Mining In e es ing Regions using
an E olu iona y Algo i hm
J.L. Al a ez
D.I.E.S.I.A.
Uni e sidad de Huel a
Huel a, Spain
[email p o ec ed]
J. Ma a
D.I.E.S.I.A.
Uni e sidad de Fiuel a
Huel a, Spain
[email p o ec ed]
Uni e sidad de Se illa
Se illa, Spain
[email p o ec ed]
ABSTRACT
In his pape , we o e a new me hod o induce in e es -
ing knowledge om he ele an se s o da a in da abases
o supe ised lea ning. Thus, in his wo k, ELLIPSES is
p esen ed as a new me hod o ien ed o disco e knowledge
acco ding o he expe 's needs, by he de ec ion o he mos
signi ican egions. The me hod essence is ound in an e olu-
iona y algo i hm ha inds hese egions one a e ano he .
The
expe decides which egions a e signi ican and de e -
mines he s op c i e ion. The ex ac ed knowledge is o e ed
h ough wo ypes o ules: Quan i a i e and Quali a i e.
The
ool also o e s a isualiza ion o each ule by pa allel
coo dina e sys ems. The ELLIPSES esul s a e compa ed
wi h C4.5 on UCI Reposi o y da ase s.
Keywo ds
Da a Mining~ Supe ised Lea ning, E olu iona y Algo i h a
1. INTRODUCTION
Nowadays, gene ally, he Knowledge Disco e y in Da a-
bases (KDD) and, pa icula ly, Da a Mining (DM) ha e
spu ed a emendous in e es in he esea che s commu-
ni y [1]. News algo i hms and ools ha e been de eloped o
Da a Analysis (DA). Classi ica ion is an use ul echnique o
disco e ing in e es ing ules in da abases.
Classi ica ion sys ems a e supe ised lea ning me hods
ha analyze a da abase o aining se o build a classi ica-
ion model. The aining se con ains a ea u e collec ion,
o objec a ibu es whose class labels a e known. The clas-
si ica ion model is a se o ules o each class based on he
da a cha ac e is ics. Such ules axe used o classi y u u e
objec s acco ding o he alue o hei a ibu es.
These
me hods a e e y use ul and ea u es ha e been jus-
i ed wi h ools ha ha e shown excellen esul s. Bu hese
echniques ha e some p oblems: hey do no allow expe 's
in e en ion o lea ning p ocess. So, classi ica ion sys ems
Pe mission o make digi al o ha d copies o all o pa o his wo k o
pe sonal o class oom use is g an ed wi hou ee p o ided ha copies a e
no
made o dis ibu ed o p o i o comme cial ad an age and ha copies
bea his no ice and he ull ci a ion on he i s page. To copy o he wise, o
epublish, o pos on se e s o o edis ibu e o lisL% equi e.~ p io speci ic
pe mission and/o a ee.
SAC '2002 Mad id,
Spain
Copy igh 2002 ACM 1-58113-445-2/02/03 ...$5.00.
no mally gene a e a big numbe o ules whose in e p e a-
ions a e di icul . In hese cases, he esul s a e useless
o an human-expe . Thus, i is necessa y o include o he
echniques because he DA sys em main ea u e is o o e
an easy in e p e a ion o induced knowledge.
This pape p esen s ELLIPSES, a ool ha pe mi s o in-
duce a se o classi ica ion ules in nume ical a ibu e space
{9][2]. These ules de e mine he mos signi ican egions o
he sea ch space, hey a e a easy in e p e a ion and he ex-
pe can also con ol he lea ning p ocess, es ablishing when
a egion is in e es ing and he s op c i e ion.
Regions sea ching p ocess is made by an e olu iona y al-
go i hm whose esul in e p e a ion is gi en by ELLIPSES
h ough wo ule models: quan i a i e and quali a i e. I
also o e s a iew o hem using pa allel coo dina e sys ems
so he ela ionship among a ibu es is shown by an image
o each ule.
