tam dao 2007 vn lcd1

Phng php kho st a chiuLebart Ludovic, Piron Marie

Lp chuyn 1

Phng php kho st a chiuLebart Ludovic, Piron Marie

Cc nguyn tc ca phng php kho st a chiu 133Bng d liu v nhc lpii mt s kin thc v thng k m t c bn 133M t hnh hc v tp hp cc im 133Nguyn tc v cc phng php phn tch 134

Cc phng php nhn t 135Tm kim cc khng gian nhn t nh 135Cc phn t tch cc v b sung 136K thut c bn v cc phng php phi sinh 136

Phn tch theo thnh phn chnh 136Din gii hnh hc 136Vn thang chia v bin i cc d liu 136Phn tch tp hp cc c th (nc) 137Phn tch tp hp cc bin (ch tiu) 137Din gii 137

Phn tch cc tng quan 139Nhn xt 139Gi thuyt c lp 140Khong cch bnh phng v phn b tng ng 141Biu din hnh hc bng d liu 141Mi quan h chuyn tip v biu din ng thi 141Cc yu t tr gip cho vic gii thch 142

Phn tch cc a tng ng 142Bng phn tuyn ton din 142Nguyn tc phn tch cc a tng ng 143Khong cch gia cc profile 144Mi quan h trng tm v biu din ng thi 144Cc quy tc gii thch 144Cc phn t b sung 145

Phng php phn lopii 145Tp hp xung quanh cc tm di ng 145Phn lopii theo trt t 146Tiu ch gp 146Thut ton kt hp 147M t t ng cc t hp 147Tnh b sung ln nhau gia phng php nhn tv phng php phn lopii 148

Chin lc x l d liu cc cuc iu tra 148M ho 148Lm vic theo ch 148Kt hp cc phng php 149Cht lng thng tin v gi trfi cc kt qu 150

Ti liu tham kho 150Danh sch hc vin 151

133Phng php kho st a chiu

Cc phng php thng k kho st a chiu nhmfinh hnh cho cc b d liu thng k s v t xc finh kt cu v lm xut hin cc chiu tim tng.Cc thut ng {Thng k kho st a chiu}, {Phn tchD liu}, hay {Khai ph D liu} (Data Mining), l nhngkhi nim c ngha gn tng ng nhau trong trnghp chng ti cp n. Cc phng php ny l sm rng ca thng k m t c bn v s dng cccng c ton hc mang tnh trc gic nhng phc tpiphn cc s bnh qun, phng sai v h s tng quanthc nghim.

1. Cc nguyn tc ca phng php khost a chiu Cc phng php kho st a chiu s dng rt nhiu kthut m t v tng hp thng tin cha trong cc bngd liu s hay cc bng xy dng t kt qu cc bphiu iu tra.

Bng d liu v nhc lpii mt s kin thc v thngk m t c bnCc d liu iu tra c trnh by di dping cc bngln hnh ch nht c gi l X (xem hnh 1). Cc dflng(i=1,...,n) ca bng biu thfi cc n c th v d nh cc itng c iu tra, cfln cc ct (j=1,...p) biu thfi cc bins p, nhng cu hi m cu tr li a ra c th l cc so, c im hay bn ghi.

Ngi ta phn bit ch yu hai lopii bin: Cc bin finh lng hay lin tc nh tui, thu nhp,

chiu cao c gi trfi c tnh trn thang s v da vocc gi trfi thc hin cc php tnh pii s nhcng, tnh bnh qun...

Cc bin finh tnh hay finh danh nh gii tnh, nghnghip, bng cp, khu vc m gi trfi ca chng lnhng dping thc cn h thng ho cc php tnhpii s c ngha.

Vic xem xt cc d liu iu tra mt cch truyn thngp dng cc k thut n gin, c kim nghim vd gii thch trn c s thng k m t c bn nhm rtgn mt bin bng phn phi ca bin hay nhmnh gi quan h gia hai bin. Cc k thut p dngs thay i ty theo bn cht ca bin. Vic phn phi mt bin da trn kt qu tnh ton: Cc ch tiu xu hng trung tm nh bnh qun, trung

vfi, mt v cc ch tiu phn phi nh phng sai, sais chun i vi cc bin finh lng.

Cc t l phn trm hay tn s i vi cc bin finhtnh (v d nh t l nam, t l n).

Mi lin h gia hai bin cho php nhn bit cch m haibin cng bin i v l kt qu tnh ton ca: Hip phng sai, h s tng quan o s ph thuc

tuyn tnh ca hai bin finh lng. Thng k ca x2 v cc tn s iu kin thu c t

cc bng s ngu nhin hay bng phn t cho ivi cc bin finh tnh.

T s tng quan gia mt bin finh lng v mtbin finh tnh.

Cc phn phi c m t trn thfi bng cc lc ,ng cong, tp hp cc im.

Phn tch thng k a chiu ph bin cc k thut c bnny thng qua nghin cu v biu din mi lin h giacc bin.

M t hnh hc v tp hp cc im nm c nguyn tc ca phng php thng kkho st a chiu, nn biu din hnh hc tp hp ccn c th (n dflng) v tp hp cc bin p (p ct) di dpinghai tp hp im, mi tp hp ny c m t bi tphp kia. Khi , i vi hai tp hp im, ta xc finhkhong cch gia cc im-dflng v im-ct m t cckt hp v mt thng k gia cc c th (dflng) v giacc bin (ct).

V d ta c mt bng im m cc c th chm chocc t1 (xem bng 1) c coi l cc bin, nhng ycng c th l cc im nh gi v mi trng (mcc bin c th l mc hi lflng v cht lng mtfia im, v an ninh, giao thng). Mt t ( y cngha l: mt bin s) l mt im m cc topi n ls im m n c th chm (tc l ngi tr li): tc lkhi tp hp p t nm trong khong khng gian nchiu. Tng t nh vy, mi c nhn l mt im ctopi l cc im s p chm cho p t; cng tng tnh vy i vi tp hp n c nhn trong mt khnggian p chiu.

