Quantification of unsertainty in mineral prospectivity prediction is an important process to support decision making In mineral exploration.
QuantificationofUncertainty inMineral Prospectivity Prediction
UsingNeuralNetworkEnsembles and Interval Neutrosophic Sets Pawalai
Krai peerapun,Kok Wai Wong, Abstract-Qnantificationof unscrtalnty
in mineral prospee tivitypredictinnisan
importantprncesstnsupportdecisinfi makingInmineralexploration,D e p
oF uncertaintycan identify lcvel of quality in thc prcdiction. This
papcr proposes an approachtopredictd w e
sofhvourabilityforgolddeposits togetherwithquantificationof
uncertaintyintheprediction. Geographic lnfurmatiunSystems(GIS)data
isappliedtothe integratinnofensembleneuralnetworksandintervalneutm-
sophipw kThreedifTewntneuralnetworkarchitectufiswe
uscdinthispaper.Theprcdictionanditsunccrtaintyarc represented int
heformoftruth-membership, indeterminacy- membership.
andfalse-memkrshipvalues,Twonetworks are createdforsash
networkarchitecturntopredictdegreesof favr)urahility for deposit
and nnn depmit, which are represented by truth add false memhership
v.sloes wspectiuely. Uncertainty or indeterminacy-mcmbcrship
valucsam~st i mat dfromboth trnth andfalsemembershipvalues.
Theresultsobtainedusing different neuralnetworkensemhle techniques
are diwussedin thispaper. Uncertainty estimation in mineral
prospectivity prediction is an important task i n order tosupport
decision making in regional-scale mineral exploration. I11this
pnper.we focus on uncertainty of type vagueness in which it refers
to boundaries t ha tcannotbedefinedprecisely.In[I].vagueobjectsare
separatedintovaguepoint,vagueTine,andvagueregion. Dilo et al.[ I ]
defined vague pointasa finite set ofdisjoint sites with
knownlocation. but the existence ofthe sites may be uncertain. This
study involves gridded map layers ina GIs database,
eachgridcellrepresentsnsitewithaknown location.
hutuncertainexiqtenceoffavourability fordeposit.Hence.
thisstudydealswithvaguepoint.Somelocationshave
onehvndredpercentoffavourabilityfordeposits.Some
locationshavezeropercentoffavourabilityformineral deposits.
Suchcells are referred toas non-depositor barren cell?.
Mostlocations havedegrees offavourabilitybetween thesetwoextremes.
Therefnre,eachcellcontains uncertain
informationaboutthedegreeoffavourabilityfordeposits,
degreeoffavourabilityforhamns.anddegreeofindeter-
minableinformationoruncertainty.Inordertostorethese
threetypesofinformationforeachcell,weapplyinterval
htwalaiKraipccmpun iswiththeSchoolofInformationTcchnolngy. Murdoch
University. Australia {emnil:[email protected].~u)
KokWaiWong1%withtheSchoolofInforn~ationTechnology.Murdoch
University.Australia {elnail. [email protected])
ChunCheFungiswiththeCcntrcforEnterpriscCollabm-
lionInInnovativeSystems,MurdochUniversity,AusmIia(cmail:
[email protected].;tul WarickBrowni s w~ththeCentre for
Exploration Targeting. The Vniver- siryof Western Australia,
Australia (email:[email protected]) ChunCheFung, and
WarickBrown neutrosophic sets[2] to keep these information in
theform oftruth-membership, falsemembership,andindeterminacy-
membership values, respectively.
