Quach Xuan Trudng vd Dtg Tap chi KHOA HOC & CONG NGHE 132(02): 109-115
KHAI PHA Dtr LIEU DIEM SINH VIEN DITA TREN
BANG QUYET DJNH THEO TIEP C^^N LY THUYET TAP THO
Quach Xuan Trudng', Nguyin Tuin Anh, Nguyen Van Sir Trudng Dai hgc Cong nghe thong tin & Truyen thong - DH Thai Nguyen TOM TAT
Ly thuyfit tSp tho do Zdzisaw Pawlak dl xuit vao diu nhung nam 80 dugc phkt triln trgn mot nIn tang toan hpc vttng chic, cung cap cdc cong cu hifu ich de giai quyet c4c bai toan phan tich dQ- lieu, phat hign luSt, nhan dang... Dac biSt, ly thuylt nay thich hgp vdi cdc bdi todn phan tich tren khoi lugng du lieu Idn, chiia dung thong tin mo hi, khong chic chin. Trong bai bdo ndy, chiing t6i lira chgn nghien ciiu phuang phdp riit ggn thugc tinh tren bang quylt djnh vd sinh luat quylt dinhdua tren bang quylt dinh theo hudng tiep can ly thuylt tap tho. TCr nghien ciiu ly thuylt, chiing toi cdi dat thir nghigm phuong phap nit gon vd sinh luattren cdc b5 sl liSu thij nghiem tii kho da li§u UCI vd img dung khai phd dit liSu tfr ca sd dtt lieu dilm hgc tap cua sinh viSn trudng dai hgc cong nghg thOng tin va truyin thflng.
Tii kh6a; Tap thd, bdng quyet dinh. Entropy thdng tin, nit ggn thugc tinh. Hi thong tin TONG QUAN TAP THO
Ly thuylt t | p thd do Zdzisaw Pawlak de xuit vao nam 1982 [8] da dugc ling dyng ngay cang rOng rSi trong ITnh vuc khoa hgc may tinh. Ly thuyet tSp thd dugc phat triln trgn mgt ngn tang toan hgc vu'ng chac, cung cap cac cdng cu huu ich de giai quyet cac bai toan phan tich dii lieu, phat hien luat, nhan dang,..
trgn khdi lugng dii lieu Idn, chiia dung thong tin mo hd, khdng chac chan. Tir khi xuat hien, ly thuyet tap thd da dugc sir dyng hieu qua trong cac budc ciia qua trinh khai pha dir lieu va kham pha tri thirc, bao gdm tien xir ly so lieu, trich Igc cac tri thiic tiem an trong dii lieu va danh gia ket qua thu dugc.
Mot so khai niem c<r ban
Trong ly thuylt tap thd, dii ligu dugc bilu dien thdng qua mdt hg thdng tin IS = {U,AjVyf)vai V la tap httu han khac rong cac ddi tugng va A la tap hiru han khac r6ng cac thu^c tinh. V = Uag^Kvdi Va la tap gia trj ciia thudc tinh a E A.
f :UxA^>V^\k ham thdng tin,
\faeA,ueU f{u,a)eV^.
Xet he thong tin IS, moi tap con cac thugc tinh P a:A xac dinh mgt quan he hai ngoi trgn U, ky hieu la IND(^P), xac dinh bdi
hoach khi do
' Tel 0989 090832. Email:
IND(P) = [(u,v)^UxU\ya&P, a(w)=a(v)}
IND[P) la quan he P-khdng phan biet dugc.
De thiy rang IND[P) la mgt quan he tuong duong tren U. Nlu [u,v) E IND{P) thi hai ddi tugng « va v khong phan biet dugc bdi cac thugc tinh trong P. Quan he tuong duong IND{^P) xac dinh mot phan hoach tren U, ky hieu la U / IND(P) hay U / P . Ky hieu Idp tuong duong trong phan f / / P chiia doi tugng u la [«] , [ul = {veU\{u,v)ElND{P)}.
