution might be division of large
cutting database and pruning of the
databaseamongprocessors.
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