Inrecentyears,neuralnetworkmethodswerefoundto givektler
mineraIprospectivitypredictionresultsthanthe conventional empirical
statistically-based methods 131. There
arevarioustypesofneuralnetworkusedtopredictdegree offavourability
formineraldeposits.Forexample,Brown etal.[ 3]
,[4]appliedbackpropagationneuralnetworkfor
mineralprospectivityprediction.Skabar[5] usedareed- forwardneural
networktoproducemineral potentialmaps. Iyer et al. [6], [7]applied
a general regression neuralnetwork and a polynomialneuralnetwork
topredict the favourability forgolddeposits.Fungctal.[XI
appliedneuralnetwork ensembles tothe
predictionofmineralprospectivity. Hansen and Salarnon [91 suggested
t hatensembles of neu- wl networks gives better resultsandless emr
thana single neuralnetwork. Ensembles of neural networks consist of
two steps: training ofindividual components in the ensembles and
combing the output from the component networks [lo]. This study
aims to apply neural network ensembles to predict the degrees of
favourability for gold deposits and also the degrees
offavwrabilityforbarrens.Thesetwo degreesarethen usedtoestimate the
degree ofuncertaintyinthe prediction
foreachgridcellonamineralprospectivitymap.Each component of neural
network ensembles applied i n this study consists of a pair of
neural networks trained to predict degree ofFavourabi
lityfordepositsanddegreeoffavourability
forbarrens,respectively.Weusethreecomponentsinthe ensemble of
neuralnetworks. These component architecrures
arefeed-forwardbackpmpagationneuralnetwork,general
regressionneuralnetwork,andpolynomialneuralnetwork. These three are
selected mainly because they havesuccessful applicationinthefield.
Amultilayer feed-forward neuralnetwork withbackprop- agation
learning is applied in this study since it is suitable for
alargevarietyofapplications. Ageneralregressionneural network i s
amemory-based supervised feed-forward network
basedonnonlinearregressiontheory.Thisnetworkisnot necessarytodefine
thenumber ofhiddenlayersinadvance
andhasfasttrainingtimecomparingtobackpropagation neuralnetwork[ I
I]. A polynomialneuralnetworkisbased
onGroupMethodofDataHandling(GMDH)[I21 which
identifiesthcnonlinearrelatiunsbctwecninputandoutput
variables.Similartogeneralregressionneuralnetwork,a topology
ofthisnetwork is not predeterminedbut developed throughlearning[TI.
In order to combine the outputs obtained from components
0-7803-9490-9/06/$20.00/2006 IEEE2006 International Joint
Conference on Neural NetworksSheraton Vancouver Wall Centre Hotel,
Vancouver, BC, CanadaJuly 16-21, 20063034Authorized licensed use
limited to: Murdoch University. Downloaded on June 15, 2009 at
03:22 from IEEE Xplore.Restrictions apply.ofensemble
neuralnetworks,wepropose andcompare six aggregation
techniqueswhicharebasedonmajorityvote, averaging, and dynamic
averaging techniques.Our proposed techniques haveapplied the three
membershipvaluesin the aggregation instead of the truth-membership
only as in most conventional approaches. The restofthispaper is
organized as follows. Section I1 presentsinterval neutrosophic
setsusedinthisstudy.Sec- tionIIIexplains
theproposedmodelforthequantification
ofuncertaintyinthepredictionoffavourabilityforgold
depositsusingintervalneutrosophicsetsandensembleof neural
networks.Section IV explains theGIs dataset used
inthispaper.Experimentalmethodologiesandresultsare also presented
inthissection.Conclusions are explainedin section V. 11.INTERVAL
NEUTROSOPHIC SETS Anintervalneutrosophicset(INS)isaninstanceof
neutrosophicset[13]whichisgeneralizedfromthecon-
ceptofaclassicalset,fuzzyset, interval-valuedfuzzyset,
intuitionisticfuzzyset,interval-valued intuitionisticfuzzy
set,paraconsistentset,dialetheistset,paradoxistset,and
tautologicalset[2].Themembership ofanelement tothe interval
neutrosophic setisexpressed bythreevalues:t , i, andf
,whichrepresenttruth-membership,indetenninacy- membership, and
false-membership,respectively. These three memberships are
independent and can be any real sub-unitary subsets. In some
special cases, they can be dependent. In this paper, the
indeterminacy-membershipvalue depends on both truth-membership and
false membership values. The interval neutrosophic set can
represent several kinds ofimperfection
suchasimprecise,incomplete,inconsistent,anduncertain information
[14]. Inthispaper,weexpress imperfection in
theformofuncertaintyoftypevagueness.Thisresearch follows
thedefinitionofan interval neutrosophic set thatis defined in[2].