Gi trfi ca bin s j theo c th i

Hnh 1: M t bng d liu

1 y l cuc iu tra chm im cho mt danh mc cc t ty theo l cm gic d chfiu hay kh chfiu khi c cc t ny(xem Lebart L., Piron M., Steiner J.-F. (2003) - La smiomtrie. Dunod, Paris).

134 Kha hc ma h Tam o 2007

Bng 1: V d mt bng im X (t 1 n 7) chm cho p = 7 t bi n = 12 ngi tham gia tr li

Trn c s bng 1 cha s im m 12 ngi tham giachm cho 7 t, hnh 1 v 2 minh ha biu din thfi haitp hp im c mi lin h ni tpii vi nhau. Tp hp ccim-im s c hnh thnh trong khng gian cc cth, y ch l hai c th R04 v R08, v khng gian haichiu mi c th biu din thfi trn mt mt phng (vd hnh 1). Tng t, tp hp 12 ngi tr li c hnhthnh trong khng gian cc bin, y l hai t pio c

v Gi cm, tc trong mt khng gian hai chiu (xemhnh 2).

i vi mi tp hp, im trung bnh, cfln gi l trng tm,c biu thfi. chnh l im G biu thfi trng tm ccim s m nhng ngi tham gia chm (xem hnh 2.a)v im G biu thfi cho trng tm ca nhng ngi thamgia chm im hai t c la chn (xem bnh 2.b).

Nguyn tc v cc phng php phn tchTa lun c th tnh ton khong cch gia cc dflngv khong cch gia cc ct ca mt bng X. Nhngkhng th ngay lp tc biu din mt cch trc quannhng khong cch ny (thng thng, vic biudin hnh hc tng ng fli hi cc khng gian lnhn hai hoc ba chiu): cn phi tin hnh bin iv xc finh mc xp x c th biu din trnmt phng.

Cc bng khong cch gn vi nhng biu din hnh hcny (n gin v mt nguyn tc, nhng phc tpip do slng ln cc chiu ca cc khng gian c lin quan) cth c m t bng hai nhm phng php chnh lphng php phn tch nhn t v phng php phn lopii.Nhm phng php u tin nhm tm kim cc hngchnh tpii cc im cch xa im trung bnh nht c thc. Nhm phng php th hai tm kim cc nhm hayt gm cc cc c th ng nht nht c th c (hnh 3).

Hnh 2.a: Biu din tp hp cc t trong khng gian hai ngitham gia tr li {R04} v {R08}

Hnh 2.b: Biu din tp hp nhng ngi tham gia tr li trongkhng hai t {Gi cm} v {pio c}


Cc phng php nhn tCc phng php nhn t cho php ng thi qun l slng ln cc d liu v h thng tng quan cc d liuv thng qua k thut nn lm xut hin kt cu ni tpiica cc d liu di dping cc mt phng thfi.

Tm kim cc khng gian nhn t nhMc ch l lm gim cc chiu ca tp hp im bngcch chiu cc im trn cc mt phng do hai ngthng (hoc trc) tpio nn. Tc l tm cc khng gian nhc t chiu hn (v d trong khong t ba n 10 chiu)iu chnh gia tp hp cc im-c th v tp hp ccim-bin cc khng gian ln cn o c trong cctiu khng gian ny phn nh mt cch trung thc nhtcc khng gian ln cn thc t. Nh vy, ta c mt khnggian pii din gi l khng gian nhn t c tpio bi cctrc qun tnh chnh v ta biu din cc im ca tp hptrong h thng trc ny (xem hnh 4). Cc trc iu chnhmt cch hiu qu nht ton b cc im theo tiu chbnh phng ti thiu truyn thng, tc l sao cho tngbnh phng khong cch gia cc im v cc trc lnh nht.

Trc u tin tng ng vi ng thng ko di ti adc theo tp hp cc im, trc th hai cng ko di theosut tp hp cc im v trc giao vi trc th nht, vc nh vy, cc trc tip theo s u trc giao vi nhau.Tnh trc giao ny th hin s c lp (thc ra l s khngi xpi) gia cc trc.

X ch bng d liu (hay ma trn d liu) c bin imt cht (v d cc bin tiu chun), X', chuyn vfi ca Xc c bng cch hon vfi vai trfl cc dflng v cc ct.

Th d u1 l vct n vfi m t trc th nht. Ta chngminh rng khi u1 l vect ring ca ma trn X'X (ktqu ma trn chuyn vfi X bng X') tng ng vi gi trfiring ln nht l1. Cc thut ton c s dng tnh ccgi trfi ring v cc vect ring ca mt ma trn rt phctpip nhng c in. Ni tm lpii, khng gian con q chiuiu chnh gia (theo hng bnh phng ti thiu) tphp cc im c tpio ra bi q vect ring u tin cama trn X'X tng ng vi q gi trfi ring ln nht. Gi trfiring la th hin qun tnh ca tp hp cc im khi cchiu ln trc a. Tng cc gi trfi ring chnh l tng quntnh ca tp hp cc im.

Quy trnh iu chnh hon ton ging nh quy trnh i vihai tp hp k trn. Do ta chng minh c tn tpii cc

Hnh 3: Hai nhm phng php chnh

Phng php nhn t(tm kim cc hng chnh)

Phng php phn lopii (tm kim cc nhm ng nht)

Cc phng php ny thng bao hm cc c th (ccdflng) v cc bin (cc ct). Vic i chiu tp hp cc c

th v tp hp cc bin lm phong ph thm cc din gii.

Hnh 4: iu chnh thfi im-c th trong khng gian cc t


quan h gin n lin kt cc trc c tnh ton tronghai khng gian l trc cc c th v trc cc bin (quanh chuyn tip gia cc im-c th v cc im-bin).

Vect ta cc im trn mi trc c gi l nhn t,l t hp tuyn tnh ca cc bin gc. Gi ca v wa l ccnhn t tng ng vi trc a trong khng gian gi l P

n

(khng gian m cc p im c topi l cc n c nhn).Cc mt phng nhn t biu din tng ng vi mtcp nhn t.