The es o he pape is o ganized as ollow. The ma he-
ma ical p elimina ies a e p esen ed in sec ion 2. Then, sec-
ion 3 desc ibes ELLIPSES algo i hm. And, in sec ion 4 is
shown he pe o mance o ou ool. This sec ion o e s he
expe imen al esul s on I is da ase and a compa ison wi h
C4.5 [13] on UCI Reposi o y da ase s [12]. The objec i e o
his compa ison is o o e a nexus be ween he classi ica ion
sys ems and ou ool, since ou ool is no eally a classi ica-
ion sys em. Finally, sec ion 5 o e s he conclusions abou
his me hod.
2.
PRELIMINARIES
Ou me hod uses conical egions o ind he mos signi i-
can ules. These egions con ain he ea u es o each class.
This sec ion o e s he basic de ini ions o he models o ules
used in ou ool.
De ini ion 1. Le be an hype elllpse he na u al ex en-
sion o an ellipse in a d-dimensional space R d.
De i ~i ion 2. Le be an hype ellipsoide he olume ha
is inside o an h~pe ellipse.
An hype ellipse ( he w appe ) is equal o an ellipses o
ci cum e ence in a wo-dimensional space R 2. An hype -
eUipsoide ( he w apped olume) is equal o an ellipsoid o
ci cle in a 2
wo-dimensional space R . Figu e 1 o e s a g aph-
ical ep esen a ion o hese concep s. Figu e la) ep esen s
an ellipse o cen e (cl, c2), g ea e axis ~1 and smalle axis
~2 o wo a ibu es Zl and z2 ( wo-dimensional space R 2)
498
I
,}
•
I
][j
Figu e 1: G aphical ep esen a ion o an ellipse.
and igu e lb) shows an hype ellipse o h ee a ibu es z ,
xa and ~a ( h ee-dimensional space Rs).
(~-ci) ~ (~-c2) 2
a~ + a] =1 (1)
(z~-Cl) 2 (~2-c2)2 <1 (2)
al + a~ -
(Z1 -- Cl) 7" (Z~ -- C2) "j (Zd -- P--d) 2 ¢: 1 (3)
al + a~ + " + u~ -
The
equa ion o he ellipse in R 2 is shown in 1. The equa-
ion o an ellipsoide is shown in 2. This equa ion is ob ained
changing = by < in he equa ion o he associa ed ellipses.
Gene alizing, in R a, he equa ion o an hype ellipsoide is
shown iu 3.
I! ~(c~, al) and ... ~d ~(~d, ad) ~ C~ (4)
h(~,a,) = {
La ge i ai > 40%A~
MLa ge i 25%A~ < al < 40%A=
Medium i 15%A= < al _< 25%A~
MSho i 5%A= < ~i _< 15%A~
Sho i al <_ 5~oA~
(5)
I
xl(el)
wid h E1 and ... and xd(Cd) wid h E~ =~ C~ (6)
The models o he ules (quan i a i e and quali a i e)
used in ou ool axe based on 1, 2 and 3. Thus, he quan-
i a i e model is ob ained di ec ly by he equa ion o he
ellipse. This model is shown in 4 and i o e s he cen al c¢
alue and he ex en (wid h) ai o each a ibu e, and he
associa ed class Ci. The quali a i e model uses i e labels
o speci y he ex en . Fo each a ibu e z:, a Ej label is
gene a ed by h(zl, ai) unc ion, acco ding o 5, whe e A~ is
~iM -- xlm, ~iM is he maximum a d xim he minimum o
zi a ibu e. The quali a i e model is shown in 6. The in-
e p e a ion o hese models o ule is e y in ui i e because
he ule does no di e om he ypical classi ica ion ules.
Thus, le be : (Yl, Y2, ..., yn), i yl E [z~ - ai, zl +al]Vi hen
he i em ~ is associa ed wi h he class Ci, acco ding o 4.
In he quali a i e model, he label es ablishes he di e ence
be ween yl and xl.