This definition is described below. LetX beaspace
ofpoints(objects).Aninterval neutro- sophic set inX is where TA is
the truth-membership function, IA is the indeterminacy-membership
function, and FA is the false-membership function. Theoperations
ofinterval neutrosophic setsarealsoap-
pliedinthispaper.Detailsoftheoperations canbefound in[14].
111.UNCERTAINTYESTIMATIONUSING INTERVAL NEUTROSOPHICSETSAND
ENSEMBLENEURAL NETWORKS This paper applies GIs input data to
ensemble neural net- works for the prediction of favourability for
gold deposits and Indeterminacy Falsity BPNN GRNNOutput Falsity
GRNN GiS input data layers Output Falsity PNN Fig. I.Uncertainty
model based on the integration of interval neutrosophic sets and
ensemble neural network utilizes the interval neutrosophic set to
express uncertainties
intheprediction.Fig.1showsourproposedmodel.The input feature
vectors ofthe proposed model represent values from co-registered
cells derived from GIs data layers which are collected and
preprocessed from the Kalgoorlie region of Western Australia.
Thesame input data set is used in every neural network created in
this paper. Inorder topredictdegrees offavourabilityfordeposits,
weapplythreetypesofneuralnetworkarchitecture: feed-
forwardbackpropagation neuralnetwork(BPNN),general regression
neuralnetwork(GRNN),andpolynomial neural neural network (PNN) for
training individual network in the ensembles.
Wecreatetwoneuralnetworksforeachneural networkarchitecture.
Thefirstnetworkisusedtopredict
thedegreeoffavourabilityfordeposits(truth-membership
values)andanothernetworkisusedtopredictthedegree offavourability
for barrens (false-membership values). Both
networkshavethesamearchitecture andareappliedwith
thesameinputfeaturedata.Thedifference betweenthese twonetworks
isthatthesecond networktrained topredict degreesoffavourability for
barrens uses the complement of targetoutputs
usedinthefirstnetworkwhichistrainedto
predictdegreesoffavourabilityfordeposits.Forexample, ifthe target
output used to train thefirst networkis0.1,its complement is 0.9.
The results from these two networks are usedtoanalyze uncertainty
intheprediction. Ifacellhas hightruth-membership
valuethenthiscellshould have low false-membership
valueandviseversa. Otherwise, thiscell contains highuncertainty.
Hence, thedegrees ofuncertainty
inthepredictionorindeterminacy-membership valuescan
becalculatedasthedifferencebetweentruth-membership and
false-membership values. If the difference between truth-
3035Authorized licensed use limited to: Murdoch University.
Downloaded on June 15, 2009 at 03:22 from IEEE Xplore.Restrictions
apply.membershipandfalse-membershipishigh thenthenncer-
taintyislow.Inconmst,ifthedifferencebetweenboth values is Inwthen
the uncertaintyis high. InFig.1, the proposed neural network
ensembles contain t h ~ e componentswhicheachconsistsofa
pairofneural networks.Thefirstpairi sfeed-forwardbackpropagation
neural networks (truth BPNN and falsity BPNN). The second
pairisgeneralregressionneuralnetworks(truthGRNN
andfalsityGRNN).Thethirdpairispolynomialneural networks( nt h
PNNand faIsityPNN3. Each pairofneural networks is trained to
predict degrees of favourability for de- posits (truth-membership
values) and degrees of favourability forbarrens(false-membership
values).Theindeterminacy- membership values are calculated from the
different between
truth-m~mbershipandfzlse-memhrshipvalues.Therefore, we
havethreeintervalneutrosophicsets whichareoutputs
fromthosethreepairsofneuralnetwarks. Wecandefine these outputsas
the following. LetXj bethesetofoutputsfromtheneuralnetrvork. Inour
case,we have threesets ofoutputs,i.e.XI,X2 and &. representitag
outputsets fromBPNN,GRNN andPNN respectively. Eachset Xj contains
the outputs from each pair of the neural networks. The output set
for BPNN is therefore represented as Xr = {xlr,2 1 2 ,.-.,.~ l i ,
--.,xln} where s r fis a cellin the output from the BPNN at Iwation
i. Let AT be an interval neutrosophic set of Xj .Aj can be defined
as where TAjis the truth(deposit) mernkrshipfunction. IAjis
theindeterminacy membership function. andFAJ is the false
(barren)membershipfunction.After!heindividualneural
networkistrainedandthethreeintervalneutto5ophicsets A,are created,
the nextstep istocombinethese threesets.