Mgt ldp dac biet cua cac he thong tin co vai tro quan trgng trong nhieu ling dyng la bang quygt djnh Bang quyet dinh la mgt he thdng tin DS vdi tap thugc tinh A dugc chia thanh hai tap khac rong rdi nhau C va D , lan lugt dugc ggi la tap thugc tinh dilu kien va tAp thugc tinh quylt dinh. Xet bang quylt dinh DS = {U,C<jD,V,f)vai CnD = 0,gia thiet ringVw e f 7 , V J e £ ) , d(u) diy dii gia trj, neu ton tai ueU va ceC sao cho
c{«) thigu gia tri dii DS dugc ggi la bang quygt djnh khdng diy du, trai lai DS dugc ggi la bang quygt djnh day du. Trong bai bao nay chung tdi ggi tat bang quylt djnh diy du la bang quygt djnh.
109
Qudch Xudn Trudng vd Dtg Tap chi KHOA HQC & CONG NGHE 132(02): 109-115 Cho he thong tin IS=(U,A,VJ) va tap
dii t u g n g X c t / . Vdi mgt tap thugc tinh Be A cho trudc, chung ta co cac ldp tuong duong cua phan hoach UIB .Trong ly thuylt tap tho truyen thong, de bieu dien tap doi tugng X bing tri thiic c6 san B, ngudi ta xap xi X bdi hgp cua mgt so hiru ban cac Idp tuong duong ciia phan hoach UIB. Co hai each xip xi tip d6i tugng X thong qua tSp thugc tinh B, dugc ggi la B-xap xi dudi va B- xip xi trgn ciia X, lo^ hieu lin lugt la BX va
BX, dugc xac dinh nhu sau:
Tap 5 X bao g6m tat ca cac phSn tu cua U chac chin thugc vao JT, con tap BX bao gdm cac ph4n tu cua U co kha nang dugc phan loai vao Xdisa vao tap thugc tinh B.
PHUONG PHAP RUT GON THUOC TINH Riit ggn thugc tinh la mot trong nhiing bii toan ung dung dien hinh nhat cua ly thuygt tap tho [4][I0][19]. Thai gian gin day da chiing ki«n sir phat trien mjnh me va soi dgng ciia Imh virc nghien ciiu vl riit ggn thugc tinh sii dung ly thuyet tap tho. Nhieu nhom nha khoa hgc tren thi giai quan tam nghien ciiu cac phuang phap nit ggn thugc tinh trong bang quyet dinh.lVliic tieu cua rut gon thugc tinh trong bang quyet dinh la tim tap con nho nhit ciia tap thugc tinh dilu kien ma bag toan thong tin phan lap cua bang quylt dinh. Dua vao tap riit ggn thu dugc, viec sinh luat va phan lop dat hi^u qua cao nhit. Vai muc tieu do, CO rit nhilu cac phuang phap rut ggn thugc tinh khac nhau da dugc dl xujt dua tren cac tieu chuan kliac nhau. Doi voi mgt bang quylt dinh co thi co nhilu tap riit ggn khac nhau.nhung phuong phap rut ggn chinh la:
phuong phap dua tren miln duong [3][7J, phuang phap sir dung cac phep toan trong diii so quan he [2], phuang phap sii dung m.a tran phan biet [1][17][18], phuang phap sir dung cac dg dg trong tinh toan hat [5][20]. Phuang phap sir dung entropy thong tin no
[9][l 1][12][I3]. Trong cac phuang phap plij.
noi tren, entropy Shannon la mgt trong nhit^
cong cu hieu qua d l giai quylt bai toan if gon thugc tinh trong he thong tin. Da co rk nhieu nhom nghien cu-u da sii dyng entropy Shannon de xay dimg cac thu|t toan heuristic tim tap rut ggn cho bang quylt dinh[12][13], Trcng pham vi bai bao nay, chung toi tjp chung giai thigu ve ly thuylt cung nhu thiic nghiem phuang phap rut ggn thudc tinh sir dung entropy shannon co dieu ki6n tren bang quyet dinh va danh gia tinh hilu qua ciing nhu kha nang sinh luit quyet dinh tren tap rut ggn dugc tim thiy dua trSn phuang phap nay, Binh nghia 1. {[16]) Cho bang quylt ainh£)5' = ( C / , C u Z ) , ^ ' , / ) . Gia sii
WC={C„Q, CJ, u/D=m,q,...,Dj.
