Synthesizing High-Utility Patterns from Different Data Sources

16 Pages·2017·1.03 MB·English

data
Article
Synthesizing High-Utility Patterns from Different
Data Sources
AbhinavMuley* ID andManishGudadhe
DepartmentofComputerEngineering,St.VincentPallottiCollegeofEngineering&Technology,Nagpur441108,
India;[email protected]
* Correspondence:[email protected];Tel.:[phone]
(cid:1)(cid:2)(cid:3)(cid:1)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:1)
(cid:1)(cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)
Received:3August2018;Accepted:30August2018;Published:3September2018
Abstract: In large organizations, it is often required to collect data from the different geographic
branchesspreadoverdifferentlocations.Extensiveamountsofdatamaybegatheredatthecentralized
locationinordertogenerateinterestingpatternsviamono-miningtheamasseddatabase. However,
itisfeasibletominetheusefulpatternsatthedatasourceitselfandforwardonlythesepatternsto
thecentralizedcompany,ratherthantheentireoriginaldatabase. Thesepatternsalsoexistinhuge
numbers,anddifferentsourcescalculatedifferentutilityvaluesforeachpattern. Thispaperproposes
aweightedmodelforaggregatingthehigh-utilitypatternsfromdifferentdatasources.Theprocedure
of pattern selection wasalso proposed toefficiently extracthigh-utility patternsin ourweighted
modelbydiscardinglow-utilitypatterns. Meanwhile,thesynthesizingmodelyieldedhigh-utility
patterns,unlikeassociationrulemining,inwhichfrequentitemsetsaregeneratedbyconsideringeach
itemwithequalutility,whichisnottrueinreallifeapplicationssuchassalestransactions. Extensive
experimentsperformedonthedatasetswithvariedcharacteristicsshowthattheproposedalgorithm
willbeeffectiveforminingverysparseandsparsedatabaseswithahugenumberoftransactions.
Ourproposedmodelalsooutperformsvariousstate-of-the-artdistributedmodelsofmininginterms
ofrunningtime.
Keywords: data integration; data mining; high-utility patterns; knowledge discovery; weighted
model;multi-databasemining;distributeddatamining
1. Introduction
Largeandsmallenterprisesarefacingthechallengesofextractingusefulinformation,sincethey
are becoming massively data rich and information poor [1]. Organizations are getting larger and
amassingcontinuouslyincreasingamountsofdata. Findingmeaningfulinformationplaysavitalrole
incross-marketingstrategiesanddecisionmakingprocessofbusinessorganizations,especiallythose
whodealwithbigdata.
The world’s biggest retailer, Walmart, has over 20,000 stores in 28 countries which process
2.5petabytesofdataeveryhour[2]. Afewweeksofdatacontains200billionrowsoftransactional
data. Dataisthekeyforthemtokeepthecompanyatthetopforgeneratingrevenues. Thecostof
transferringthedataatthecentralnodecanbecut-downiftheyfocusonminingthedataatthelocal
nodeitselfandforwardingonlyretrievedpatterns,ratherthanacompletedatabase. Swiggy,oneof
India’ssuccessfulstart-ups,generatesterabytesofdataeveryweekfrom35,000restaurantsspread
across15citiestodeliverthefoodtotheconsumer’sdoorstep[3]. Itreliesonthisdatafortheefficiency
ofdeliveryandahassle-freeexperienceforconsumers. Ifthedataisminedatthecity-basedlocal
nodesandonlytheextractedpatternsareforwarded,itwouldhelpthemtodelivertheirservicesat
lightningfastspeed.
Data2018,3,32;doi:10.3390/data3030032 www.mdpi.com/journal/data
Data2018,3,32 2of16
Traditionalknowledgediscoverytechniquesarecapableofminingatasinglesourceplatform.
These techniques are insufficient for mining the data of large companies scattered across multiple
locations.Whilecollectingallthedatafrommultiplesourcesmightgatherahugechunkofdatabasesfor
centralizedprocessing,itisunrealistictocombinethedatatogetherfrommultipledatasourcesbecause
ofthesizeofthedatatobetransportedandprivacy-relatedissues.Somesourcesofanorganizationmay
sendtheirextractedpatternsbutnottheirentiredatasetduetoprivacyconcerns. Henceitisfeasibleto
minethepatternsatdifferentdatasourcesandsendonlytheextractedpatterns,ratherthantheoriginal
database,tothecentralbranchofthecompany. Thepatternminingateachsourceisalsoimportantfor
decisionsupportatthelocallevel. However,thenumberofpatternscollectedfromdifferentsources
maybetoohigh,sothatfindingvalidpatternsfromthepatternsetcanbedifficultforthecentralized
company. The proposed weighted model compresses the set of patterns and generates high voted
patterns. Forconvenience,theworkpresentedinthispaperfocusesonpost-mining,thatis,gathering,
analyzingandsynthesizingthepatternsextractedfrommultipledatabases.