Insteadofusingonlytruthmembershipvaluestopredict thefavourability
forgolddeposits.thef~llowingsareour
propusedaggregationtechniquesusingtruth-membership,
false-membership, and indeterminacy-membership values, 1)Majority
vote using T&F Foreachinternalneutrosophicset.A,,ifaccIlx
hastruth-membershipvalueTA~(X$greaterthana
thresholdvaluethenthiscelli sclassified as deposit,
otherwiseitisclassifiedasbarren.Inthispaper,we
usethresholdvaluesranging from0.1to 0,9 i n steps of0.1.
Ifacellhasfalse-membershipvalueFA,(x) Iessthana
thresholdvaluethenthiscellisclassified
asdeposit,otherwiseitisclassifiedasbarren.The
resultscalculatedfromthebestthresholdfortruth- membership values
and the results calculated fmm the
bestthresholdforfalse-membershipvaluesarethen
calculatedusingthelogicaloperatorandtoprovide the prediction
results for each cell x i n each output Xj. The degree of
uncefiainty for each cell, is expressed by
theindeterminacy-membership value, IAj (x). Afterthe
threeoutputsate classified, the nextstepis to
combinetheseoutputs.Themajorityvoteisthen applied in order to
aggregate the three outputs. For each cell, iftwoor more
outputsareclassified as deposits then the cell is deposit.
Othewise, the cell is classified
asbarren.Theuncertaintyvalueforeach"deposit"
cellisestimatedfromtheaverageindeterminacy-
membershipvalueforalltheneuralnerworkpairs
intheensemblethatclassifiedtheinputpatternas adepsi t
.Likewise,uncertaintyvaluesfor"barren" celIsarecalculatedas
theaverage ofindeterminacy- membership values fromthe members of
the network pairsthat gave a classification ofbarren. 2)Majoriry
vote usingT > F This technique is more flexible than the first
technique. The threshold valueis not required for the prediction.
For every ccll i n each interval neutrosophic set Aj ,if
thetruth-membershipvalueisgreaterthanthe false- membership
value(TA$(x)> FA~(X))thenthecell
isclassifiedasdeposit.Otherwiseitisclassifiedas
barren.Thedegreeofuncertaintyforeachcellis
representedbytheindeterminacy-membership value,
IA,(x).Similartothefirsttechnique,themajority
voteisthenusedtocombinethethreeoutputsand
theindeteminacy-memkrshipvaluesarecalculated according to the
predicted cell type for each individual output.
31AveragingusingT&F Inthistechnique,
thethreeintervalneutrtlsophicsets AJ , j= 1, 2, 3 areaveraged.LetO
beanaveraged output mp .O = {or, 02, ..., on)whereq is a cell~f
theaveragedoutput mapat locationi. LetAvgbean
intervalneutrosophicsetoftheaveragedoutputmap 0. Avgcanbecalculated
asfollow Ifa cell has averaged truth-memhrship value TA,,(o)
greater than a threshold value then this cell is classified as
deposit, otherwise the cell is classified as barren. If a cell has
averaped false-membership value FA~ J O) less thana threshold value
then this cell is classified as de- posit, otherwise this cell is
classified as barsen. Similar to thefirst technique, the
logicaloperator andis used
tocalculatethepredictionfromtheresultsobtained from the best
threshold for buthtruth-membership and false-membership values.The
degree of unceflaintyis expmswd bythe
averagedindeterminacy-memkrship value I A ~ ~ (0). 4)Averaging
usingT > F In thistechnique.thethreeinterval neutrosophicsets
are also averagedand the results arestored in Avg.if the averaged
truth-membership value is greater than the 3036Authorized licensed
use limited to: Murdoch University. Downloaded on June 15, 2009 at
03:22 from IEEE Xplore.Restrictions
apply.averagedfalse-~nernbershipvalue.T.;-T;l,?,(o):r F.;-T;l,,,(o)
thenthe cellis clnssifiedas deposit. Otherwise the cell
isclassifiedasbarr.en.Thedegree ofiincertnintyfor eac I1 cellis
repr.esented by the averagedi~~rletesminacy-
iilerribersllipvalueT.,A,,,(O). 5 )Dynamic nver.ngingusing'I'k 1.'
