Phin nay trlnh bay cd sd 19 lu~n dE dinh nghia va tinh tmin h~ s6 pht;1 thuQc thue}ctinh md fe}ng.
Dinh nghia 1.29. Ham phan anh muc de}bao ham
Cho ngU'ongdo mue dQ bao ham 8e[0,1], gQi ~(S,T) la ham phan anh mue dQbao ham cua Strong T, ham ~(S,T) dU<;fC(t!nhnghia nhu san:
59
J.lc (S,T)
=
ISII T)IIISI (1.12)Neu J.lc(S,T);::: 8, thi t~p h<;1pS du'<jcgQi la baa ham trang T vdi mUGdQ baa ham la 8. Neu 8=1,0 thi S c T
Dtnh nghia 1.30. Xa'p Xldu'oimd fQng
Vdi dinh nghla cila ham philo anh mue dQ baa ham, co th~ dinh nghia Xa'pXlmo fQngB**(X)trong Iy thuyet t~p tho nhu'sau:
B**(X)
=
{ u E 0 I J.lc([U]ind(B),X);:::8J\ U EX} (1.13)Dtnh nghia 1.31. H~ s6 ph\! thuQcthuQctfnhmd fQng
H~ s6 ph\! thuQcmo fQng du'<;1cdinh nghla qua ham phan anh mue dQ baa
ham. Cho hai t~p thuQctinh U va t~p thuQctinh V, M s6 ph\! thuQcthuQctinh mo fQngcila V vao U du'<;1cky hi~u Ia '¥ (U,V)va du'<;1cd!nh nghia nhu'sau:
'¥ (U,V)
= II U..(X)l1!0 I
XeO/V
(1.14)
Vi dl,lI.13 sail day neu leD kha Dangphan ldp cila h~ s6 ph\! thuQcthuQc tinh md fQng.
~{'
Vi dl} 1.13: Xet bang quyet dinh 1.12, cho U={b} va V={c}, ta co:
. Voi U={b} se co cae lop tu'dngdu'dng:
[01]ind(U)=[02]ind(U)=[03]ind(U)=[08]ind(U)={ 01,02,03,08} [04]ind(U)=[05]ind(U)=[06]ind(U)=[07]ind(U)={04,05,06,07} . Voi V= {c}se eo cae lop tu'dngdu'dng:-
[ol]ind(B)=[04]ind(B) =[05]ind(B)= [07]ind(B)= {ol,04.05, 07} [02]ind(B)=[03]ind(B)=[06]ind(B)= [08]ind(B)= {o2,03, 06, 08}
Dung h~ s6 ph\! thuQcthuQctinh truy~n th6ng y(U,V)
= II
U.(X) 1/101=
060
Trong 1:9thuytt t~p tho khi y(U,V)=Oco nghla l?iV khong ph\,!thuQcVaG U, nhung theo yeu cftu cua pIlau lap gftn dung v~n co th8 suy fa duQCV tIcU.
Tit hai lu~t phan ldp :
<b, 4> ~ <c,7>, dQchfnh xac cua pMn lap
=
0,75 <b, 5>~ <C,6>, dQchinh xaccua pMn Idp =0,75D\fa VaGnh~n xet tren, lu~n an md fQngkhai ni~m xa'p XlduOicua t~p tho nh~m (ijnh nghla h~ s6 ph1,1thuQcthuQctinh md fQng \fI(U,V).
Vdi cac t~p cd sd cua phan ho~ch ON va muc dQbaa ham e =0,75:
Vdi Xl= {oI,04.a5, a7}, U..(XI)={a4,05, 07} Vdi X2= {02,03, 06, 08}, U..(X2)={a2, 03, 08}
\fI (U,V) = II U..(X) I/ 10 I = (I {04,05, a7}1+I{02,03,08} I)/101=6/8=0,75
XeOIV "
,
Do v~y M s6 ph1,1thuQcthuQc tinh md fQng co kha DangpMn ldp t6t hdn h~ s6 ph1,1thuQcthuQctinh truy~n th6ng, d~c bi~t l?icac pMn lap g~n dung [91.
Nhq.n xet:Khi nguong do mue dQbaa ham 8=1,0 thl '¥ (U,V) =y(U,V).
1.8.4.1. Chuyin tl/Jibang quye'Fi1/nhtTong Ii thuylt tljp tho sang bang quylt dink nhjphlin
IAII
Cho h~ th6ng thong tin (O,A=HRuHC,fs), V=Udom(a,), gQiD Ia t~p h<jp
;=1
cac em baa d= <a,v>eAxV va thoa ham is. Tit (O,A=HRuHC,fs) t~o quaDh~ hai ngoi RcOxD, saDcho 0 R d <=>o(a)=v va d=<a,v>.
Bang 1.1I Ia bang quytt dinh nhi pMn du<jcchuy~n d6i tu bang quytt dinh truy~n th6ng (bang 1.12) vdi cac chI baa d nhu san:
dl=<a,l> ; d2=<a,2>; d3 = < a,3>; d4=<b, 4>; d5=<b, 5>; cl=<c,6>; c2=<c,7> Xet ham attributes duQcdinh nghla nhu san:
61
v SeD, attributes(S)
=
{ a e A I<a,V>-e S } (1.15)Ham attributes d~ la'yten cac thuQctinh trong t~p con S cac chi baa cua D. Tinh chat 1.6: Voi c~p ham (p, A) dfi dtnh nghia
a
ireD, gQi U eA va OIU la mQtphilo ho~ch o thee quaDh~ ba't kha philo ind(U) va U1,Uz,., Ukla cac ~p cd sa cua philo ho~ch OIU thi p(A(Uj»=UjV j=I,...,k.Vi dl} 1.14: Voi U={a, b} va t~p cd sa cua phan hOi;lChOIU ung voi lop tttdng
du'dng U5=[o5]ind(U)=[o7]ind(U)={o5,o7} du'<;1cxac dtnh bai: <a,3> va <b, 5>.