Hai tp hp cc im, tc tp hp cc t v tp hp nhngngi tham gia tr li, c mi lin h ni tpii vi nhau vc cc kt cu ging nhau: lc th cc nhn t s m ttng quan gia cc t, cfln lc khc th m t cc kt hpgia nhng ngi tham gia tr li v chnh nhng tngquan v kt hp ny s xc finh cc trc.

Cc phn t tch cc v b sung Cc phn t (cc bin hay cc c th) tham gia vo victnh ton v xc finh cc trc l nhng phn t tch cc.Chnh nhng phn t ny cho php xc finh c imca cc trc.

C th b sung thm nhng im (hay phn t) m takhng mun chng tc ng vo vic xc finh kt cuv hnh thnh cc trc nhng vn mun bit vfi tr cachng trong cc khng gian nhn t, nhng phn t nygi l phn t b sung (hay minh ha). Khi ta chiucc im ny ln sau khi xy dng cc trc nhn ttheo mc mi mt cch rt n gin bng vic s dngcc cng thc gi l cng thc chuyn tip tnh topi ca cc trc nhn t.

C th nu ra hai l do cho vic b sung thm mt im:1) lm phong ph thm v hp thc vic th hin cc trcbng cc bin (c bn cht hoc ch khc vi bn chthoc ch ca cc phn t tch cc) khng tham giavo vic hnh thnh cc trc ny ; 2) a ra d bo bngvic chiu cc bin b sung vo trong khng gian cc cth. Nhng bin ny c {gii thch} bng cc phn ttch cc.

K thut c bn v cc phng php phi sinhPhng php nhn t lm gim mt s biu din {achiu} v ch yu tpio ra cc thfi biu din cc phn ttrn mt phng hay i khi l ba chiu. Bn cht ccthng tin, vic m ho chng trong cc bng d liu, ccc im ring ca lnh vc ng dng s tpio ra cc binthc trong phng php nhn t vn da trn hai k thutc bn: phn tch theo thnh phn chnh (xem mc 3)p dng cho cc bng o lng (cc dflng l cc c thcfln cc ct l cc bin lin tc hay bin finh lng), phntch cc tng ng (xem mc 4) p dng cho cc bngs ngu nhin hay bng m (cc dflng v ct biu thfidping thc ca hai bin finh danh hay bin finh tnh).Chng ti cng s gii thiu phng php phn tch cc

a tng ng phc tpip (xem mc 5), phng php nyl m rng lnh vc ng dng ca phn tch nhn t cctng ng cho cc bng phn tuyn ton din. y lnhng bng bin finh danh ln, v d nh cc phiu iutra kinh t-x hi hay y t. Dflng ca nhng bng nythng l cc c th hay cc quan st (c th c hngngn); cc ct l nhng dping thc ca bin. Chng tacng lu vic phn tch cc d liu vn bn ph hp vicc cu hi m mt phn cng da vo vic phn tch cctng ng p dng cho cc bng s ngu nhin t vng.

Phn tch theo thnh phn chnhPhng php Phn tch theo Thnh phn Chnh p dngcho cc bin c gi trfi l cc con s (cc s o, s phntrm, cc t...) biu thfi di dping mt bng o lng hnhch nht R v rij c cc ct l cc bin v cc dflng biuthfi cc c th m trn cc bin c xc finh. ychng ta xem xt bng 7 ch tiu nhn khu cho 7 nc(xem bng 2).

Din gii hnh hcCc biu din hnh hc gia mt bn l cc dflng (nc)v mt bn l cc ct (cc ch tiu) ca bng d liu chophp th hin cc ln cn gia hai c th (nc v giacc bin (ch tiu).

Trong Pp, hai im-c th (nc) rt gn nhau nu xt v

tng th cc ta p rt gn. Hai nc c lin quan cth hin bng cc gi trfi gn nh l bng nhau i vi mibin (ch tiu). Khong cch c s dng l khong cch-clt thng thng.

Trong Pn, nu cc gi trfi do hai bin (ch tiu) c th xc

finh rt gn nhau i vi mi nc, nhng bin ny sc biu thfi bng hai im rt gn nhau trong khnggian ny. iu ny mun ni rng cc bin o cng mti tng hay cc bin c mi lin h c bit.

Nhng cc n vfi o bin c th rt khc nhau v do vycn phi bin i bng d liu.

Vn thang chia v bin i cc d liu Ta mun khong cch gia hai c th (nc) c lp vicc n vfi ca bin (ch tiu) cc bin c vai trfl gingnhau. Mun vy, ngi ta gn cho mi bin j cng mtch s tn bng cch chiatng gi trfi ca bin cho lch chun sj, s lng mbnh phng (phng sai)c vit thnh:

Ngoi ra, bit c cch cc c th tch xa khigi trfi bnh qun, ta t im trung bnh vo trung tmca thfi cc c th. Topi ca im trung bnhchnh l gi trfi bnh qun ca cc bin c chmim s:


Ly im ny lm gc tcl tr i gi trfi bnh qunca mi bin j.

Nh vy, ta iu chnh cc thang ng thi bin bngd liu R thnh mt bngd liu X mi bng cchsau:

Cc bin tiu chun nh vy u c phng sai, s2(xj),bng 1/n v bnh qun, bng 0. Nh vy c th sosnh vai trfl cc bin vi nhau. Nh vy, phn tch cchun ho.

Phn tch tp hp cc c th (nc) Vic bin i d liu dn n vic tfinh tin gc topi titrng tm ca tp hp v thay i (trong trng hp phntch chun ho) t l trn cc trc.

phn tch tp hp cc im-nc trong Pp, ma trn X'Xcn biu din theo ng cho trong khng gian ny lma trn cc tng quan (bng 3 l mt v d) c cch tnhchung nh sau:

cjj l h s tng quan gia cc bin j v j'.

Cc topi ca n im-c th trn trc nhn t ua l nthnh phn ca vect ca = Xua.

Hnh 5a biu din thfi cc c th-nc trong mt phngchnh (1,2).