Illsteadofusingequalweightaveraginp.tliistecli-
niqiieuscsdynan~icweightaveragingi nwhichthe
weightistheco~riple~nentof theuncertaintyvalueor
indeterminacy-~nernbership value for eaclicell.Irnccr-
taintyisintegratedintotruth-rnernbershipandfalse-
inernbershipvaluestosupporqtheco~lfidericeofthe prediction.LctY he
a dy~a mi c averagedoutpi~tInnp. Y= {gL?U2,.,,,
gIL)where3~isacellofdynamic averagedoutpi~tatlocntio~iE.
LctDheaninterval neutrosophicset of the dyrlari~icaveragedoutpi~tY.
II callbe definedas follow u~here I f occllhas
truth-mcmhcrshipvalue 'I?>( 9) grcalcr than 3 ~I~i-csl~wld~ a l
u c I ~ C I I hiscvllis~Iassificdasdcpusir, ottler~lisethecelli
xcli~ssifiet-las hiil.en. On(he olher hand.i f
acellhasr;~l\e-rnen~bershipvalueFD( y)Irsx
thanathresholdvaluethenthir;celli qclassifiedax
depocit,otherwisethecellisclahsifiedasharretl.The
resultsobtainedfrornthebestthresholdtorbothtruth-
membershipandfalse-me~nhershl valuecarethe11
combinedusliigtliclogicalopcratol.irnrltoprovidc
lhcpredictionrcsults.Thudcgrccofuncertaintyis cx- prcsscdbythe i i
i dct ~mi nacy- n~anba. shi pvalueID(y) whichi
scaluulatcdasthedii'i'crcntbct~vccn truth-
incn~bcrshipilndL~lsc-mcmbcrshipl,alues.
6)nynarr~icaveragingusingT> F
Inthistechnique,anintervalneutrosnphicxetI3is
createdusingthesameprevioustechnique.Inorder
topredictthefavourabilityfordepocits.ifthettuth- membership valueis
greater thanthe false-membership ualucI
>)(?I)>&A(!!)thcnthecellisclassifiedaa
duposit.Othc~.wiscthcccllisulassificdas barren. Thc
dcg~.ucol'unccrtaiiiryfureachccllisrcprcscntcdby
thcindc~crminacq.-ii~c~l~bc~-shipvalucIn (y).A.GIS rlrrrusat
Thedatasetusedintliisstudywasobtainedfroina11 approxiinately100 x
100 k111 arcaoftheArcllaen~iYilgarn Block, ncnr Kalgoorlie.
WcstcniAustralia. This data set W C ~ Cpreprocessecland
compiledinto GISlayers fr.oi11 avarietyof soutrcssuch as geology.
geochernistsy, andgeophysics.Lt'r: usedtenlayersinraster-format to
create input feature vecto~.s forwrnod
el.Theselayersreprwentdifferent~ ~ r i a b l e
ssucliasfavourabilityofhostrnckc,distancet o thenearest
regional-scalefault,anddistaricetothenearestirlagnetic
noomnly.Enclilayer- is dividedillto a gsiclofsqilnrc cells of 100
111 side.IIcncc,the]nap arcacontnios1.254.00Q cells.
Eachccllstoresasingleattributevaluewhichisscaledto therangc[0,
I].Forexarnple.a ccllinalayer- representing the distarice to the
nearestfaultcontaiosavalueofdistarice scaledt otheraLlgc[O,
11.Eachsinglegridcellisalso
classifiedintodepositor'barrencell.Thecellscontaining greatel-
than1.000kgtotalcontainedgoldarc,labeledas
deposits.Allothercellsatcclassifiedasnon-depositsor
barrencells.Inthispnpcr.wcl i st : 268cellswhichatc
separatedinto120 depositcellsand148 barrencells.These cellsarc
dividedinto tsainitigandtestdntasets.L k iisc 85 deposit cells
and102 barrencells fortsninitig data.Fur testing data,w~usc: 35
depositcells and16 barrencells.