Thereareexistingparalleldataminingalgorithmswhichemployparallelmachinestoimplement
dataminingalgorithmscalledMiningAssociationRulesonParalleling(MARP)[4–8].Thesealgorithms
haveprovedtobeeffectiveinminingfromverylargedatabases. However,therearecertainlimitations
tothesealgorithmsbecausetheydon’tgeneratelocalpatternsatthelocaldatasource,whicharevery
usefulinreal-worldapplications. Inaddition,itrequiresmassivelyparallelmachinesforcomputing
anddedicatedsoftwareforprocessingofparallelmachines. Someminingalgorithmsaresequentialin
natureandcannotbetestedonparallelmachines.
Various techniques are developed for data mining from distributed data sources [9–16].
Wuetal.[17]havealreadyproposedasynthesismodeltoextracthigh-frequencyassociationrulesfrom
differentdatasourcesusingFrequentItemsetMining(FIM)astheirdataminingtechnique. Thismodel
cannotbeappliedtoHigh-utilityItemsetMining(HUIM)forthefollowingreasons:
• FIMassumesthateveryitemcanappearonlyonceineachtransactionandhasthesameutilityin
termsofoccurrencesandunitprofit.
• FIMmaintainstheanti-monotonicityofthesupportwhichisnotapplicabletotheproblemof
High-utilityItemsetMining(HUIM)discussedinalatersection.
T.Ramkumaretal.[18]havealsoproposedasynthesismodelalongsimilarlinestoWu’smodel,
butthemaindrawbackofthismodelisthatthetransactionpopulationofadatasourceintermsof
thepopulationofotherdatasourcesmustbeknownbeforehand,whichisnotpossibleduetoprivacy
concernsofdatasharing. Thispaperemphasizessynthesizinglocalhigh-utilitypatternsratherthan
frequentrules,tofindthepatternsvalidthroughouttheorganization. Themodelpresentedinthis
paperdoesn’trequireanassumptionoftransactionpopulationtobeknowninadvance.
Theproblemstatementforsynthesizingthepatternsfromdifferentdatasourcescanbeformulated
as: There are ‘n’ data sources present in a large organization: DS , DS , DS , ... , DS . Each site
1 2 3 n
supportsasetoflocalpatterns. Weareinterestedin: (1)miningeverydatasourcetofindlocalpatterns
supportedbythesource;and(2)developinganalgorithmtosynthesizetheselocalpatternstofind
onlytheusefulpatterns(withhigh-utility),whicharevalidforthewholeorganizationandcalculate
theirsynthesized/globalutility. Itisassumedthatthecleaningandpre-processingofdatahasbeen
performedalready. Patternsobtainedfrommono-miningtheunionofalldatasourcesisourgoal.
2. RelatedWork
Data mining is the process of semi-automated analysis on large databases to find significant
patterns and relationships which are novel, valid and previously unknown. Data mining is a
componentofaprocesscalledKnowledgediscoveryfromdatabases(KDD).Theaimofdataminingis
toseekoutrules,patternsandtrendsinthedataandinfertheassociationsfromthesepatterns. Ina
transactiondatabase,FrequentItemsetMining(FIM)discoversfrequentitemsetsthatarethecollection
ofitemsetsappearingmostfrequentlyinatransactiondatabase[19]. Marketbasketanalysisisthe
Data2018,3,32 3of16
mostpopularapplicationofFIM.Theretailmanagersusefrequentitemsetsminedfromanalyzingthe
transactionstostrategizestorestructure,offers,andclassificationofcustomers[20,21]. Asdiscussed
earlier, the FIM has following limitations: (1) it assumes that every item can appear only once in
each transaction; and (2) it has the same utility in terms of occurrences and unit profit. In market
basket analysis, it may happen that customer buys multiple units of the same item, for example,
3packetsofalmondsor5packetsofbread,andsoon. Andeveryitemdoesn’thavethesameunit
profit,forexample,sellingthepacketofalmondsyieldsmoreprofitthansellingapacketofbread.
