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An Evolutionary Quantum Behaved Particle Swarm Optimization for Mining

Association Rules

K.Indira

Research Scholar,Department of CSE,

Pondicherry Engg. College,

Puducherry, India

induharini@gmail.com

S.Kanmani

Professor,Department of IT,

Pondicherry Engg. College,

Puducherry, India

Kanmani@pec.edu

R.agan, !."ala#i, $.%ilton oseph

$inal &ear IT

Pondicherry Engg. College,

Puducherry, India

Abstract' Association Rule Mining is a techniue of datamining that aims in e!tracting interesting patterns" freuent

correlations or associations among set of items in the

transaction data#ases$ Particle Swarm Optimization %PSO& is

one of several methods for mining Association Rules$ 't is atechniue used to e!plore the search space of a given pro#lem

to find the settings or parameters reuired to ma!imize a

particular o#(ective$ )owever" avoiding local optima and

improving the convergence speed is still a tedious tas*$ 'n this

wor*" an Evolutionary Quantum #ehaved Particle Swarm

Optimization %QPSO& algorithm is proposed #y com#ining the

classical PSO philosophy and uantum mechanics to improve

the performance of PSO$ 't is a glo#al+convergence guaranteed

algorithm and has a #etter search a#ility than the traditional

PSO$ ,he performance of QPSO is compared with #asic PSO"

and three other variants of PSO and the e!perimental results

shows that the proposed algorithm outperforms PSO uite

significantly and is also found to #e as effective as the PSO

variants with marginally #etter computational efficiency$

Keywords+ Particle Swarm Optimization- QuantumBehavior- Association Rule Mining- .lo#al convergence$

I. I(TR)D*CTI)(

Data mining, also +non as Knoledge Disco-ery in

Dataases is the process of e/tracting the patterns from data

and ta+ing an action ased on the category of the pattern. 0s

the amount of data stored in dataases and types ofdataases increases rapidly e/tracting the critical hidden

information from these dataases has ecome an importantissue. Se-eral methods such as association rules, clustering

and classification ha-e een used to otain interesting factsfrom data. 0mong these models, association rule mining is

the most idely applied method.

Initially traditional algorithms li+e 0priori, DynamicItemset Counting, $P1!roth tree ha-e een used for

e/tracting the interesting patterns. "ut, as the numer of

rules and the correlations in dataases increases, the

computational comple/ity continues to gro rapidly. 2ater

E-olutionary algorithms such as !enetic 0lgorithms 3!0s4and Particle Sarm )ptimi5ation 3PS)4 ha-e een

introduced for mining association rules. The mainmoti-ation for using !0 in the disco-ery of association

rules is that they cope etter ith attriute interactionthrough mutation and crosso-er operators. 0lthough !0

disco-ers high le-el prediction rules ith etter attriute

interaction, the operators tends to increase the comple/ity of

computation. Similar to !0, PS) is also a population1asediterati-e algorithm. The fundamental prolem in PS) is its

imalanced local and gloal search and also hile trying to

reduce the con-ergence time it gets trapped in local optimal

region hen sol-ing comple/ multimodal prolems. Theseea+nesses ha-e restricted ider applications of PS).

Therefore, accelerating con-ergence speed and a-oidingthe local optima ha-e ecome the to most important and

appealing goals in PS) research. In this or+, an

E-olutionary 6uantum eha-ed Particle Sarm

)ptimi5ation algorithm that features etter search efficiencyy a-oiding local optima and impro-ing the con-ergence

speed is proposed.

The paper is organi5ed as follos. In section II thepreliminaries as association rule mining, PS) are discussed.

Section III analy5es the e/isting literature on PS) and its

-ariants. The proposed 6PS) methodology along ith

e-aluation parameters are gi-en in section I7. Section 7n

discusses the e/perimental results folloed y theconclusion in section 7I.

II. PRE2I%I(0RIES

A. Association Rule Mining

0ssociation rule mining is a techni8ue of data mining that

is -ery idely used to deduce inferences from largedataases. Typically the relationship ill e in the form of a

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rule9 I$ :;Conse8uent?. The rule

should e such that ;& A .