Intliispnpcr.twopnirsofneuralnetworkstrainedusing
feed-forwal-dbackpropagatio~~neural~ieiwork andpenenl
regrecsionneuraltietworkarecreatedusingMatlah..4pair ut
polynomialncuralnetworksI StraincdusingPKN onlinc-
soft\vnrcdcvclupcdby Tctkoctal[15]. Eachpairofncurrtl
networksisrrnincdtopredictdugrccsorhvoui-;rbilityfor
depo\i(sariddegreesoffavou~abilily forbarrenswllich are
truth-tiie~nhershipT., (.c)andfalw-tne~rthershipF d , (;c),
reqpectively.Thew twovalue3 a1.rthenu5edtncalculatethe indetrrmi
nacy-mt.mbr3rchi1,ibrclip vnluecI, , , (.I:).Thethreeoutputs
obtained from thcsct111.c~iictivork aruliitccturcs arc comhincd
usingllicproposedcnsc~nblctccliniqucs.Allrcsultsshown
inthispaperarccaluulatcdI'romllictcsrdataset.
TableI2ndTahle11showthepercentageoftotalcnrtect
cell5obtainedfromindividualtieurn1networknrchitectures using a
range otthresholdvaluec to the truth-membershi p and to
thufalsc-mcmbcrshipvrtlucs.rcspcutivcly. Thc hcstthrcsli-
uldstorhctruth-mcmhcrshipforl3PNN.GKNS. andPKN mc0.5. 0.b.i~nd0.5.
rcspcctivcly. 'l'hcbcstthresholdstothc rillst-m~i11b~i.shipTor
BPNN. CRNN. i ~ndPNNa1.c0.4. 0.4, and0.5. rer;pectively. Table111
shoivs thepel-centage of total col-recicellsobtained~ I ~ I I I
thecompari\onbet \veel1iruih- membrr~hi pand
falce-ttie~nbrrshipvalues T,,, (z)> F,,;( , r ) ,and obtained
usingthelogicaloperator rrrrdtotheprediction
rcsultsusingtlichcstthrcaholdfortruth-mcmbcrshipand
tlichcstthresholdfort al rc-~t i ci i l crshi valucs.TableIV
showstllcpcrucnragcofloraluurrcctcellsublaincdfro111
ctlunlwcightavcriigingandd!niimicwvighriivvritgingusing
arangeofthrcsholdvalucslottlc11xth-nicnlbcrship \ : ~ I I U C S(T
:-.thresholdval i~es)andto the false-~nernbershipvalues ( F<
thresholdvalues). 'lablcVshuwsthvclassification accuracy for the
testdnta setusirigour. proposedcnse~tibletechniquesincludingthe
accu racyobtainedf1.oi11 theexistirigtechniquesthatapply only
truth-member-sl~ipvalues and the accuracyobtainedby applyingonly
false-~nernbershipvalues.The comparisonof
accuracyamongthesetechniquesshowsthattheaccuracy 3037Authorized
licensed use limited to: Murdoch University. Downloaded on June 15,
2009 at 03:22 from IEEE Xplore.Restrictions
apply.ohlailledTl.nrnnurp~,nposedtech~liques i~sirig holhtl.iltll-
rnemhet.shipandfalse-mernhersliipvaluesissinlilnrtothe
oucuriicyublaincdfrointhccxistingtcuhniqucsusingunly
truth-mcmburshipvalucsandalsusimilarlo~ h c i i ccul ~i l ~~
obtainedfr.0111 thetecli~iiques~isirigo ~l l y false-111e111bership
values.Indynamicweightaveragingtechnique,theiinccr-
tnilityorindetzrminacy-11ie1111)erqhipvaluerareintegrated
illtoIlicrrurh-mcmbcrsliipandL'i~lsc-mcmbcrship valucslu suppol ~t
heconfidenceoft heprediction.Thi sproposed
techniquep~.nvidesaxlightlybetteraccuracythanthenther