FIMdoesn’ttakeintoaccountthenumberofitemspurchasedinatransaction. ThusFIMonlycounts
the frequency of items rather than the utility or profit of items. As a consequence, the infrequent
patternswithhigh-utilityaremissedandfrequentpatternswithlow-utilityaregenerated. Frequent
items may contribute to only a minor portion of the total profit, whereas non-frequent items may
contributetoamajorportionofthetotalprofitofabusiness. Thesupportandconfidenceframeworkof
FIMestablishedbyAgrawaletal.[22]arethemeasurestogeneratethehigh-frequencyrules,buthigh
confidencemaynotalwaysimplythehigh-profitcorrelationbetweentheitems. Anotherexampleis
click-streamdata,whereastreamofwebpagesvisitedcanbedefinedasatransaction. Thetimespent
onawebpagecontributestoitsutilityincontrasttothefrequentvisitscountedinFIM.
To address this limitation of FIM, the concept of High-utility Itemset Mining (HUIM) [23–25]
wasdefined. UnlikeFIM,theHUIMtakesintoaccountthequantityofanitemineachtransaction
anditscorrespondingweight(e.g.,profit/unit). HUIMdiscoversitemsetswithhigh-utility(profit).
Thisallowsitemstoappearmorethanonceinatransaction.TheproblemofHUIMisknowntobemore
difficultthantheFIM,becausethedownward-closurepropertydoesn’tholdtrueforutilitymining,
thatis,theutilityofanitemsetisnotanti-monotonicormonotonic. Thus,theutilityofanitemset
canbehigher,equalorlowerthantheutilityofanysubsetofthatitemset. Thetargetofhigh-utility
miningistogeneratehigh-utilitypatternswhichyieldamajorportionofthetotalprofit. Interestingly,
FIMassumestheutilityofeveryitemtobe1,thatis,thequantityofeachitemandweight/unitare
equal. HenceFIMisconsideredtobeaspecialcaseofHUIM.Let’sconsiderthesampledatabasein
Table1. Ithasfivetransactions(T ,T ,T ,T ,andT ). Itemsp,r,andsappearinthetransactionT
1 2 3 4 5 1
havinganinternalutility(e.g.,quantityofitem)2,3and5respectively.
Table1.Sampletransactiondatabase.
TID Transaction(Item,Quantity)
T1 (p,2),(r,3),(s,5)
T2 (p,3),(r,7),(t,3),(v,6)
T3 (p,2),(q,3),(r,2),(s,7),(t,2),(u,6)
T4 (q,5),(r,4),(s,4),(t,2)
T5 (q,3),(r,3),(t,2),(v,3)
Table2showstheexternalutility(e.g.,profit/unit)oftheitemsp,randsare6,2and3respectively.
TheutilityU(i,T)ofanyitemiinatransactionT iscalculatedase(i)×X(i,T)wheree(i)denotes
i i i
externalutilityasperTable2andX(i,T)denotesinternalutilityasperTable1. TheutilityU(i,T)
i i
denotes the profit generated by selling an item i in the transaction T. For example, utility of the
i
transactionT iscalculatedasexternalutilityofallitemsinT ×internalutilityofrespectiveitemsin
1 1
T i.e.,(2×6)+(3×2)+(5×3)=33.
1
Table2.Externalutility.
Item p q r s t u v
Profit 6 3 2 3 4 2 2
AnitemsetZislabelledasahigh-utilityitemsetwhentheutilitycalculatedismorethantheutility
thresholdminutilsetbytheuserotherwiseitiscalledalow-utilityitemset. TheHUIMdiscoversallthe
high-utilityitemsetssatisfyingtheminutil.
Data2018,3,32 4of16
3. Method: ProposedSynthesisModel
Inthissection,weproposeaweightedmodelforsynthesizinghigh-utilitypatternsforwarded
bydifferentandknownsources. LetPbethesetofpatternsforwardedbyndifferentdatasources
DS ,DS ,DS ,... ,DS . ForapatternXY,supposeW(DS ),W(DS ),W(DS ),... ,W(DS )arethe
1 2 3 n 1 2 3 n
respectiveweightsofDS ,DS ,DS ,... ,DS . ThesynthesizedutilityforpatternXYiscalculatedas:
1 2 3 n
util(XY)=W(DS )×util (XY)+W(DS )×util (XY)+W(DS )×util (XY)+... +
1 1 2 2 3 3
(1)
W(DS )×util (XY)
n n
whereutil(XY)istheutilityofpatternXYinDS fori=1,2,3,... ,n.
i i
WeadopttheGood’sidea[26]basedontheweightofevidenceforallocatingweightstoourdata
sourcesasthesamewasalsoadoptedbyWu’sproposedmodel[17]. Itestablishesthattheweightof
evidenceisasimportantastheprobabilityitself. Forconvenience,wenormalizetheweightsinthe
interval0–1andtheweightofeachpatternisimportant,basedonitspresenceintheoriginaldatabase.