The to parameter that indicate the importance of

association rules are Bsupport and Bconfidence.

Thesupport indicates ho often the rule holds in a set ofdata. It is gi-en y

onstransactiofno.Total

;,ithonstransacti(o.of43sup =Xport

34

The confidence for a gi-en rule is a measure of

ho often the conse8uent is true, gi-en that the antecedentis true. If the conse8uent is false hile the antecedent is

true, then the rule is also false. If the antecedent is not

matched y a gi-en data item, then this item does not

contriute to the determination of the confidence of the rule.It is gi-en y

34

B. PSO Algorithm

PS) introduced y Kennedy and EerhartFG simulates

the eha-iors of ird floc+ing. In PS), the solutions to theprolem are represented as particles in the search space.

PS) is initiali5ed ith a group of random particles

3solutions4 and then searches for optimum -alue y updatingparticles in successi-e generations. In each iteration, all theparticles are updated y folloing to est -alues. The first

one is the est solution 3fitness4 it has achie-ed so far. This

-alue is called Bp#est. 0nother HestH -alue that is trac+ed

y the particle sarm optimi5er is the est -alue, otainedso far y any particle in the population. This est -alue is a

gloal est and called Bg#est.

Particle Sarm has to primary operations9 7elocityupdate and Position update. During each generation each

particle is accelerated toard the particles pre-ious est

position and the gloal est position. 0t each iteration, a

ne -elocity -alue for each particle is calculated ased on

its current -elocity, the distance from its pre-ious estposition, and the distance from the gloal est position. The

ne -elocity -alue is then used to calculate the ne/t position

of the particle in the search space. This process is theniterated a set numer of times or until a minimum error is

achie-ed.

0fter finding the to est -alues, the particle updates its-elocity and positions ith the folloing formulae

34

3J4

here -FG is the particle -elocity, presentFG is the currentparticle. pestFG and gestFG are local est and gloal est

position of particles. rand 34 is a random numer eteen

3,4. c and c are learning factors. *sually c A c A .

The outline of asic Particle Sarm )ptimi5er is as follos

Step /0 Initiali5e the population

Step 10 E-aluate fitness of the indi-idual particle 3update

pest4

Step 20 Keep trac+ of the indi-idual?s highest fitness 3gest4

Step 30 %odify -elocities ased on pest and gest

Step 40 *pdate the particle position

Step 50 Terminate if the condition is met

Step 60 !o to step

III. 2ITER0T*RERE7IEL

Particle sarm optimi5ation 3PS)4 is a population1

ased stochastic optimi5ation algorithm ased on the

metaphor of social interaction and communication such asird floc+ing and fish schooling F,G. In order to gain a

deep insight into the mechanism of PS), many theoretical

analyses ha-e een done on the algorithm. 0s for the

algorithm itself, 7an den "ergh FJGpro-ed that the canonicalPS) is not a gloal search algorithm, e-en not a local one,

according to the con-ergence criteria pro-ided y Solis and

Lets FMG.

In addition to the theoretical analyses mentioned

ao-e, there has een a considerale amount of or+ done

in de-eloping the original -ersion of PS), through

empirical simulations. Shi and Eerhart FG introduced theconcept of inertia eight to the original PS), in order to

alance the local and gloal search during the optimi5ation

process. 0ngeline FNG introduced a tournament selection into

PS) ased on the particle?s current fitness so that the

43sup

43sup43

Xport

YXportYXConfidence

=

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properties that ma+e some solutions superior ere

transferred directly to some of the less effecti-e particles.

This techni8ue impro-ed the performance of the PS)

algorithm on some enchmar+ functions.

Recently, inspired y 8uantum mechanics and tra#ectory

analysis of PS) FOG, Sun et al. used a strategy ased on a

8uantum d potential ell model to sample around thepre-ious est pointsFG, and later introduced the mean est

position into the algorithm and proposed a ne -ersion of

PS), 8uantum1eha-ed particle sarm optimi5ation

36PS)4 FQ,G. The iterati-e e8uation of 6PS) is -erydifferent from that of PS). "esides, unli+e PS), 6PS)

needs no -elocity -ectors for particles, and also has feer

parameters to ad#ust, ma+ing it easier to implement. The

6PS) algorithm has een shon to successfully sol-e aide range of continuous optimi5ation prolems and many

efficient strategies ha-e een proposed to impro-e the

algorithm F,G. This paper applies the 6PS)

methodology for mining association rules.