Phn tch tp hp cc bin (ch tiu)Cc topi nhn t waj ca cc im-bin trn trc a lthnh phn ca v ta c: waj = cor (j, ca).

Nh vy, topi waj ca mt im-bin j trn trc a chnhl h s tng quan ca bin ny vi ca (t hp tuyn tnh

ca cc bin gc) c coi l mt bin gi c ta chnh thnh t n ln chiu cc c th trn trc ny.

Do cc trc nhn t trc giao tng cp mt, ta thu cmt chui cc bin gi khng tng quan vi nhau cgi l cc thnh phn chnh1 tng hp cc tng quan caton b cc bin gc.

Trn hnh 5b, cng nh trn ma trn tng quan tngng (bng 3), tui th v t l bit ch ngi ln tngquan cht ch thun chiu vi nhau, tc giao nhau theocng mt chiu. Hai ch tiu ny cng tng quan chtch nhng nghfich chiu vi t l t vong tr em, cc gitrfi thp ca tui th (v t l bit ch ngi ln) tngquan vi cc gi trfi cao ca t l t vong tr em (vngc lpii).

Din gii Cc bin tng quan cht ch vi mt trc s gp phnxc finh trc2. Mi tng quan ny th hin trc tip trn thfi v y chnh l topi ca im-bin j trn trc a.

Ta quan tm trc ht ti cc bin c topi ln nht v tas gii thch cc thnh phn chnh trn c s kt qu phnt mt s bin v so snh vi cc bin khc.

Hnh 5a m t tp hp cc im-nc trn mt phng chnh(1,2). Lo v Cam-pu-chia gn nhau trn hnh ny v ilp vi cc nc khc.

Hnh 5b, biu din tp hp cc im-ch tiu cho chng tathy rng hai nc ny c t l t vong tr em cao v tuith v t l bit ch ngi ln thp; hai nc ny khc vicc nc khc c t l t vong tr em thp v tui th vt l bit ch ngi ln cao hn.

Ma-lai-xi-a (hnh 5a) ni ln vi Thu nhp bnh qun tnh theou ngi v T l dn thnh thfi cao (hnh 5b). So snh haihnh 5a v 5b cng cho thy dn s In--n-xi-a ng nht.

Ta s thy trong hnh biu din ny, tt c cc im-binnm trn mt phpim vi bn knh 1 hng vo gc cc trc3.Cc mt phng iu chnh s ct phpim vi ny thnh ccvflng trfln ln (bn knh 1), gi l cc vflng trfln tng quan,trong cc im-bin c xc finh vfi tr.

1 Phn tch theo cc thnh phn chnh ch th hin cc mi quan h tuyn tnh gia cc bin. Hai bin c h s tng quanthp c ngha l cc bin ny c lp tuyn tnh, trong khi c th c mt mi quan h phi tuyn tnh.

2 V d ny tt nhin khng pii din gii thch mt phng m ch nhm kt hp bng d liu v kt qu.3 Khng phn tch cc im-bin trong Pn so vi trng tm ca thfi (khc vi phn tch cc im-c th) m so vi gc cc

trc. Khong cch t mt j n gc O chnh l:


Bng 2: Bng 7 ch tiu dn s ca cc quc gia ng Nam

Bng 3: Ma trn tng quan

Hnh 5a: Phn tch theo thnh phn chnh trn bng cc ch tiu dn s ca ng Nam Biu din 7 quc gia trn mt phng (1,2).

Nhn xt Th d l tng tt c cc phn t kij ca bngs ngu nhin K (tc k= 198742 c th l dn s lao ng).

Ta c eij = kij/k l cc tn s tng i (th d cc t l phntrm trn ton b tng th) vi

l cc tn s cn bin tng i.


Hnh 5b: Phn tch theo thnh phn chnh trn bng cc ch tiu dn s ca ng Nam Biu din 7 ch tiu dn s trn mt phng (1,2).

Phn tch cc tng quanVic phn tch cc tng quan p dng trc ht vi mtbng s ngu nhin K, cfln c gi l bng phn tcho, c n dflng v p ct, phn b mt tng th theo haibin finh lng n v p dping thc. Nh vy cc dflng vct c vai trfl nh nhau.

V d xem xt bng s ngu nhin sau y c c bngcch phn b dn s lao ng theo khu vc hopit ngv theo vng tpii Php (xem bng 4).

Bng 4: Bng s ngu nhin giao nhau gia cc khu vc hopit ng v cc vng

v


Php ton ny a ra cc kt qu v d nh 1,2% dn slao ng ca vng Paris lm vic trong khu vc II, 31%dn s lao ng ca vng Ty-Nam lm vic trong khuvc II... Lm th no nh gi ngha ca mt con sc th trong bng trc ? Trn thc t, cc t l phntrm xut hin mi dflng phi c so snh vi t lphn trm ca dflng tng ng vi ton b nc Php,tc profile bnh qun.

Nh vy, t l 26,7% dn lao ng lm vic trong khu vcII tpii min Ty Nam nc Php ch c ngha khi em sosnh vi bnh qun ton quc l 14,7%: hopit ng nngnghip chim t trng rt ln tpii min Ty-Nam trong khichim t trng rt nh tpii vng Paris (1,2%) v n tngng vi ton b nc Php lc fia.

Ta quan tm n profile ca cc dflng v ta tm cc vngc t l phn b lao ng theo khu vc hopit ng cchxa t l phn b ca ton b dn s nht. Nhng ta cngtm cc dflng ging nhau hay i lp nhau nhiu nht.y l trng hp ca min Ty v min Ty-Nam cprofile kh ging nhau v rt khc so vi vng Paris. Dovy c th nhm min Ty v Ty-Nam vo thnh t.

Lu l c s khc bit quan trng gia phng phpphn tch cc tng quan v phng php phn tch theocc thnh phn chnh: cc php bin i tin hnh trncc dflng v cc ct ca bng l ging nhau (v cc tphp c cc tng ng vi nhau ng vai trfl nh nhau):khng c cc bin v c th m l cc tp hp theo dflngv theo ct).