Entropy Shannon co dilu kien cua D khi da biet Cdugc dinh nghTa bai
^ ' ' i f r M ^ \c,\ ^' \c\
Dinh nghia 2. ([14]) Cho bang quylt djnh DS = {U.C<jD,V,f), thugc tinh asC dugc ggi la khong cSn thilt (du thira) trong DSim tren entropy Shannon co dieu kien nlu //(£l|C) = //(£>|C-{fl}); Ngugc 1,1, a ggi la can thilt. Tap tit ca cac thugc tinh cin thilt trong DS dugc ggi la tap lai dua tren entropy Shannon cc dieu kien va ky hieu la HCORE(C).
Binh nghia 3. ([14])Cho bang quyet dinh DS = (U,C^D,r,f) va tap thugc tinh .S c C . Nlu
i).H{D\R) = H{D\c)
thi R ia mgt t | p rtit ggn cua C dua tren entropy Shannon co dilu kien, ggi tit la tap rut ggn Entropy Shannon.
Ky hieu HRED(C) la hg tit ca cac tip rif gPn Entropy Shannon. Theo
l'fl.Hco;!£(c)= n «.
Qudch XuSn Truing vo Big Tap chi KHOA HQC & CONG NGHE 132(02): 109- 115 Thuat toan tim tap loi
ThuSt toan 1. Thu|t toan tim tap loi su dyng entropy Shannon
Input: Bang quyet d j n h f l S = ( C / , C u B , f ' , / ) .
Output:Tap loi HCORE{C).
Method:
HCORE(C) = 0;
T i n h / / ( D I G ) ; For each a^C Begin TmhH[D\C-{a});
\f H[D\C-{a))* H(D\C) t\im HCORE{C):= HCORE{C)u{a};
End;
Return HCORE(C);
Tham khao thult toan trong tai li$u[6] dl tinhC//C CO dg phiic tap la 0 ( | C | | ; / | ) . Do do, d6 phiic tap dl tinh H{D\C) la 0 ( | C | j t / | j . Vi v^y, do phiic tap cua vong lap For tir dong lenh thir 3 din dong lenh thu 7 la OuCf \U\\ va do phtic tap cua Thuat toan I l a 0 ( | C | ' | C / | ) .
Thuat toan 2. Tinh phan hoach UIRvj{a}
khi bilt UIR
Input:Phan hoach UI R = {if,,.Rj,...,.»,}
Output:Phan hoach UIR^{a]
Method:
TMP = 0 ;
For each R,£U/R do Begin
Tinh phan hoach R, /{a] ; TMP = TMP u R,/{a};
End;
Return (TMP);
CQng trong thuat toan trong tai lieu [6] dl tinh phan hoach R^ I {a.} vol do phirc tap 0(|i?J)thi dg phiic tap cua thuat toan 2 la
Y.o[\R.\) = o{\u\).
Thuat loan heuristic tim tap rut goa tot nhat
Y tudng ciia thuat toan la xuSt phat tir tSp loi R = HC0RE(C), lin lugt b6 sung vao tap R cac thugc tinh cd do quan trgng Idn nhit cho dgn khi tim dugc tap rut ggn.
Thuat toan i{CEBARKCC{\S]):
Input:Bang£)5 (U, CuD, V. f).
RcC,aeC-R
Output:Mgt tSp riit ggn R.
Method:
Tim i / C O i ! £ ( C ) theo thuat toan 1;
R = HCORE{C);
II Them ddn vdo R cdc thuoc tinh co dq quan trong Idn nhat
'^\\i\zH[D\R)^H[D\c) do Begin
For each a e C - i?