cnscmblctcchniqucsshowninthispnper.l:u~thcrmorc. iill
ourproposecltechniquescallrepresent~incertairlty int he
predictionfor each celllocation. Tablt:VIshowssampleoutpi~tsfro111
e n~e mbl e ofncu-
lal11etnn1-ksusingdyrialnicweight,ave~.ngirigbyconsid-
eringthecornparisonbetweentr.utli-membershipandfalse- n~ci nbashi
pvalucs(Y'U(g)>k h( g) ) . Vuantificationof uncei-hin ~ y
cansuppor!thudcci si unmaking.Forex;jmplc, t
hethirdrow~ftliihtablecontaint heuncertaintyvalue 0.2949i
nwhichthedecision~nakercallacceptthisresult
withinnrecorifidence.Sometirrles,~~ncei-tairltyfor3cellis
high.]:orcxomplc.rhcrourthrowandrhc scvcnth row ofthis table
containucryhighuncertaintyvalueswhicharc 0.8475 and0.97 16,
respectively.Thet r n t l ~ - ~ ~ ~ e ~ ~ i l e s s l ~ i
pandfalse- n~cmbzrshipToreachuT thesecellsareveryclo\eingether.
Tltecellatthefnurlhrnwispredictedtn1,e 3 depnsitwhich 1s
correct.The cellat theseventh rowisalso predictedtobe
;Idcpositbutilisinuorrccr.Inlliis casc, thedccision~n~i
kcrcanrcmakcdccisionfurthccellsthalcontainhighdcgrcc of
uncei~ainly. Inth i hpaper,intervalrle~ltrnsophic bet+areintegrated
i nkcnscmbluoT ncul.nlnctworkstoplrdicrdcprccsof
favnulakilityfordepn+it>andhanenh. Theyarealsousedto
quantifyuncc~tointyintheprediction.Threepairsul" ncuriil
networksarctrainediisirigt hr wdiffer.entneuralnctwcrrk archi
tttcturehi t ) nrdertoprovidet hl wintervalneutrnmphic scr s
whicharc then combincd using our propuscd aggregation
techniques.Thethreeneuralnetworkaschitecturesusedin this
paperarefeed-forwardhackl,~.npagatior~1le~1ra1rietwo~.!i,
genuriilrcgrcssionncuralnctwork.andpulynomiiilncuriil
Tlu.c.;tloldKPNSGKNSIPNS valhc( k CO~TCI T kC O ~ T C I ( kC O ~ Y
C I0. I5h. 7950.7958.02. 0.259.2662.4659.26 0. 371.6072.8465.43
V,475, 3181,4867.41) 0 . 5 72.84$0.2569. I4 0. b70..3776.54b4.10
U,764.204 . 4 6?3b 4,8.%.O'L W.2V59.26 U,939,3843. 2 150.62
tlelwork.Theerperimelltalrewltrshow[hatourproposed .- erlcerrthle
techniquespm\;idesilnilnraccuracytootherexist-
in:,et~sernbletechniquesappliedinthispaper:Resultsfrom
thccspcrimcntshavcnotidcntificdanyapproachwhichis --
oblctuprovidcasigniliciintiinprovcmcntvvcrtheothcrs.
Ilowcvcr.thcclynaiuiciivcrapiilgappruilchh;js2sligh~lq.
better-perforlnance.The keyc~nt r i but i v~i i n t hi sstudyis
thatnllt he proposedtecliriiquesarc capable of representing
uncertaintyint hepredictionof favourabilityfor enclicell
locaticln.While t hi s pnpw focuses only on t he uncertaintyi nt he
prediction outpi~t.researchis cuntinued on t he assehslnznt of
uncertaintyintheCISitlpi~tdata pr-iot-to npplyitigrot he
prcdicriui~s)stcm. 3038Authorized licensed use limited to: Murdoch
University. Downloaded on June 15, 2009 at 03:22 from IEEE
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