Therefore,weusethepresenceofpatternstoevaluatetheweightofthepattern. Figure1outlinesthe
proposedmethod. Ourweightedmodelisdesignedinfollowingsectionswithanexample. Pattern
selectionalgorithmisconstructedtodealwithlow-utilitypatterns.

DS 1 DS2 …………………… DS n

Local Pattern Analysis

P1 P2 …………………… Pn

Synthesis model by weighting

SPS

Figure 1. The proposed model of synthesizing patterns by weighting. DS i—ith data source;
Pi—PatternsetminedfromDSi;SPS—Thesynthesizedpatternsetwithnormalizedutility.
3.1. AllocatingWeightstoPatterns
The weight of each data source needs to be calculated in order to synthesize the high-utility
patternsforwardedbydifferentandknowndatasources. LetPbethesetofpatternsforwardedby
ndifferentdatasourcesDS ,DS ,DS ,... ,DS andP=P ∪P ∪P ∪... ∪P whereP istheset
1 2 3 n 1 2 3 n i
ofpatternsforwardedbyDS. AccordingtoGood’sideaofallocatingweight,wetakethenumberof
i
occurrencesofPatternRinPtoassignweightW(R)toR.High-utilitypatternshavehigherchancesof
becomingavalidpatternthanlow-utilitypatterns,inthecombinationofallthedatasources. Thus,
theweightofapatterndependsuponthenumberofdatasourcesthatsupport/voteforit. Inreality,
abusinessorganizationisinterestedinminingpatternsvotedbymostofitsbranchesforgenerating
maximumprofit. Theweightofdatasourcealsodependsuponthenumberofhigh-utilitypatternsit
supports. Thefollowingexampleillustratesthisidea:
• Let P be the set of patterns mined from DS having patterns: ABC, AD and BE where
1 1
util (ABC)=3,544,830;util (AD)=1,728,899;util (BE)=1,464,888
1 1 1
• Let P be the set of patterns mined from DS having patterns: ABC and AD where
2 2
util (ABC)=3,591,954;util (AD)=1,745,716
2 2
• Let P be the set of patterns mined from DS having patterns: BC, AD and BE where
3 3
util3(BC)=1,252,220;util3(AD)=1,749,528;u1t il3(BE)=1,461,862
Data2018,3,32 5of16
Ifthereare3datasourcesviz.,DS ,DS ,DS thenP=P ∪P ∪P havingfourpatternsinP:
1 2 3 1 2 3
• R : ABC;Numberofoccurrences=2
1
• R : AD;Numberofoccurrences=3
2
• R : BE;Numberofoccurrences=2
3
• R : BC;Numberofoccurrences=1
4
Weassumethattheminimumutilitythreshold(minutil)issetto800,000forrunningexampleand
theminimumvotingdegree,µ=0.4(NumberofoccurrencesinP/Numberoftotaldatasources)inthe
patternselectionalgorithm. Hence,thepatternsselectedare:
• µ(R )=2/3=0.6>µ(keep)
1
• µ(R )=3/3=1>µ(keep)
2
• µ(R )=2/3=0.6>µ(keep)
3
• µ(R )=1/3=0.3<µ(wipedout)
4
Pattern R is voted by 2 data sources, pattern R is voted by all 3 data sources, pattern R is
1 2 3
votedby2sourcesandpatternR isvotedbyonly1datasourcesoitiswipedoutinpatternselection
4
procedure. Toassigntheweightstopatterns,weuseGood’sweightedmodel,thatis,thenumberof
occurrencesofapatterninPisusedtodefinetheweightofthepattern. Theweightsofpatternsare
assignedas:
• W(R )=2/(2+3+2)=0.29
1
• W(R )=3/(2+3+2)=0.42
2
• W(R )=2/(2+3+2)=0.29
3
Forndifferentdatasources,wehaveP=P ∪P ∪P ∪,... ,∪P andPcontainsR ,R ,R ,... ,
1 2 3 n 1 2 3
R patterns. Hence,theweightofanypatternR canbegivenas:
m i
∑
W(R)=Occurrence(R)/ Occurrence(R) (2)
i i j
wherej=1,2,3,... ,nandOccurrence(R)=NumberofoccurrencesofpatternR inP.