The me hod used o ob ain he class Ci o an hype ellip-
soide will be p esen ed in he nex sec ions, bu his sec ion
o e s he basic idea. Le be : (xl, x2, ..., Zd, Ci) i em, i i
sa is ies he equa ion 3 hen he i em is wi hin he olume
o he hype ellipsoide. Thus, he majo i y class wi hin he
hype ellipses is he associa ed class o i .
ELLIPSES Algo i hm
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
1,5.
16.
17.
END.
T +-- Read T aining se
Repea
i e ~-- i e
+ 1
Pi ~- Inicialice popula ion on T
Repea
E alua e P~ on T
Selec he bes in Pl o P~+I
Selec 10~ in Pi o Pi+l
C osso e Pi indi iduals o Pi+l
Mu a e P~+x
P~+I is P~
Un il numbe gene a ions
+-- Selec he bes o Pi
i alpha( )>ALPHA THEN add(R, )
Un il (i e =ITER o be a(R)>BETA)
Show R ules
Visualiza ion R by Pa allel Coo dina es
Figu e 2: ELLIPSES Algo i hm
3. ELLIPSES ALGORITHM
The main objec i e o ou ool is o induce he sea ch
space egions wi h a g ea e numbe o he i ems belonging
o he same class and o pe mi he human-expe in e ac-
ion in o de o es ablish some c i e ia o he sea ch p ocess.
The inal esul shows a educed and easily in e p e able se
o ules. ELLIPSES is a DA ool based on E olu iona y
Algo i hm (EA) [5][6][11]. EAs axe a heu is ic sea ch ech-
nique ha has demons a ed o be obus o a a ie y o
complex sea ch space [4][14 ].
The echnique main ains a popula ion o indi iduals whe e
each indi idual encodes a easible solu ion o he p oblem.
I e a i ely, a new popula ion is gene a ed by eplacing he
p e ious popula ion, acco ding o Da win's su i al p in-
ciple. So, each indi idual is e alua ed o gi e i s ela i e
me i ( i ness) as a solu ion. The new popula ions esul
om selec ion, c osso e and mu a ion o p e ious popula-
ions. The e olu iona y p ocess is i e a ed by a p ede ined
numbe o gene a ions. The bes indi idual o he e olu-
iona y p ocess is he solu ion o he algo i hm
The EA has been used wi h excellen esul s [3][8][10]. In
ou me hod, a egion is a conical su ace. An EA is used
o ob ain he bes egions. Figu e 2 shows he ELLIPSES
algo i hm.
I e a i ely, he EA inds he bes hype ellipse based
on he numbe o posi i e and nega i e i ems in he hy-
pe ellipsoide. Le be alpha( ) he pe cen age o he same
class i ems in , i alpha( ) is g ea e han he p ede med
human-expe pe cen age ALPHA, hen egion is consid-
e ed. This p ocess is epea ed un il eaching a p ede ined
human-expe numbe o ules o p ede ined human-expe
pe cen age BETA. Finally, he ules a e shown acco ding
o 4 and 6 (quan i a i e and quali a i e models), and hey
a e shown by pa allel coo dina e sys ems.
3.1 Da a s uc u e o he indi iduals
An indi idual (a easible solu ion) is a se I
={Cl,...,Cd,
al,...,a~} whe e d is he numbe o a ibu es and ci,ai E
axe he cen e and ex en o he zl a ibu e and hey
ep esen he equa ion o an hype ellipsoide acco ding o 3.
499
Figu e 3: Rep esen a ion o an indi idual.
Figu e 3 shows a g aphical ep esen a ion o he indi iduals.
In p ac ice, an indi idual ep esen s a sea ch space egion.
Each egion will be associa ed o a class ha will be deduced
by he majo i y class o he da a i ems in he hype ellipsoide.
3.2 Ini ial and nex popula ion
The p ocess o gene a e he ini ial popula ion consis s in
selec ing, in a andom way, ea _.h cen e ci om he a ibu es
ange xl ([xi,,, ziM]) and each ex en ai be ween 5% and
30%
o he a ibu es ange xl.