Begin l{xihH[D\RKj{a})
TmhSIGi,(a)=H[D\RyH[D\R^[a});
End
Chgn a^ eC-R sao cho SIG,{a,) = Mca{SlG,{a)};
R = R^{a,};
Tinh H(D\R) End;
R* = R-HCORE{C);
Qukch Xuan Trudng vd Dtg Tap chi KHOA HQC & CONG NGHE 132(02): 109-115 For each as R*
Begin TinhH(D\R-la})
If H(D\R-{a])=H(D\c) then R = R-{a};
End Return 7?;
Trong thuat toan 3, vdi budc thgm din vao R cac thugc tinh cd dg quan trgng Idn nhat, tap thugc tinh R thu dugc tii cau lenh tii 3 dgn 13 thoa man digu ki?n bao toan entropy Shannon//(£)| R)=H[D\ C).Vdi budc loai bo cac thugc tinh du thira, cau lenh ttr 14 dgn 19 dam bao tap R la t6i thigu, nghTa la Vr G R, H(D\ (R-{r})) ^ H{B\ C).Theo dinh nghTa 2, R la tap riit ggn dua tren entrgpy Shannon.
Xet vong lap While tir ddng lenh so 3 dgn dong lenh so 13, theo cdng thiic
^^'""i-^l('
|flr^D,| \R,riD,\1^1 Kl
dg tinh -S/G^ ( a ) , ta chi can tinh phan hoach VIR\j\a\ va phan hoach UIR da dugc tinh d budc trudc. Tir thuat toan 1, dg phirc tap thdi gian de tinh IJIRKj\a\ khi bigt If IR la 0 ( | t / | ) n e n do phuc tap thdi gian de tinh tat ca cac SIG^ ( a ) la
(|C| + ( | c | - l ) + . . . - H l ) * | C / | =
= (|c|-(|c|-i)/2)*M = o(|cf|;y|) D6 phiic tap thdi gian dg chgn thugc tinh c6 dd quan trong Idn nhSt la jCl+(|^-l)+...+l=|Cl.(M-l)/2=0(|Cl').
Vong lap For tai dong lenh 17 thuc hien VR
lin, moi lin ta phai tinh H(p\R') voi dg phiic tap thai gianO(|i?||f/|). Do do, dg phirc tap thai gian ciia dong lenh 17 la 0(|ii'|[i?||C/|V Vi vay, dg phiic t^p thoi gian ciia thuat toan l a O N c f |U[j.
SINH LUAT TREN B A N G QUYET DINH Cho bang quylt djnh DS = {U,C'uD), gia s<lU/C = {X„X„...,XJyk
U/D={Y,,Y2,...,YJ la cac phan hoach dugc sinh bai C, D. Vai X, eU/C, Y^ GUID va X , n y ^ # 0 , kyhieu des(X,) va des{Y^]
lan lugt la cac mo ta cua cdc lop tuong duong X^ va Y trong bang quyet djnh DS. Mgt luat quyet dinh don co dang Zj : Jes(A',)->(fei(y^).Mgt trong nhilu thuat tgan sinh luat quylt dinh su dung ly thuyet tap tho la thuat toan RuleExtract. Thuat toan dugc mo ta nhu sau: Cho bang quylt djnh DS = {U,C^D), gia sir
U/C = {X„X,....,XJ va UID={Y„Y„...,YJ. Vai X,eUIC,
Y^eUID va X,r^Y^*0. Thuat toanRukExtract hiln thi cac lu^t quylt djnh dang Z,^ : d e i ( J r , ) - > c f e s ( 7 , ) vai do chjc chin / < ( z j = |jr, n 7 ^ | / | ; r , | va d6 ho trg s ( z j = | j r , n y , | / | i 7 | tuong ling.
Thuat toan RuleExtract
Input: Bang quylt dinh DS = (U, CUD, V.fi.
Output:Hiln thi danh sach cac luat v6i dg chic chin fl va dg hd trg j . Tinh phan hoach UIC;
For each X,<EUIC Begin
Tinh XID;
Quach XuSn Trudmg v<i Dtg Tap chi KHOA HOC & CONG NGHE 132(02): 109-115 For each Y^^XJ D
Begin
Sinh luat Z , :rfes(X,)->rfes(}'J Tinh,u(Z,)=|rJ/]jr,|;
Tlnh.(Z,) = |7j/|f/|;
Hien thi luat Z , do chac chan / / ( Z I, do ho tra5(Z,^);
End;
End;
Return.