i i
3.2. AllocatingWeightstoDataSources
Here,itisclearlyseenthatweightofdatasourceisdirectlyproportionaltotheweightofpatterns
minedbyit. Theweightofthedatasourcesisassignedas:
• W(DS )=(2×0.29)+(3×0.42)+(2×0.29)=2.42
1
• W(DS )=(2×0.29)+(3×0.42)=1.84
2
• W(DS )=(2×0.29)+(3×0.42)=1.84
3
Sincethevaluesareexceedingbeyondtherange,wenormalizeandreassigntheweightsas:
• W(DS )=2.42/(2.42+1.84+1.84)=0.396
1
• W(DS )=1.84/(2.42+1.84+1.84)=0.302
2
• W(DS )=1.84/(2.42+1.84+1.84)=0.302
3
DatasourceDS hasthehighestweightsinceitvotesmostpatternswithhigh-utilityanddata
1
sourceDS hasthelowestweightsinceitvotesleastpatternswithhigh-utility. Forndifferentdata
2
sources, we have P = P ∪ P ∪ P ∪ ... ∪ P and P contains R , R , R , ... , R patterns. Hence,
1 2 3 n 1 2 3 m
theweightofanydatasourceDS canbegivenas:
i
∑ ∑∑
W(DS)= Occurrence(R )×W(R )/ Occurrence(R )×W(R ) (3)
i x x y y
where,i=1,2,3,... ,n;j=1,2,3,... ,n;R ∈ P;R ∈P.
x i y j
Data2018,3,32 6of16
3.3. SynthesizingtheUtilityofPatterns
Wecansynthesizetheutilitypatternsafterallthedifferentdatasourcesareassignedweights. The
synthesizingprocessofpatternsisdemonstratedbelow:
• PatternR :ABC
1
util(ABC)=[W(DS )×util (ABC)]+[W(DS )×util (ABC)]=[0.396×3,544,830]+
1 1 2 2
(4)
[0.302×3,591,954]=2,488,523
• PatternR :AD
2
util(AD)=[W(DS )×util (AD)]+[W(DS )×util (AD)]+[W(DS )×util (AD)]=
1 1 2 2 3 3
(5)
[0.396×1,728,899]+[0.302×1,745,716]+[0.302×1,749,528]=1,740,208
• PatternR :BE
3
util(BE)=[W(DS )×util (BE)]+[W(DS )×util (BE)]=[0.396×1,464,888]+[0.302×
1 1 3 3
(6)
1,461,862]=1,021,578
Alloftheselectedpatternssatisfytheminimumthresholdofutility,sotheyareforwardedas
itisfornormalizingtheirutility,otherwise,theyarewipedoutagain. Forndifferentdatasources,
wehaveP=P ∪P ∪P ∪... ∪P andPcontainsR ,R ,R ,... ,R patterns. Hence,theutilityof
1 2 3 n 1 2 3 m
anypatternutil(R)canbecalculatedas:
i
∑
util(R)= W(DS)×util(R) (7)
i i i i
3.4. NormalizingtheUtilityofPatterns
Thesynthesizedutilityobtainedafterallocatingtheweightscanbeinthelargerrangedepending
upon the utilities specified for an item in the transaction database. According to Good’s idea,
this synthesized utility can be normalized in the interval 0–1 for our simplicity. To calculate the
normalized utility, the maximum profit generated in that transaction database and the number of
occurrences of the pattern are used. The maximum profit generated by any item(s) after mining
the union of DS , DS and DS , is 17,824,032. Hence, this value is used as Maximum_Profit while
1 2 3
normalizingtheutilityofpatterns. Thenormalizationofsynthesizedutilityisdemonstrated:
• PatternR :ABC
1
Nutil(ABC)=(2,488,523×2)/17,824,032=0.28 (8)
• PatternR :AD
2
Nutil(AD)=(1,740,208×3)/17,824,032=0.293 (9)
• PatternR :BE
3
Nutil(BE)=(1,021,578×2)/17,824,032=0.115 (10)
From the above results, the ranking of patterns is R (nutil = 0.293), R (nutil = 0.28) and R
2 1 3
(nutil=0.115). Forndifferentdatasources,wehaveP=P ∪P ∪P ∪... ∪P andPcontainsR ,R ,
1 2 3 n 1 2
R ,... ,R patterns. HencethenormalizedutilityforanypatternR Canbegivenas:
3 m i
Nutil(R)=[util(R)×Occurrence(R)]/Maximum_Profit (11)
i i i
Data2018,3,32 7of16
4. AlgorithmDesign
Whenwecombineallofthehigh-utilitypatternsfromdifferentdatasources,itcanamassahuge