The e olu iona y p ocess includes eli is : he bes indi id-
ual o e e y gene a ion is eplica ed o he nex one. Indi-
iduals a e ob ained h ough he copies o he p e ious pop-
ula ion. These indi iduals a e andomly and p opo ionally
selec ed o hei ela i e me i as a solu ion ( i ness). The
popula ion emaining is o med h ough c osso e s. A e -
wa ds, mu a ion is applied depending on a p obabili y.
3.3 Fi ness unc ion
The i ness (o me i as a solu ion) o an indi idual is
ob ained by aining se i em analysis. An i em can be in
o ou o he hype ellipse. The ou i ems a e igno ed. The
di e en classes o he i ems in he hype ellipse a e coun ed
and he associa ed class o he indi idual is he majo i y
class. Thus, he i ems wi h he same class axe posi i e cases
and he i ems wi h di e en classes axe nega i e cases.
Fu he mo e, nex i e a ion mus di ec he e olu iona y
p ocess o o he egions. Thus, he posi i e cases co e ed by
disco e ed ules axe conside ed co e ed cases, Finally, ou
me hod needs o ob ain he g ea es egion. Thus, he am-
pli ude o he hype ellipse is he hype ellipse olume di ide
by sea ch spaces olume.
g)
= Pos(~) - iVeg(~) - Co, e (~) * FC + A,.pl(~)
(7)
Ou algo i hm maximizes he i ness unc ion o each
indi idual i. The i ness unc ion is gi en in 7, whe e
Pos(i)
and Neg(i) a e
he posi i e and nega i e cases in he hype -
elipsoide ha ep esen he indi idual i,
Co e (i) axe
he
co e ed cases by p e ious hype eUipses,
FC
is he co e u e
ac o and
Acnpl(i)
is he hype ellipse ampli ude. Co e u e
ac o
(FC)
is a alue in he in e al [0..1], and i o e s he
possibili y o elaxing he co e ed cases, so, i
FC
is closed
o 1, hen he co e ed cases a e conside ed nega i e cases,
and i
FC
is closed o 0, hen he co e ed cases a e igno ed.
3.4 Gene ic
ope a o s
The e a e ee gene ic ope a o s: selec ion, c osso e and
mu a ion. To o m a new popula ion ( he nex gene a ion),
he indi iduals a e selec ed acco ding o hei i ness by he
' selec ion ope a o . Many selec ion p ocedu es a e cu en ly
in use, ou algo i hm uses oule e wheel p ocedu e, whe e
indi iduals a e selec ed wi h a p opo ional p obabili y o
hei ela i e i ness. This ensu es ha an indi idual is cho-
sen in a expec ed numbe o imes app oxima ely p opo -
ional o i s ela i e pe o mance in he popula ion. Thus,
I¢,1 ..-I ' Icdl ' I" 1
' "/
Ell lmlmw 4
Figu e 4: The middle poin c osso e ope a o .
.-. N
Figu e 5: The uni o m c osso e ope a o .
high- i ness (good) indi iduals s and a be e chance o se-
lec ing, while low- i ness indi iduals a e mo e likely o dis-
appea .
Selec ion canno in oduce any new indi iduals in o he
popula ion. These indi iduals a e gene a ed h ough c oss-
o e and mu a ion ope a o s. C osso e ope a o is pe -
o med by selec ing wo indi iduals called pa en s, and gen-
e a ing new indi iduals called o sp ing. In ou algo i hm,
he c osso e ope a o has wo componen s: he middle poin
c osso e and he uni o m c osso e . They a e pe o med
wi h a p obabili y p ..... ha chooses be ween he middle
poin c osso e mad ~.he uni o m c osso e . The middle poin
c osso e andomly spli s he indi iduals in wo pa s. Then
he agmen s a e exchanged gene a ing wo new indi idu-
als. Figu e 4 g aphically shows his p ocess. The uni o m
c osso e decides , independen ly o each coe icien o an
indi idual, whe he i con ibu e o no o he new indi id-
ual. An example o his p ocedu e is shown in igu e 5.
ii
= ~j 4-
Quan * Pe Mu * ii
(8)
Finally, he mu a ion ope a o is in oduced o p e en
p ema u e con e gence o local op imum by andomly sam-
pling new poin s in he sea ch space. Th ee a ian s a e
implemen ed: cen e mu a ion, ampli ude mu a ion and ex-
eme mu a ion. Mu a ion is pe o med wi h p obabili y
p,~ on an indi idual. When an indi idual mus be mu-
a ed, a p obabili y chooses be ween he di e en ope a o s.