Gi thuyt c lp Vic lin kt gia hai bin finh tnh chnh l xem liugia hai bin ny c s c lp vi nhau hay khng. Tabit l gia hai bin bin i c s c lp nu nh vimi i v mi j: ij = i x j

Ta c bng cc tn s quan st c (xem bng 6), tcbng cc t l phn trm tnh trn ton b s dn: ij = kij/k.

Trong s 21,5% lc lng lao ng ca vng Paris, theogi thuyt v s c lp ta s thy 14,7% lc lng laong lm vic trong khu vc I (tc chim 3,2% ton blc lng lao ng, thay v 0,3% thc s quan st c),39,1% lc lng lao ng lm vic trong khu vc II (s l8,4% thay v 8,9%)...

Bng {cc tn s l thuyt} (xem bng 7) ij = i x j thhin gi thuyt hai bin c lp vi nhau. Gi thuyt nycng c th hin trn cc profile-dflng. Trn thc t, vimi j, ta c kt qu: ij/i =j.Nu tt c cc profile {Vng}ging nhau v nh vy ging vi profile bnh qun tngng th gia vng v khu vc hopit ng c s c lp dovic bit n vng khng lm thay i s phn b cc khuvc hopit ng. Cng tng t nh vy i vi cc profile-ct vi bt k i ta c:ij/j = i:

Bng s ngu nhin K mt mt c bin i thnh bngprofile-dflng (cc t l phn trm theo dflng) (xem bng 5.a)

v mt khc thnh bng profile-ct (cc t l phn trm(xem bng 5.b).

Bng 5.a: Bng cc profile-dflng Bng 5.b: Bng cc profile-ct

Bng 6: Bng cc tn s quan st c

Do , xem xt cc yu t ln cn gia cc profile tc lxem xt s ln cn gia tng profile vi profile bnh qun,iu ny cho php nghin cu mi lin h gia hai binfinh tnh, tc mc c lp.

Trn mt bng ln, rt kh c trc tip cc profile-dflngv profile-ct cng nh so snh cc profile ny vi profilebnh qun. Do vy, ta phi tin hnh phn tch cc tngng.

Khong cch bnh phng v phn b tng ng Bng d liu d gii thch trc chng t vic la chncc profile biu thfi mt dflng l ph hp. By gi chngta tm cch lng t ha s ging v khc bit gia haivng, tc tnh ton khong cch gia profile ca chng. tm ra s chnh lch gia hai profile, mt mt ta sdng khong cch ca x2 gia hai im-dflng i v i' v mtkhc gia hai im-ct. Nhng khong cch ny l ktqu ca cc phng trnh sau:

Khong cch ca x2 cho php kim chng nguyn tcphn b tng ng. Nguyn tc ny m bo s chcchn ca kt qu phn tch cc tng ng khi phn tchmt cch ch quan theo dping thc. Ni dung ca nguyntc ny l: nu hai dflng (hoc hai ct) ca bng s ngunhin c cng profile (t l vi nhau) th vic kt hpchng khng tc ng ti khong cch gia cc ct (hoc

dflng). Khi ta thu c mt im-dflng mi (hoc im-ct mi) c profile tng t v c coi l tng cc tn sca hai im-dflng (hoc hai im-ct).

c tnh ny quan trng do n m bo cho cc kt qubt bin so vi danh mc c la chn xy dng ccdping thc ca mt bin finh tnh.

Biu din hnh hc bng d liuChng ta hy xem xt bng profile-dflng. Biu din bnghnh hc bng ny bng cch gn vi mi dflng ca bngl mt im i trong khng gian cc ct P

pc topi l ij/i

vi mi jd p. (Tng t nh vy vi im j ca Pnc topi

l ij/i vi mi i d n).Vi mi im ta gn mt trngbng vi tn s ca dflng.

Ln cn ca hai im i v i' trong khng gian Pp

c tnhn s ging nhau gia profile ca dflng i v i'. Nh vy,trong trng hp bng cc khu vc hopit ng, ta c:

V d vng Paris c xc finh trong khng gian cc khuvc hopit ng bi cc topi (1,2; 41,4; 57,4), min Tybi cc topi (30; 29,8; 40,2) v min Ty-Nam bi cctopi (26,7; 31; 42,3). Profile ca cc min Ty vTrung-Ty l gn nhau. y l nhng vng c s phnb cc khu vc hopit ng ging nhau v rt khc so vivng Paris khin cho cc vng cch xa nhau.

Mi quan h chuyn tip v biu din ng thi i vi trng hp bng s ngu nhin, mi quan hchuyn tip lin kt cc trc c tnh ton trong haikhng gian (khng gian im-dflng v khng gian im-bin), th hin mi quan h trng tm vi h s. Topi ca dping thc i ca mt trong nhng bin l bnh quncc dping thc j ca mt bin khc c iu chnh h sbng cc tn s iu kin ca profile i. Tng t, miquan h chng t topi ca dping thc j l bnh qun ca


Bng 7: Bng cc tn s l thuyt

Hnh 6: thfi profile-dflng (Cc Vng)


Cc yu t tr gip cho vic gii thchBa chui h s cung cp thng tin b sung bn cpinh ccta nhn t:- Cc t trng ng gp, cfln gi l t trng ng gp

tuyt i, l phn ca mt dping thc ca bin trongqun tnh (hay phng sai) {c gii thch} bi mtnhn t. H s ny cho php xc finh cc dping thcc ng gp vo vic hnh thnh v xc finh nhn t.i vi cc phn t b sung, h s ny bng 0.

- Cc bnh phng cosin, cfln gi l t trng ng gptng i hay cht lng biu din, l phn ca nhnt trong ch s tn ca mt dping thc ca bin. H sny hu ch i vi cc phn t b sung.

- Cc gi trfi-kim finh cho php nhanh chng nh gixem mt dping thc ca bin finh danh c vfi tr quantrng trn mt trc hay khng. Cc gi trfi-kim finhny c chc nng ging bnh phng cosin nhng dhiu hn.