Theo cach ma hoa ireD,hai chi baa tttdng ung la d2=<a,2>; d5=<b, 5>. Dung c~p
ham p,A da du'<;1cdtnh nghia
a
ireD, ta co:A(05, o7)={d2,d5,cl}; p(A-(o5, 07») = p({d2,dS,cl})={o5,o7} = U5
1.8.4.4. Tinh hf srfphI} thul)c thul)c tinh md rl)ng qua dl) tin cljy va dl)phil bitn cua luat kit hd,rp "-
.. ,
Rtl dl 1.1: Cho SeD va TeD, muc dQcua peS)bao ham trong peT) du'<;1ctlnh:
J.Ic(p(S) ,peT»~
=
Ip(S) tlp(T)llIp(S)1=
CF(S-+ T) (1.16) -.}-.,~.
Dinh Ii 1.7([9]).Cho (O,A=HRuHC,fs) la bang quye't dtnh va bang chuy~n d6i quye't dtnh nht philo (O,D=HuC,R) tttdng ung, gQiU va VIa hai t?P h<;1pcon cua
A, Uj la cac t?P cd sa cua philo hOi;lChOIU va X la t?P cd sa cua philo hOi;lCh ON, J la t~p cac chi s6 sao rho VjeJ, !lc(Uj,X)~ e thi:
'I' (U,V)
=
I I(CF(A.(Uj)-+A,(X»*SP(A,(Uj)))XeOlVjeJ
(1.17)
Trang do D la t~p chi baa cua bang quye't dtnh nht phan (O,D,R) dtt<;1c
62
Chung minh: Gqi J Ia ~p cac chi s6 saGcho 'v'jeJ, J.1c(Uj,X);::e voi l!j Ia ~p cd
sd cua phin ho~ch 01U, co th€ tinh I(U (X»I bhg:
I(U (X»I
=
IIUj(JXIjeJ
Do l(Uv cD, A.(X)g), lu~t ke't h<;1pA.(Uj)-+A.(X)di'idu<;1etlnh dQ ph6 bie'n va dQ tin c~y Den CF(A(Uj)-+A,(X»= Ip(A,(Uj»(\ p(A,(X)l/lp(A(Uj»1.Theo tlnh cha't 1.6 do Uj va X la cac t~p co sd eua phin ho~ch Den p(A(Uj»=Ujva
p(A(X)=X,do v~y Ip(A.(Uj»n p(A.(X)I=IUjn XI = CF(A(Uj)~A(X»* IV). Ngoai
fa, dQ ph6 bie'n cua ~p h<;fp A(Uj)Ia SP(A,(Uj»= Ip(A(Uj))I/IOI=IUpIOI,Den IUjl=SP(A(Uv)* 101. Tom l~i:IUjn XI
=
CF(A(Uj)~A(X»* SP(I..(Uj»* 101Ne'uA.(Uj ) la t~p ph6 bie'n va A(Uj)~A(X) la lu~t ke't h<;fp,co th€ tlnh h~ s6 ph1:lthuQcthuQc tinh md rQng nhu san:
'¥ (U,V)=
I I( GtF(A(U)
~ A(X»*SP(A(Uj)))XeD/V jeJ
1.8.4.5 Xliytb!ng thuQ.t giai dJ!a tren hi siJphlJ. thllQCthuQc tilllz mll TQng
Cho bang quye't dinh (O,A=HRuCR,fs) va nglliJng dQ ehlnh xae cua phin
~.
lOpminprecisione[O,I], fun cae lu~t'phin lop S~T voi S ~HR va TcCR, saGtho do chlnh xae cua lu~t phin lop S~ V Ion hon ho~c bing minprecision. Cho bang
quye't dinh (O,A=HRuCR,fs), gQi (O,D=HuC,R) la bang quye't djnh nb! phin dU<;fCehuy~n d6i tU bang quye't djnh (O,A=HRuCR,fs). Cho trUoc cac nglliJng minsupp, minconf, minprecision. GQi FS(O,D=HuC,R,minsupp) la t~p cae t~p ph6 bie'n cia (O,D=HuC,R) va R(O,D=HuC,R,minsupp,mincont) la t~p cae lu~t ke't h<;fpeo d~ng lu~t phin lop S~ T, saGcho S~H va Tcc.A=Huc.
Thu~t giai 1.11. san dfty sa d1:lngh~ s6 ph1:lthuQcthuQetinh md rQngd~ tlm lu~( phan Idp dli li~u.
63
Thu4t giiii 1.11: TIm lu~t phan lop dt!a tren h~ 56 ph1:1thuQcmd rQng
Vao: Bang quy~t djnh (O,A=HR0CR,fs)
NgU'Ongminsupp, mineonf, minpreeision
Ra: T~p cae lu~t phan lop S ~ T, sac cho S c H, T c C, A=HuC, ngU'Qngphan
lOp la minprecision.
BlIUc 1: Chuy~n bang quy~t dtnh (O,A=HRuCR,fs) sang bang quy€t djnh nht phan (O,D=HuC, R)