The cen e and ampli ude mu a ion ope a o s al e he cen-
e
(cl, ..., Cd)
and he ex en (al,...,
ad)
o he hype eUipse,
espec i ely, acco ding o 8, whe e ~j is he ac o o al e ,
Q~an and
Pe Mu
ake hei alues om [0..1],
Qua L~
is
he andom quan i y ha ii is al e ed and
Pe Mu
is he
pe cen age o mu a ion ha de e mines how he mu a ion
in luence on ii. The ex eme mu a ion ope a o al e s bo h
cen e (ci) and ex en (ai) o an a ibu e (zl). Thus, he
mu a ion le he middle alue o
XiM -- zi,,
o cl and le
=~M-=~ o al. The objec i e o his ope a o is o co e
z
he a ibu e.
3.5 Pa allel coo dina e
sys ems
Al hough ou ool o e s wo models o ules and he qual-
i a i e model is easily in e p e ed, some imes i is necessa y
o p o ide he in o ma ion using a~ao he philosophy. Thus,
a isualiza ion o he ela ionships among he a ibu es o -
e s a good suppo o he expe . The isualiza ion ech-
nique used in ou algo i hm is shown in his sec ion. This
500
x~ x2 x~ x,, x~ x2 x3 x,,
a)
b)
Figu e 6: Pa allel Coo dina e Sys ems.
echnique o e s he ela ionships among a ibu es by pa -
allel coo dina es [7].
A pa allel coo dina e sys em is composed by a se o pa al-
lel axes sepa a ed by a ixed dis ance. Each axis co esponds
wi h an a ibu e and hey a e escala ed on he ange o he
a ibu e. Thus, d axes a e necessa y o ep esen d a -
ibu es. In his sys em, a line ep esen s each da a i em.
This line in e sec s wi h each axis on he alue o he i em
o ha a ibu e. Figu e 6a) shows he adi ional pa allel
coo dina e sys em.
In ou me hod, each egion is ep esen ed on a pa allel
coo dina e sys em. Bu , all da a i ems in a egion axe no
ep esen ed on
pa allel
coo dina e sys em. Thus, only he
minimal alue and he maximal alue, o each a ibu e, a e
ep esen ed on each axis and hese alues a e joined by illed
polygonal. Figu e 6b) o e s an example o his me hod. The
in e nal lines a e elimina ed. The objec i e o his a ian
is o o e a clea e and compac ision o he ela ionships
be ween he a ibu es.
4.
RESULTS
In o de o e alua e he pe o mance o ou ool his sec-
ion o e s he esul s on UCI Reposi o y da ase s [12]. Thus,
i shows he ob ained ules and hei isualiza ion on pa allel
coo dina e sys ems on he adicinal I is da ase in sec ion
4.1. Fu he mo e, sec ion 4.2 o e s a compa ison be ween
ELLISPES and C4.5.
4.1 I is
da ase
To illus a e he esul s induced by ELLIPSES, his sec-
ion o e s he esul s ha has been disco e ed on I is da ase .
x/p~(o.3, 0.67) ~ Se .(5o/o/o)(.~%)
I
~m (2.5, 0.73) =~ Vi .(45/l/O)(30%) (9)
I1 p O.9, 0.94) ~ Ve .(4e/3/o)Ca1%)
I. pw(0.3)
~gd h
MLARGE =#...% .(50/0/0)
I.