Ch sau khi xem xt cc h s ta mi c th gii thch cc thfi nhn t ng thi c tnh n cc mi quan hchuyn tip.

Phn tch cc a tng ng

Phng php phn tch cc tng ng c gii thiu chng bn trn c th c p dng rng ri trongtrng hp c hn hai bin c t tng ng vi nhau.Vic ny dn n vic phn tch cc a tng ng ccho l rt ph hp m t cc bng bin finh tnh ln,cc b phiu iu tra l nhng v d tiu biu v cc bnglopii ny.

Bng phn tuyn ton din Mt kha cpinh quan trng ca phng php ny l vicxy dng mt bng d liu tp trung vo vic m ho lpiicc bin.

Bng d liu {th} R, tc l bng d liu di dping mha rt gn, c th c coi nh kt qu mt bng hinhm tm cu tr li ca cc c th cho cc cu hi (xemhnh 8). Nhng mt bng s liu nh vy khng khai thcc: cc tng theo dflng v ct khng c ngha. Do vycn phi m ho lpii cc bin. Vic m ho phn tuynton din cho php ng nht cc d liu gm cc bin

Hnh 7: Mt phng nhn t u tin phn tch bng s ngu nhin Vng v khu vc hopit ng

tp hp dping thc i c iu chnh h s bng cc tn siu kin ca profile j.

Cc mi quan h chuyn tip tpio c s cho vic biu dinng thi cc dflng v cc ct. Thc vy, nu cc phngphp nhn t da trn vic tnh ton khong cch giacc im-dflng v khong cch gia cc im-ct,khong cch gia mt im-dflng v mt im-ct khngc ngha v nhng im ny nm trong cc khng giankhc nhau. Tuy nhin vic phn tch cc tng ng gipta c th finh vfi v gii thch mt im ca mt tp hp

lin quan n mt khng gian so vi tp hp cc imkhc c xc finh trong khng gian khc.

Hnh 7 minh ha vic biu din ng thi cc vng caPhp v cc khu vc hopit ng. Cc vng min Ty chopit ng nng nghip chim t trng rt cao cfln vngParis v vng ng-Nam l cc hopit ng dfich v, vngpha ng v vng pha Bc nc Php l cc hopit ngthuc khu vc II. Profile ca vng lflng cho Paris (gnvi trng tm ca thfi) tng ng vi kt qu phn bcc khu vc hopit ng trn ton nc Php.


Cc bin theo dflng cabng phn tuyn ton dinc finh v bng s lng scu hi:

Cc bin theo ct tngng vi s lng ccch th la chn dpingthc j ca cu hi q:

Ta kim tra sao cho i vimi bng con Zq, s lngtng l ng:

Tng cc bin chnh ltng s z ca bng Z hay

Nguyn tc phn tch cc a tng ngPhn tch cc a tng ng chnh l phn tch cc tngng ca mt bng phn tuyn ton din. Nguyn tc caphng php phn tch ny chnh l nguyn tc caphng php phn tch tng ng, tc:- cng bin i bng d liu thnh profile-dflng v

profile-ct;- cng tiu ch iu chnh vi vic iu chnh cc im

1 Mt bin finh lng c th c bin i thnh mt bin finh tnh bng cch phn t cc gi trfi ca bin. Mi t tng ngvi mt dping thc.

Hnh 9: Phn tch cc a tng ng

bng profile cn bin;- cng khong cch, tc khong cch x2.

Tuy nhin phng php phn tch cc a tng ng cnhng c tnh ring do bn cht ca bng phn tuynton din.

finh tnh hay finh lng1: cc dping thc tr li lopii tr lnnhau, v bt buc phi chn ra mt dping thc.

Coi I l tp hp cc n c th tr li bng hi v coi p ltng s cc dping thc ca scu hi. Ta c trong pq l tp hp cc dping thc ca mt cu hi. Ta xy

dng bng phn tuyn ton din Z (xem hnh 8) sao chozij = 1 hay zij = 0 tu theo vic c th i l a chn dpingthc j ca cu hi q hay khng. Vic m ho mang tnhphn tuyn v cc dping thc ca cng mt bin lopii tr lnnhau v vic m ho l ton din v bt buc mt c th phi tr li mt cu hi.

Hnh 8: Xy dng mt bng phn tuyn ton din Z


Khong cch gia cc profile Khong cch Chi - bnh phng p dng cho bng phntuyn ton din c mt ngha:

Khong cch gia hai dping thc c m t nh sau:

Hai dping thc c chn bi cng cc c th th trng hpvi nhau. Ngoi ra, cc dping thc c s lng nh bfi lchtm so vi cc dping thc khc. Khong cch gia hai c th c m t bng:

Hai c th gn nhau nu c cng dping thc. Hai c thcch xa nhau nu khng tr li ging nhau.

Lu l dping thc j no cng tc ng nhiu ti victnh ton khong cch gia hai c th th khi ca nthp. Mt dping thc him c th hnh thnh nhng tphp nh gm mt lng hpin ch cc c th lch tm vicc c th khc.

Mi quan h trng tm v biu din ng thi Mi quan h trng tm c th hin qua vic: 1) mt c th trng tm cc dping thc m c th

la chn (vi cng gin n) ; 2) mt dping thc c chiu ln trng tm cc c th

la chn dping thc ny (vi cng gin n).

Tp hp cc dping thc trong Pn c th tch thnh s tphp nh, q ln tng ng vi tp hp cc pq dping thcca bin q. Cc tp hp nh ny c cng trng tm G ltrng tm ca ton b tp hp cc im.

C mt cch n gin biu din tp hp cc dping thct tp hp cc c th. Gi thit c mt tp hp cc c thvi hai c trng, a v b c ln lt 2 v 3 dping thc. Thayv biu din trong khng gian nhn t cc c th vnthng khuyt danh v ta ch quan tm n c trng cachng ( tui, gii tnh, hay mt thuc tnh no ), thnn xc finh vfi tr cc trng tm ca cc nhm c thtng ng vi cc thuc tnh ca chng (nam gii, n gii, tui,...).