numberofpatternsoverall. Todealwiththisproblem,wefirstdesignapatternselectionalgorithmfor
selectingonlythosepatternsoccurringmorethanthenumberoftimesspecifiedbytheuser,thatis,
byspecifyingaminimumvotingdegree,µ. Theminimumvotingdegree,µisauser-specifiedvalue
intherange0–1. Forexample,ifwewantonlythosepatternswhoseoccurrenceisinmorethan60%
ofdatasourcesthenµissettobe0.6. Thisalgorithmonlyenhancesoursynthesismodelbywiping
outpatternswhoseoccurrencesisbelowthethresholdµ. Thepatternshavingasmallernumberof
occurrencesareseenasnoiseandconsideredtobeirrelevantinthesetofallpatterns. Theseirrelevant
patternsareremovedbeforeassigningweightstodatasources. Theoutputofthisalgorithmwillbea
setoffilteredpatterns. WedesignapatternselectionalgorithmasAlgorithm1below:
Algorithm1:Pattern_Selection(P):
Input:P-Setof‘N’patternsforwardedbydifferentdatasources;n—Numberofdifferentsources;
µ—Minimumvotingdegree.
Output:ThefilteredsetofpatternsP.
1. fori=1toNdo
a. Occurrence(R)=NumberofoccurrencesofR inP;
i i
b. if(Occurrence(R)/n<µ)
i
i. P=P−{R};
i
2. endfor;
3. returnP;
LetDS ,DS ,DS ,... ,DS bendifferentdatasources,generatingtheuniversalsetofpatterns
1 2 3 n
P=P ∪P ∪P ∪... ∪P wherePisthesetofpatternsforwardedbyDS (i=1,2,3,... ,n).util(R)is
1 2 3 n i i j
theutilityofpatternR inDS.minutilandMaximum_Profitarethethresholdssetbytheuser.Wedesign
j i
thefollowingAlgorithm2forsynthesizingpatternsfromdifferentdatasources:
Algorithm2:Pattern_Synthesis():
Input:PatternsetsP1,P2,P3,... ,Pn;minimumutilitythreshold-minutil;Maximum_Profit.
Output:Synthesizedpatternswiththeirutility.
1. CombineallsetsP1,P2,P3,... ,PnintoPbyassigningPatternIDtoeachdistinguishedpattern.
2. callPattern_Selection(P);
3. for∀R ∈Pdo
i
a. Occurrence(R)=NumberofoccurrencesofR inP;
i i
b. W(R)=Occurrence(R)/∑Occurrence(R ∈P);
i i j
4. fori=1tondo
a. W(DSi)=∑Occurrence(Rx∈Pi)×W(Rx)/∑∑Occurrence(Ry∈Pj)×W(Ry);j=1,2,3,... ,n.
5. for∀R ∈Pdo
i
a. util(R)=∑W(DS)×util(R);
i i i i
b. if(util(R)<minutil)
i
i. P=P−{R};
i
c. else
i. Nutil(R)=[util(R)×Occurrence(R)]/Maximum_Profit;
i i i
6. sortallthepatternsinPbytheirnormalizedutilityi.e.,Nutil(R);
i
7. returnalltherulesrankedbytheirNutil(R);
i
end.
The above pattern synthesis algorithm synthesizes high-utility patterns ranked by their
normalized utility. Step 1 combines all the sets of patterns forwarded by different data sources
andassignsauniquepatternID.Step2callsthealgorithmPattern_Selection(Algorithm1)forremoving
Data2018,3,32 8of16
thepatternsoccurringbelowthethresholdµ. Step3assignstheweightstoallpatterns. Step4assigns
the weight to all data sources. Step 5 calculates the synthesized utility and normalized utility of
selectedpatterns. Steps6and7returnsthesynthesizedpatternswiththeirrankwiseutility.
5. DataDescription
The mining algorithms were used from SPMF Open-Source Data Mining Library [27] for
performing mining through various datasets. We used Microsoft Excel for calculations and data
visualization. AllofthedatasetsusedweretakenfromthesameSPMFlibrary. Thetransactionsinthe
datasetsarealreadyhavingtheinternalutilityandprofitperitem,hencethereisnoneedtoassignany
kindofutilityfactortoanyitem. Weevaluatetheeffectivenessoftheproposedsynthesismodelby
extensivelyexperimentingwiththedatasetswithvariedcharacteristics.