p,,,(~..5) ,,,~d h MZ, AeGE ~ Vi,-.(45/1/0) 00)
I
p/(3.9)
wid h MEDIUM ::~ Ve .(46/3/O)
The quan i a i e model o he ules is shown in 9. The
in e p e a ion is e y in ui i e al hough his is he quan i-
a i e model. So, o example, he i s ule shows ha i
he
pw (pe al wid h) a ibu e is ound o 0.3 wi h am ex-
en o 4- 0.67 hen he ob ained class is I is-Se osa. The
quali a i e model is shown in 9. This model uses a label o
ep esen he ampli ude. This label o e s quali a i e in o -
ma ion o he ampli ude o he ule on an a ibu e espec
o he ange o he a ibu e, acco ding o 5. The ules show
he numbe o posi i e, nega i e and co e ed cases and he
pe cen age o posi i e cases.
m
el Bw pl pw
Se osa
gl mw pl pw
mL sw pl
pw
V'n~dca V~colo
Figu e 7: I is Da nse Visualiza ion.
The isualiza ion o his ules by pa allel coo dina e sys-
ems is shown in igu e 7. This ep esen a ion o e s a g aph-
ical desc ip ion o he p e ious ules. Fo example, i shows
he ollowing: i pw akes sho alues he class is I is-se osa,
i pw akes high alues hen he class is I is-Vi ginica and,
in o he case, i pl akes middle alues hen he class is I is-
Ve sicolo . This isualiza ion o e s a e y in ui i e and easy
in e p e a ion o he ules.
4.2
ELLIPSES s
C4.5: A
compa ison
This sec ion o e s a compa ison o he esul s o EL-
LIPSES e sue C4.5. Though ELLIPSES is no a classi-
ica ion sys em, a me hod is p esen ed in o de o e alua e
ou ool. This me hod compa es he esul s ob ained by EL-
LIPSES wi h he esul s ob ained by C4.5 on six UCI Repos-
i o y da ase s. The ea u es o hese da ase s a e shown in
able 1.
Fo his, i o e s a compa ison based on he numbe o
ules ob ained by ELLIPSES. Thus, able 2 shows he pe -
cen age o posi i e cases o each class (column %c/s), he
pe cen age o posi i e cases on he o al (column
% al) and
he pe cen age o nega i e cases o e o a e (column %e ).
As C4.5 is a classi ica ion sys em, i inds mo e ules han
ou ool hus he mos meaning ul ules (column ) axe only
used in he compa ison. The ules ha mo e i ems collec
a e he mos meaning ul ules.
To cla i y he con en o able 2, we o e an explana ion
o he esul s on PIMA da ase . This da ase ham 768 i ems,
8 a ibu es and wo class deno ed wi h 0 and 1, as able 1
shows. ELLIPSES induces wo ules o he class 0. These
ules co e 52.2% o he i ems o he 0 class, his is 33.9%
on all i ems and he pe cen age o e o is 2.8%.
C4.5 induces 15 ules o class 0. In his compa ison he
wo ules ha co e mo e i ems a e conside ed. The wo
mos meaning ul ules co e 54.8% o he i ems o he 0
class, 35.6% o all i ems aa- d he pe cen age o e o is 2.9%.
In a same way, ELLIPSES induces a ule o class 1 ha
co e s 20.5% o he class, 7.2% o all i ems and 0.6% e o .
C4.5 induce 7 ules whe e he mos meaning ul ule co e s
29.8% o he class, 10.4% o all i ems and 1.5~ e o .
The p e ious esul s show ha he accu acy o he classi-
ica ion in bo h me hods is e y simila , al hough he mos
signi ican ules a e only used. Fu he mo e, he a e o
e o is ligh ly in e io in ELLIPSES. These esul s de e -
mine ha ELLIPSES is a good ool o ob ain in e es ing
ules ( egions). Fu he mo e, ELLIPSES has o he ad an-
age: "human expe 's in e ac ion". Thus, human expe s
can de e mine he numbe , he suppo and he con idence
o he ules. Tha is o say, hey de e mine he impo ance
o he egions.