Nh vy khi xc finh trc tip tng c th trong thfibng cc cu tr li ca c th cho hai cu hi v tip xc finh vfi tr cc im bnh qun cc c th la chncc dping thc ging nhau, ta thu c hai kt qu phnb nh sau cho tng cu hi (xem hnh 11). Khi t hai

thfi chng ln nhau v vi cng mt gin n, ta cc s phn b ca cc dping thc (xem hnh 12).

Cc quy tc gii thch Nu ni rng gia cc cu tr li c s tng ng tccho rng c cc c th ng thi la chn tt c hayhu nh ton b cc cu tr li ny.

Vic phn tch cc a tng ng lm r cc lopii c th chin trping ging nhau v cc thuc tnh m t chng.Do khong cch gia cc phn t ca bng phn tuynton din v mi quan h trng tm c bit, ta th hin - s gn k gia cc c th v mc ging nhau:

Hai c th ging nhau nu h la chn cc dping thcging nhau.

Hnh 10: Phn b cc c th trong phn tch bng phn tuynton din

Hnh 11: Xc finh cu tr li cho hai cu hi a v b trong phnb cc c th

Hnh 12: Phn b cc dping thc cho hai cu hi a v b


- s gn k gia dping thc cc bin khc nhau v skt hp:Cc dping thc ny tng ng vi cc im trung bnhca cc c th la chn chng v gn nhau v ccdping thc ny nhn chung lin quan n cng cc cth hay cc c th ging nhau.

- s gn k gia hai dping thc ca cng mt bin vmc ging nhau:Cc dping thc ca cng mt bin lopii tr nhau. Nucc dping thc ny gn nhau, s gn k c gii thchnh mc ging gia cc nhm c th la chncc dping thc ny (so vi cc bin khc c tc ngca vic phn tch).

- Cc quy tc gii thch cc kt qu (topi , mc ng gp, bnh phng cosin) lin quan n ccphn t tch cc ca phng php phn tch atng ng thng ging vi cc quy tc p dng chophng php phn tch cc tng ng n gin. Tatnh ton mc ng gp v cht lng biu dinca tng dping thc v ca tng c th nu nhnhng c th ny khng khuyt danh khi phn tch.Ngc lpii, cc quy tc gii thch cc gi trfi ring vt l qun tnh s khc.

Cc phn t b sung Vic s dng cc phn t b sung trong phn tch cc atng ng cho php xem xt tt c thng tin c th h trcho vic hiu hay phn tch cc lopii hnh theo cc phnt ng.

iu ny c bit c ch khi tp hp cc bin c phnra theo ch , tc phn thnh cc nhm bin ng nhtv mt ni dung.

Khi phn tch bng phn tuyn ton din, ta s ccphn t b sung tc ng vo :- lm phong ph thm kt qu gii thch cc trc bng

cc bin khng tham gia vo vic hnh thnh cc trcny. Khi ta s chiu vo khng gian cc bin trngtm cc nhm c th c xc finh bi cc dping thcca cc bin b sung.

- p dng cch d bo bng cch chiu cc bin bsung trong khng gian cc c th. Cc bin b sungny s c {gii thch} bi cc bin ng. Ta c thchiu cc c th b sung vo khng gian cc bin finh vfi cc c th ny so vi cc c th hay nhm cth ng phn bit chng vi nhau.

Ty theo l cc bin b sung, finh danh hay lin tc,s c gii thch khc nhau v trfi tr ca bin trn cc trcnhn t.

Phng php phn lopiiCc k thut phn lopii t ng nhm cc i tng hayc th c m t bi mt s cc bin hay c tnh. Bicnh s dng cc k thut ny cng tng t nh khi s

dng cc phng php phn tch nhn t mang tnh chtm t c gii thiu cc mc trc .

C nhiu lopii thut ton phn lopii: thut ton phn cpphn hopich cc i tng theo trt t tng dn v ccthut ton phn hopich trc tip nh cc phng phpgp xung quanh cc tm di ng. Nguyn tc chung chocc k thut phn lopii theo trt t tng dn ny kh ngin. Gi s khng gian P

pcha n im-c th c mt

khong cch ph hp c gi l d (thng l khongcch -clt thng dng hoc khong cch x2) v tpii migiai opin ca thut ton tpio ra mt kt qu phn hopichbng cch gp tng i mt cc phn t gn nhau nht.

Tp hp xung quanh cc tm di ng Phng php ny c bit hu dng i vi cc tp dliu in t ln v cc d liu c x l trc tip cho phps dng mt cch tt nht cc c tnh ca vic m hod liu, gip gim thi gian tnh ton trong trng hp mho phn tuyn.

V d cn phn hopich mt tp hp I gm n c th c pc im hay bin. Ta mun hnh thnh mt cch ti aq t. Cc giai opin ca thut ton c m t tpii hnh 13.

- Giai opin 0: Ta xc finh q tm ca t tpim thi (v dbng cch chn mt cch ngu nhin m khng aq c th vo lpii tng th cn phi phn lopii). Cc qtm: {C1

0,..., Ck

0,..., Cq

0} tpio ra phn hopich u tin P0

ca tp hp cc c th I trong q t hp: {I1

0,...,Ik

0,..., Iq

0} . Nh vy, c th i thuc v nhm nu c

th ny gn hn so vi cc tm khc. - Giai opin 1: Xc finh q tm t mi:

{C11,..., Ck

1,..., Cq

1} bng cch ly trng tm ca

cc t hp va c c: {I10,...,Ik

0,..., Iq

0} . Cc tm

mi ny tpio ra mt phn hopich mi P1 ca I chnh thnh theo cng mt quy tc nh i vi P0.Phn hopich P1 c hnh thnh t cc t hp c khiu: {I1

1,...,Ik

1,..., Iq

1}.

Hnh 13: Cc giai opin ca thut ton


- Giai opin m: Xc finh q tm t mi: {C1m,..., Ck

m,..., Cq

m}

bng cch ly trng tm cc t hp c c t giaiopin trc , {I1

m-1,...,Ik

m-1,..., Iq

m-1} . Cc tm mi ny tpio

ra mt phn hopich mi Pm ca tp hp I c hnhthnh t cc t hp: I1

m,..., Ik

m,..., Iq

m}.