I7. %ET=)D)2)!&

A. Quantum behaed PSO

The 6uantum inspired Particle Sarm )ptimi5ation

36PS)4 is one of the recent optimi5ation methods ased on

8uantum mechanics. 2i+e any other e-olutionary algorithm,

a 8uantum inspired particle sarm algorithm relies on therepresentation of the indi-idual, the e-aluation function and

the population dynamics. The particularity of 8uantum

particle sarm algorithm stems from the 8uantumrepresentation it adopts hich allos representing thesuperposition of all potential solutions for a gi-en prolem.

%oreo-er, the position of a particle depends on the

proaility amplitudes a andb of the a-e function .

6PS) also stems from the 8uantum operators it uses toe-ol-e the entire population through generations. 6PS)

constitutes a poerful strategy to di-ersify the 6PS)

population and enhance the 6PS)?s performance in

a-oiding premature con-ergence to local optima.

In terms of classical mechanics, a particle is depicted y

its position -ector /iand -elocity -ector -i, hich determine

the tra!ector" of the particle. The particle mo-es along adetermined tra#ectory folloing (etonian mechanics, ut

this is not the case in 8uantum mechanics. In 8uantum

orld, the term tra!ector" is meaningless, ecause / i and

-iof a particle cannot e determined simultaneouslyaccording to uncertaint" principle. Therefore, if indi-idual

particles in a PS) system ha-e 8uantum eha-ior, the PS)

algorithm is ound to or+ in a different fashion.

In the 8uantum model of a PS), the state of a particle is

depicted y a-e function 3#, t4, instead of position and

-elocity. The dynamic eha-ior of the particle is idely

di-ergent from that of the particle in traditional PS)systems. The particles mo-e according to the folloing

iterati-e e8uations9

/3t4 A p U Vmest W /3t4V U ln3Xu4, if + YA .M/3t4 A pWUVmestW/3t4VUln3Xu4, if +Z.M 3M4

Lhere,

p A 3cpid cpgd4X 3c c4

u,+,c,care uniformly distriuted random numers in the

inter-al F,G.

is the contraction1e/pansion coefficient.

pidis the pest of the ithparticle.

pgdis the gloal est particle.

%ean est position or %ainstream Though point 3mest4 of

the population is defined as the mean of the est position of

all particle.

3N4

The steps in-ol-ed in 6uantum Particle Sarm )ptimi5er

are as follos

Step /0 Initiali5e the population

Step 10 E-aluate fitness of the indi-idual particle 3update

pest4

Step 20 Keep trac+ of the indi-idual?s highest fitness 3gest4

Step 30 Calculate mest 3mean of the pest of all particles4

Step 40 *pdate the particle position

Step 50 Terminate if the condition is met

Step 60 !o to step

B. $aluation Parameters

%uch or+ on association rule mining has een donefocusing on efficiency, effecti-eness and redundancy. $ocus

is also needed on the 8uality of rules mined. In this paper

association rule mining using 6PS) is treated as a multi1

o#ecti-e prolem here rules are e-aluated 8uantitati-elyand 8ualitati-ely ased on the folloing measures.

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Predictive Accuracy Predicti-e 0ccuracy 3P04 measures

the effecti-eness of the rules mined. The mined rules must

ha-e high predicti-e accuracy. The formula is gi-en y9

3O4

Lhere V;[&V is the numer of records that satisfy oth theantecedent ; and conse8uent &, V;V is the numer of rules

satisfying the antecedent ;.

7um#er of rules generated 0The count of the rulesgenerated ao-e a certain P0.