501
Table I: UCI Reposi o y Da ase s ~able 3"- Pa ame e s and de aul alues
Da ase s #I ems #A . #Class Class
BCW 699 I0 2 2,4
BUPA 345 6 2 1,2
GLASS 214 9 7 1,2,3,5,6,7
HAYES 132 5 3 1,2,3
IRIS 150 4 3 s, j
PIMA 768 8
2
0,I
Table 9.: ELLIPSES s. C4.5: A Compa ison
ELLIPSES C4.5
c
%cls % al %e ~/ocls °To al
%e
BCW
2 1 90.1 59.1
0.2
81.0
53.0
0.1
4 1 71.4 24.6 0.4 67.6 23.3 0.3
BUPA 1 3 32.4 13.6 1.1 36.5 15.3 1.4
2 5 40.0 23.1 0.2 74.5 43.1 11.8
GLASS 1
3
81.4 26.6
0.4
78.5 25.7
0
4
2 3 64.4 22.8 2.8 64.4 22.8 3,2
3 2 64.7 5.1 0.4 47.0 3.7 0.0
5 1 76.9 4.6 0.4 92.3 5.6 0.4
6 1 66,6 2.8 0.0 100.0 4.0 0.0
7 1 82.7 11.2 0.0 93.1 12.6 0.4
HAYES 1 3 68.6 26.5 0.0 64.7 25.0 0.0
2 3 64.7 25.0 1.5 62.7 24.2 0.7
3 3 100.0 22.7 0.0 100.0 22.7 0.0
IRIS
s 1
100.0 33.3 0.0
100.0
33.3 0.0
1 94.0 31.3 0.0 94.0 31.3 0.1
i 1 88.0 29.3 0.0 90.0 30.0 0.1
PIMA
0
2 52.2 33.9 2.8 54.8 35.6 2.9
1 1 20.5
7.2
0.6 29.8 10.4 1.5
As disad an ages, ou ool has he handicap o he e olu-
iona y compu a ion: high compu a ional cos . Howe e , in
his case he esul s show ha in ela i ely ew gene a ions,
he ound egions a e su icien ly alid. I is necessa y o
know ha he inal pu pose o ou ool is no a classi ica ion
sys em ha op imizes he e o a e, since he pu pose is o
ind quali a i ely in e es ing egions.
Table 3 shows he undamen al pa ame e s and hei de-
aul s alues used o induce he p e ious esul s.
5. CONCLUSION
In his pape , we p esen a new supe ised lea ning ool
in o DM ield. The main objec i e is o induce a se o
ules (knowledge) abou quali a i e in e es ing egions on a
da abase. These ules a e easie o in e p e o a human
expe because hey a e shown ia h ee o ma s: quan i a-
i e, quali a i e and pa allel coo dina e sys ems. Fu he -
mo e, his ool pe mi s humans expe s in e ac ion by he
de ini ion o pa ame e s in he lea ning p ocess.
Analyzing he p e ious sec ion, i can be deduced ha
ELLIPSES is no a classi ica ion sys em, since hei main
objec i e is no o op imize he e o a e. Thus, he ob-
ained esul s axe no he same ha he esul s o a classi i-
ca ion sys em, as C4.5. Bu , wi hou any doub , analyzing
also he esul s in able 2, we can conclude ha ELLIPSES
ac s as a classi ica ion sys em when he objec i e is o ind
he mos in e es ing egions, a he he ules ha de e mine
Pa ame e De aul alue
ALPHA 10.0%
BETA 90.0%
ITER 10
num Gene a ions 200
hum Indi iduals 200
%
selec ed indi iduMs
10%
P obabili y o c osso e 50%
P obabili y o mu a ions 33%
Pe cen age o mu a ion
70%
egions wi h an in e es ing olume o i ems.
Summa izing, ou ool o e s he human in e ac ion in he
lea ning p ocess, wo models o ules: quan i a i e and qual-
i a i e, and a isualiza ion by pa allel coo dina e sys ems,
so we can conclude ha i is an excellen ool in da a mining
ield.
6. ACKNOWLEDGMENTS
This wo k has been suppo ed by Spanish R,esea ch Agency
CICYT unde g an TIC2001-1143-C03-02
7.
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