6. ExperimentalEvaluation
ThepatternIDdenotesthenumbergiventoeachitemsetinthetransactiondatabase. Theitemset
showstheitemsappearingtogetherinapattern. Thedeviationmeasurebetweentheproposedmethod
andmono-miningiscalculatedbyfollowingformula:
Deviation=|Nutil MM −Nutil SM| (12)
i i
whereNutil MM=Util(R)intheunionofallthedatabases/Maximum_ProfitofthedatabaseandNutil
i i i
SMisthesynthesizedutilitycalculatedbytheproposedmodel.
6.1. Study1
Kosarak is a very sparse dataset containing 990,000 sequences of click-stream data from
a Hungarian news portal, having 41,270 distinct items. It is partitioned into 5 databases with
198,000transactionseach,representing5differentdatasources. Wefirstperformedmono-miningon
theunionofthese5databasesusingtheD2HUPalgorithm[28]andcalculatedthenormalizedutility
denotedbyNutil MM. Thenweminedthese5databasesseparatelybyusingtheD2HUPalgorithm
i
and then applied our synthesis model to calculate normalized utility denoted by Nutil SM when
i
minutil=800,000,µ=0.4,Maximum_Profit=17,824,032. Theaveragedeviationwasfoundtobe0.001for
twodifferentmethods. Thepatternsminedfromdifferentdatabasesandrankedwithitssynthesized
utilityaretabulatedinTable3.
Table3.ExperimentalresultsforKosarakdataset.
PatternID Itemset NutiliMM NutiliSM Deviation
P1 11,6 1 0.999 0.001
P2 3,11,6 0.488 0.487 0.001
P3 3,6 0.41 0.409 0.001
P4 3,11 0.348 0.348 0.000
P6 1,11,6 0.293 0.292 0.001
P5 148,218,11,6 0.293 0.291 0.002
P7 148,11,6 0.29 0.290 0.000
P8 148,218,11 0.232 0.232 0.000
P9 148,218,6 0.228 0.228 0.000
6.2. Study2
Chainstoreisaverysparsedatasetcontaining1,112,949sequencesofcustomertransactionsfrom
a retail store, obtained and transformed from NU-Mine Bench, having 46,086 distinct items. It is
partitioned into 5 databases with 222,589 transactions each, representing 5 different data sources.
Wefirstperformedmono-miningontheunionofthese5databasesbyD2HUPalgorithm[28]and
calculatedthenormalizedutilitydenotedbyNutil MM. Thenweminedthese5databasesseparately
i
Data2018,3,32 9of16
byusingtheD2HUPalgorithmandthenappliedoursynthesismodeltocalculatenormalizedutility
denotedbyNutil SMwhenminutil=500,000,µ=0.6,Maximum_Profit=82,362,000.Theaveragedeviation
i
wasfoundtobe0.004fortwodifferentmethods. Thepatternsminedfromdifferentdatabasesand
rankedwithitssynthesizedutilityaretabulatedinTable4.
Table4.ExperimentalresultsforChainstoredataset.
PatternID Itemset NutiliMM NutiliSM Deviation
P1 39,171,39,688 0.078 0.077 0.001
P5 39,692,39,690 0.062 0.063 0.001
P4 5166,16,967 0.051 0.052 0.001
P3 21,283,21,308 0.05 0.051 0.001
P6 16,977,16,967 0.05 0.051 0.001
P9 22,900,21,308 0.049 0.049 0.000
P7 39,206,39,182 0.055 0.044 0.011
P8 10,481,16,967 0.042 0.042 0.000
P2 39,143,39,182 0.052 0.029 0.023
6.3. Study3
Retailisasparsedatasetcontaining88,162sequencesofanonymousretailmarketbasketdata
fromananonymousBelgianretailstore,having16,470distinctitems. Itispartitionedinto4databases
with22,040transactionseach,representing4differentdatasources. Wefirstperformedmono-mining
ontheunionofthese4databasesusingtheEFIMalgorithm[20]andcalculatedthenormalizedutility
denoted by Nutil MM. Then we mined these 4 databases separately by using the EFIM algorithm,
i
and then applied our synthesis model to calculate normalized utility denoted by Nutil SM when
i
minutil=20,000,µ=0.75,Maximum_Profit=481,021. Theaveragedeviationwasfoundtobe0.025for
twodifferentmethods. Thepatternsminedfromdifferentdatabasesandrankedwithitssynthesized
utilityaretabulatedinTable5.
