Th ee Geome ic App oaches o ep esen ing Decision Rules in a
Supe ised Lea ning Sys em
Jesús Aguila , José Riquelme y Miguel To o
Depa amen o de Lenguajes y Sis emas In o má icos.
Facul ad de In o má ica y Es adís ica. Uni e sidad de Se illa.
E-mail: {aguila , iquelme, m o o}@lsi.us.es
This pape desc ibes a sys em o lea ning ules based on di e en geome ic ep esen a ions. The
me hod uses a gene ic algo i hm (GA) o ind ou decision ules acco ding o one o he h ee possible
shapes: hype ec angles, o a ed hype ec angles and hype ellipses. These geome ic ep esen a ion a e
in e nally codi ied as indi iduals o he popula ion o he GA. The esul is a decision queue (DQ) o
each ep esen a ion. I means ha he ob ained ules mus be applied in speci ic o de . Wi h his policy,
he numbe o ules may be educed because he ules could be one inside o ano he . The use decides
wha ep esen a ion p o ides he bes accu acy and wha p oduces he smalle numbe o ules.
Some imes, he linguis ic in e p e a ion o he ule se –wi h ew ules- is mo e impo an han he exac
classi ica ion o an unseen example –wi h oo many ules-. The e o e, he sys em o e s an ideal ool o
selec he bes solu ions o ien ed o ou pa icula p oblem.
In p e ious wo ks [1,3], we p esen ed a sys em o classi y da abases by using hype ec angles (axis-
pa allel). This sys em used a GA o sea ch he bes solu ions and p oduced a hie a chical se o ules. The
hie a chy ollows ha an example will be classi ied by he i- ule i i does no sa is y he condi ions o he
i-1 p eceden ules. The ules a e sequen ially ob ained un il he space is o ally co e ed. The beha io is
simila o a queue, o ha eason we ha e gi en he name decision queue (DQ) o he p oduced ule se .
This concep is based on he k-DL, he se o decision lis s wi h conjunc i e clauses o size a mos k a
each decision [4].
DQ is based on DL. Really, DQ is a DL-gene aliza ion because i pe mi s codi ying unc ions i o
con inuous a ibu es and he alues i can belong o any se .
DQ p esen s he ollowing s uc u e:
I condi ions Then class
Else I
condi ions Then class
Else I
condi ions Then class
............................................
Else “unknown class”
The expe imen s desc ibed in his sec ion a e om UCI Reposi o y.
DATABAS C4.5 AXIS-PARALLEL ROTATED HYPERREC. HYPERELLIPTICAL
#RULES ERROR #RULES ERROR #RULES ERROR #RULES ERROR
IRIS 4.4 6.3 3.4 7.47 3.6 4.83 4.2 5.6
PIMA 77.6 28.4 20.0 27.2 17.4 26.35 7.4 26.8
CANCER 5.2 13.8 2.2 4.24 2.2 5.38 2.6 5.0
Table. Da abases (numbe o examples, dimension, numbe o classes).
The numbe o ules is educed wi h ega d o o he sys ems, like C4.5 [2], and imp o es he lexibili y
o cons uc a classi ie a ying he elaxing coe icien .
Re e ences:
[1] Aguila , J., Riquelme, J. and To o, M. A Tool o ob ain a Hie a chical Quali a i e Se o Rules om
Quan i a i e Da a. Lec u es No es in A i icial In elligence 1415. pp 336-346. Sp inge -Ve lag, 1998.
[2] Quinlan, J. R. C4.5: p og ams o Machine Lea ning. Mo gan Kau mann Pub.,1993.
[3] Riquelme J. and Aguila , J. Re is a Ibe oame icana de In eligencia A i icial nº 5. A GA-based Tool o ob ain a
Hie a chical Classi ie o Supe ised Lea ning. (in spanish) pp 38-43, 1998.
[4] Ri es , R.L. Lea ning Decision Lis s. Machine Lea ning, 87. pp. 229-246.