THl/C NGHIEM
Sii dung thuat toan ndi trgn chiing toi da thii:
nghiem, danh gia thuat toan riit ggn thugc tinh sir dung entropy Shannon vdi 8 bg s6 lieu vua va nho liy ttr kho du lieu UCI. Va thii nghiem thuat toan sinh luat quygt dinh RuleExtract trgn tap riit ggn tim dugc vdi bg s6 lieu Soybean - small.data.
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Cac luflt tien bang quyet djnh rut gou c4(J) cnidc22(2) ==> Z>7 c4(l) andc22(0} => Di c4(2) cmdc22f3) ==> D2 c4(l) a)tdc22(Si) = > D2 c4(0) andc22<D = > D3 c4(l) andc22l2) = > D4 c4(0) audc22(2) => D4
M 1 1 1 1 ' 1 1 I
5 0.L2766 0.08511 0.12766 1,0-08511 0.21277 0.21277 0.14894 Bang 2 Cac luat phan lap uen bang quyet duili
nit ggn \'ai bo so lieu soybean-small ITNGDUNG
Khai pha du lieu giao due dang dugc diu tu nghien cihi va ling dung de giai quygt nhigu van de cap bach nham nang cao chat lugng giao due cung nhu nang cao nang luc hgc tap ciia sinh vign, dac biet la trong mo hinh dao tao theo hgc che tin chi. Ben canh do cac trudng cao dang dai hgc hien dang luu trii CSDL diem cua sinh vign rat Idn. Mdt van dg dat ra va can giai quygt la tir cac thong tin ciia sinh vien va cac digm s6 tinh lily trong qua trinh hgc tap dg du doan hoac dua ra nhiing kinh nghiem de dinh hudng giup sinh vien cd thg cd cac su lira chgn phii hgp hoac dua ra cac kg hoach hoach tSp phu hop vdi nang luc va hien trang cua sinh vign. Can day so lugng sinh vign bj canh bao hgc vu va bugc thoi hgc cd chigu hudng gia tang. Mdt trong nhirng nguygn nhan la do sinh vien khong c6 kinh nghiem trong viec lira chgn mon hgc va cd ke hoach hoac tap phii hgp vdi kha nang ciia minh, day la mgt ton that Idn cho sinh vign, gia dinh, nha trudng va xa hgi.
sinh vien
cac thuoc tinh
svl sv2 5V3 sv4 sv5
Khu vuc 1 2 3 I 3
dantpc K K DI K DT
aiemthi vao
IS 14 13 13 16
m o n l 7.S 6.5 5.5 2.5 3.4
mon 2 8 5.8 6.5 4 2
mon 3 8 6 7 3.5
2
mon n 8.2
4 7 4 1
Phan loai Tot
IB TB CB CO
Bang 3. Bans dinh dang du* Heu diem sinh \ien
Quach Xuan Trudng vd Dtg Tap chi KHOA HOC & CONG NGHE 132(02): 109-115 Dg xac dinh dugc kgt qua hgc tap ciia mgt
sinh vign trong moi mgt dot hgc cua tiing khoa phu thugc rit nhigu vao cac ygu to anh hudng: hoan canh gia dinh, khu vuc sinh s6ng, digm diu vao, digm tinh liiy, va digm cac mon hgc cua ky hgc, .... Trong bai bao nay, chiing toi tap trung nghign ciiu ling dung giai phap rut ggn cac thuoc tinh trong bang quyet dinh da trinh bay d phan trudc dg lira chgn cac yeu to co anh hudng dgn viec phan ldp sinh vien theo tmh trang ket qua hgc tap, thong qua bang quygt dinh tim ra cac luat quygt dinh phan Idp tmh hinh hgc tap ciia sinh vien.