8aplace0 It is a confidence estimator that ta+es support into

account, ecoming more pessimistic as the support of ;

decreases. It is useful to detect spurious rules that may occury chance. It is defined as

34

9itness 0 $itness -alue is utili5ed to e-aluate the importanceof each particle. It is gi-en y

$itness3+4 A confidence3+4 Ulog3support3+44 U length3+4

3Q4

The o#ecti-e of this fitness function is ma/imi5ation. The

larger the particle support and confidence, the greater thestrength of the association, meaning that it is an important

association rule.

:onviction 0 Con-iction measures the ea+ness ofconfidence. Con-iction is infinite for logical implications

3confidence 4, and is if ; and & are independent.

34

7. RES*2TS0(DDISC*SSI)(

The goal of this section is to determine the o-erall

performance of 6PS) hen applied for association rule

mining. The proposed algorithm as tested on fi-e

enchmar+ datasets.

2enses, Car e-aluation, Post1)perati-e Patient Care,

=aerman?s Sur-i-al and \oo datasets ere ta+en up from

*CI Ir-ine repository for the e/periment. The effecti-eness

of 6PS) is compared ith !0 and PS) methodology formining association rules FG. To confirm the effecti-eness of

PS) and 6PS), oth the algorithms ere coded in a-a.

The details of the datasets are listed in Tale . The

efficiency of the algorithms as compared y utili5ing theoutput parameters mentioned earlier.

T0"2E I. D0T0SET DESCRIPTI)(

;ataset Attri#utes Swarm

Size

:lasses

2enses J J

Car E-aluation N O J

=aerman?s Sur-i-al

Post1operati-e Patient Care O

\oo N O

A. Predictie Accurac"

The predicti-e accuracy of the association rules mined

y proposed 6PS) methodology is compared ith the

results of !0 an PS) is plotted in $igure .

$igure . Predicti-e 0ccuracy Comparison

The predicti-e accuracy achie-ed y 6PS) is etter

compared to !0 and PS) for all the fi-e datasets ta+en upfor study.

B. %umber of rules generated

The numer of rules generated y 6PS) ith predicti-e

accuracy less than .M percentage of the ma/imum

predicti-e accuracy arri-ed is taulated for mining

X

YXcurac"edictieAc[

Pr =

E43sup

D43sup43

+

+=

Xport

YXportYXlapl

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association rules in comparison ith !0 and PS)

methodology for the datasets as shon in Tale .

T0"2E . C)%P0RIS)( )$ T=E (*%"ER )$ R*2ES !E(ER0TED

;atasets

.A PSO QPSO

2enses3J4

Car E-aluation

3O4

M N M

=aerman?sSur-i-al 34

J

Postoperati-e

Patient3O4

J Q J

\oo34O N M

It is noted that the 6PS) methodology generates

more numer of rules hen compared ith !0 and PS)

0ccuracy alone is not the o#ecti-e of mining

association rules. The interestingness of the association

rules mined is also measured through 2aplace, Con-ictionand 2e-erage measures. Tale presents the results of

2aplace, Con-iction and 2e-erage measures of the rules

mined from the datasets ta+en up for analysis.

T0"2E . %E0S*RES )$ 0SS)CI0TI)( R*2E %I(I(! LIT=

6PS)

;atasets 8aplace :onviction 8everage2enses .MQJ infinity .N

=aerman]s

Sur-i-al

.MN infinity .Q

Car E-aluation .MJ infinity .QJ

Postoperati-e

Patient

.M infinity .

\oo .MJ infinity .JQ

7I. C)(C2*SI)(

The 6PS) algorithm is superior to the standard PS)mainly in three aspects. $irstly, 8uantum theory is an

uncertain system in hich different state of the particles anda ider searching space of the algorithm can e generated.

Secondly, the introduction of mest into 6PS) is a

enchmar+ in 6uantum Theory. In the standard PS), it

con-erges fast, ut at times, the fast con-ergence happens in

the first fe iterations utfalls into a local optimal situationeasily in the ne/t fe iterations. Lith the introduction of

mest in 6PS), the a-erage error is loered, since each

particle cannot con-erge fast ithout considering its

colleagues, hich ma+es the fre8uency loer than PS).2astly, 6PS) has feer parameters compared to standard

PS) and it is much easier to implement and run. =ence the

performance of the algorithm is significantly impro-ed y

6PS).

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