Table5.ExperimentalresultsfortheRetaildataset.
PatternID Itemset NutiliMM NutiliSM Deviation
P1 49,40 1 1 0.000
P2 49 0.963 0.964 0.001
P7 40 0.579 0.579 0.000
P8 33 0.523 0.524 0.001
P9 33,49 0.461 0.463 0.002
P3 42,40 0.522 0.422 0.100
P5 42,49 0.516 0.418 0.098
P4 42 0.513 0.416 0.097
P6 42,49,40 0.506 0.409 0.097
P10 33,40 0.387 0.388 0.001
P12 33,49,40 0.372 0.373 0.001
P17 39,49 0.363 0.363 0.000
P14 39 0.353 0.353 0.000
P16 39,40 0.353 0.353 0.000
P20 39,49,40 0.349 0.349 0.000
P19 37,39 0.317 0.327 0.010
P25 37 0.268 0.266 0.002
P27 37,39,40 0.243 0.242 0.001
P26 171,39 0.207 0.208 0.001
P28 37,40 0.209 0.208 0.001
P30 37,39,49 0.186 0.184 0.002
P13 39,42 0.224 0.182 0.042
P11 33,42 0.219 0.177 0.042
P15 39,42,40 0.211 0.171 0.040
P22 39,42,49 0.191 0.155 0.036
P21 33,42,49 0.189 0.153 0.036
P18 33,42,40 0.187 0.152 0.035
P24 39,42,49,40 0.183 0.148 0.035
P23 33,42,49,40 0.169 0.137 0.032
Data2018,3,32 10of16
6.4. Study4
BMSisasparsedatasetcontaining59,601sequencesofclickstreamdatafromane-commerce
having497distinctitems. Itispartitionedinto3databaseswith19,867transactionseach,representing
3differentdatasources. Wefirstperformedmono-miningontheunionofthese3databasesusingthe
EFIMalgorithm[20]andcalculatedthenormalizedutilitydenotedbyNutil MM. Thenweminedthese
i
3databasesseparatelybyusingtheEFIMalgorithm,andthenappliedoursynthesismodeltocalculate
normalizedutilitydenotedbyNutil SMwhenminutil=500,000,µ=0.3,Maximum_Profit=9,449,280.
i
Theaveragedeviationwasfoundtobe0.032forthetwodifferentmethods. Thepatternsminedfrom
differentdatabasesandrankedwithitssynthesizedutilityaretabulatedinTable6.
Table6.ExperimentalresultsforBMSdataset.
PatternID Itemset Nutil MM Nutil SM Deviation
i i
P1 306,315 0.2032 0.1871 0.016
P3 151,168 0.1768 0.1255 0.051
P2 148,168 0.1642 0.1250 0.039
P5 306,310 0.1426 0.1185 0.024
P4 5,168 0.1387 0.1073 0.031
6.5. Study5
Foodmart1isasparsedatasetcontaining4591sequencesofcustomertransactionsfromaretail
store,obtainedandtransformedfromtheSQL-Server2000,having1559distinctitems. Itispartitioned
into3databaseswith1530transactionseach,representing3differentdatasources. Wefirstperformed
mono-mining on the union of these 3 databases using the EFIM algorithm [20] and calculated the
normalizedutilitydenotedbyNutil MM. Thenweminedthese3databasesseparatelybyusingthe
i
EFIM algorithm and then applied our synthesis model to calculate normalized utility denoted by
Nutil SM whenminutil=9000,µ=0.3,Maximum_Profit=30,240. Theaveragedeviationwasfoundto
i
be0.524fortwodifferentmethods. Thepatternsminedfromdifferentdatabasesandrankedwithits
synthesizedutilityaretabulatedinTable7.
Table7.ExperimentalresultsfortheFoodmart1dataset.
PatternID Nutil MM Nutil SM Deviation
i i
P10 0.901 0.530 0.371
P11 0.848 0.504 0.344
P3 0.845 0.448 0.397
P9 0.836 0.413 0.423
P26 1 0.220 0.780
P12 0.94 0.188 0.752
P1 0.572 0.165 0.407
P13 0.726 0.155 0.571
P2 0.685 0.148 0.537
P14 0.783 0.140 0.643
P4 0.578 0.137 0.441
P5 0.582 0.135 0.447
P6 0.483 0.132 0.351
P15 0.644 0.132 0.512
P7 0.667 0.131 0.536
P16 0.667 0.127 0.540
P8 0.657 0.124 0.533
P17 0.58 0.121 0.459