Trong qua trinh thuc nghiem, chiing t6i sii dung bang du lieu la bang tong kgt cac mon hgc trong hgc ky ciia nhiing sinh vien nam thii nhat va bao gom thgm mgt so thugc tinh mo ta cac thong tin ve khu vuc, digm thi dau vao, din tgc nhu sau:
Tri thuc trinh bay trong luat quyet dinh duoc nit trich ra va co the bigu dign dudi dang cac luat IF.. THEN. Vi du nhu trgn bang du Heu ta c6 the bieu dien luat nhu sau:
!F(KV=3)AND(DT=DT)AND(DiemVao=16) AND(mon 1 =3.4)AND(mon2=2)... AND(mon n=l) THEN (Phanloai=CB);
lF(KV=l)AND(DT=K)AND(DiemVao=18)A ND(mon l=7.8)AND(mon2=8.0)... AND(mon n=8.2) THEN (Phanloai=ToT);
Cac luat noi tren co thg ho trg phan ldp nang lire hgc tSp ciia sinh vign, tir do c6 thg riit ra cac tri thiic cho viec dinh hudng hgc tap, lua chon mon hgc theo nang luc ca nhan va ho trg cac thong tin cap nhat va dieu chinh chuang trinh dao tao trong nha trudng.
KET LUAN
Bai bao tap trung vao hudng nghign ciiu ly thuygt vdi ngi dung tren co sd t6ng kgt cac ket qua da cong bo vg hudng nghign ciiu nit ggn thugc tinh trong bang quygt dinh, bao gom nhom cac phuong phap riit ggn thugc tinh, trong do tap chung di sau phan tich va cai dat thii nghiemphuong phap rut ggn thugc tinh sii dung entropy Shannon va phuang
phap sinh luat quyet dinh trgn cac bg so lieu thii nghiem tir kho dir lieu UCI. Tir do, ling dung phuong phap noi trgn vao khai pha luat quygt dinh trgn kho dir ligu digm sinh vien nhim dua ra tri thiic trg giiip h6 trg, dinh hudng cho sinh vign va nha trudng trong cong tac theo doi, dieu chinh va nang cao chit lugng dao tao,hgc tap trong trudng dai hgc.
T A I L I E U THAM KHAO 1. Andrzej Skowron and Rauszer C (1992), "The Disceraibility Matrices and Functions in Information Systems", Interlligent Decision Support, Handbook of Applications and Advances of the Rough Sets Theory, Kluwer, Dordrecht, pp.
331-362.
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Discrete Mathematical Structures ( fifth ed.), Prentice-Hall, Inc., 2003.
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"Improvement to Quick Attribution Reduction Algorithm", Journal of Computers, Vol.30, No.2, pp. 308-312.
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(2001). Knowledge Reduction Based on Rough Set and information Entropy, The World MuUi-
Quach Xu5n Tnidng va Dtg Tap chi KHOA HOC & CONG NGHE 132(02): 1 0 9 - 1 1 5
conference on Systemics, Cybernetics and Informatics, Orlando, Florida, pp. 555-560.
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13. Wang G.Y., Vu H. and Yang D.C. (2002),
"Decision table reduction based on conditional information entropy". Journal of Computers, Vo).
25 No. 7, pp. 759-766.
14. Wang G.Y. (2001), "Algebra view and information view of rough sets theory". In.
Dasarathy BV,editor. Data mining and knowledge discovery: Theory, tools, and technology III, Proceedings of SPIE, pp. 200-207.
15. Wang G.Y., Yu H. and Yang D.C. (2002),-
"Decision table reduction based on conditional information entropy". Journal of Computers, Vol.
25 No. 7, pp. 759-766.
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S U M M A R Y
U S I N G D E C I S I O N T A B L E S O F R O U G H T H E O R Y F O R D A T A M I N I N G O N S T U D E N T R E C O R D S
Quach Xuan Truong*, Nguyen Tuan Anh, Nguyen Van Su College of Information and Communication Technology- TNU Rough theory, proposed by Zdzisaw Pawlak in 1980, has been considered as one of the most powerful methematical tools in solving problems of data analysis, discover mles, recognition, and so on. Specifically, the rough theory can be used to solve big data problems in which the information is unlcear or uncertainty. In this paper, we use the atttibutes reduction method on the decision table and generate association rules on the basis of the decision table by using rough theory approach. Accordingly, we implement our proposal on the UCI data, and then apply it for student database of College of Information Technology and Communications.
Keywords: Rough theory, decision table, Informationentropy, Attributes reduction, association rules.
Ngdy nhdn bdi: 18/01/2015; Ngayphdn bifn: 05/02/2015. Ngdy duyet ddng: 05/3/2015
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