Qu trnh ny cn phi n finh v thut ton kt thc khihai ln lp lpii lin tip em lpii cng mt kt qu phnhopich, v d nh khi mt tiu ch c la chn mt cchph hp (v d o phng sai ni b t hp) ngng gimmt cch ng k, hay v d khi mt s lng ti a cctrng hp lp lpii c xc finh t trc. Nhn chung,kt qu phn hopich ph thuc vo s la chn ban ucc tm.

Phn lopii theo trt tThut ton c bn phn lopii theo trt t tng dn tpiora th t trn c s phn hopich theo mi phn t cnphn lopii tpio thnh mt t hp, c th tpio ra cc phnhopich ch gm duy nht mt t hp cha tt c cc phnt. Khi coi cc c th hay i tng cn phn lopii lphn t v tp hp cc c th c tpio ra t thut ton. giai opin u, nh vy c n phn t cn phi phn lopiil n c th. Ta lp ma trn khong cch gia cc n phnt v tm hai phn t gn nhau nht v gp thnh mtphn t mi. Ta lp mt ma trn mi ca cc khong cchc c t vic gp, ng thi tnh ton khong cch migia phn t mi v cc phn t cfln lpii. Cc iu kinging nh trong giai opin 1 nhng ch vi (n-1) phn tcn phn lopii, ta tip tc tm hai phn t gn nhau nhtv gp chng lpii. Ta lp lpii qu trnh ny cho ti khi chcfln duy nht mt phn t tp hp tt c cc i tng vhnh thnh nn phn hopich cui cng. Vi n phn t cnphn lopii th thut ton gm n giai opin.

Chng ta minh ha qu trnh ny bng cch ly 5 iml i tng phn lopii (hnh 14).

Thut ton khng tpio ra kt qu phn hopich gm q tca mt tp hp n i tng m tpio ra mt trt t cc phnhopich, c hnh cc cy cfln gi l lc hnh cy vcha n-1 phn hopich (xem hnh 15). Li ch ca cc lc hnh cy ny l chng cho ta bit s lng cc t hinc trong tng th. Mi mt opin ngn ca lc hnhcy tpio thnh mt phn hopich.

Tiu ch gp Tpii mi giai opin xc finh, hai t hp c gp thnh mtt hp nu nh chng gn nhau. Hai phng php nyda trn tiu ch gp theo phng sai.

Qun tnh ca m phn b (tc phn tn ca n) ltng khong cch c iu chnh tt c cc im tpiitrng tm G. Qun tnh ny phn thnh qun tnh gia cct v qun tnh ni b t (xem hnh 16).

Tpii giai opin gc, qun tnh ni b t hp bng 0 v quntnh gia cc t hp bng vi tng qun tnh ca mphn b bi v mi phn t cui khi tpio thnh mt thp mi. Tpii giai opin cui cng, chnh qun tnh gia cct hp bng khng cfln qun tnh ni b t tng ngvi tng qun tnh bi v khi ta c c kt qu phnhopich thnh mt t hp duy nht (xem giai opin 5 ca hnh 14).

Do , ta cng gp th qun tnh ni b t hp cng tngcfln qun tnh lin t hp cng gim. Nguyn tc caphp ton gp theo phng sai l tpii mi giai opin tm ramt phn hopich ni phng sai ca mi t thp nhtv do vy phng sai gia cc t cao nht.

Chin lc ny cho php tnh ton sao cho thu cmt {phn hopich hiu qu} (xem hnh 17) nhngkhng c g ch ra rng ngay lp tc ta c th pit cphn hopich hiu qu nht c th vi mt s lng tnht finh.

Hnh 14: Ln lt gp 5 im

Hnh 15: Lc hnh cy hay cy phn lopii theo trt t


Thut ton kt hpCc thut ton s dng phn lopii ph hp vi vicqun l mt s lng ln cc i tng cn phn lopii. Ccphng php phn hopich (gp cc t xung quanh cctm di ng hay bn t t chc) c nhng u th khngth ph nhn v cc phng php ny cho php pit cmt phn hopich trn mt tng th s cc d liu vichi ph thp, tuy nhin c im bt li l cn phi xc finht trc s lng cc t v tpio ra cc phn hopich phthuc vo cc tm c chn ban u. Ngc lpii, phnlopii theo trt t l mt lopii thut ton c th coi l {c tnhxc finh} (v d cc d liu ging nhau lun tpio ra cc ktqu ging nhau). Tuy nhin, nu cc thut ton em lpiinhng ch dn v s lng cc t cn phn lopii th lpiikhng ph hp vi lng d liu s. Do , ngi tathng s dng phng php phn lopii kt hp tp hpcc im mpinh ca hai phng php phn lopii.

M t t ng cc t hp Khi nim t hp mang tnh trc gic: y l tp hp cc

phn t ging nhau v tiu ch la chn. Cfln lpii l cnphi bit cc tiu ch ca vic phn t ny. Do vy ta chom t t ng cc t hp v y l giai opin cui cngkhng th thiu c trong mi quy trnh phn lopii1.

Cc yu t tr gip cho vic gii thch cc t thng datrn vic so snh cc kt qu trung bnh hay t l phntrm cc bin trong cc t vi trung bnh v t l phn trmc c trn tp hp cc phn t cn phn lopii.

chn ra cc bin lin tc hay cc dping thc ca cc binfinh danh tiu biu nht cho mi t hp, ta tin hnh o lch gi a cc gi trfi lin quan n t hp v cc gi trfi tngth. Cc kt qu thng k c th c chuyn i thnhmt tiu ch gi l cc gi trfi-kim finh kt hp, da theotiu ch ny ta tin hnh l a chn cc bin. Cc bin cngc ngha khi cc gi trfi-kim finh ln tnh theo gi trfi tuyti2.Do vy ta c th sp xp cc bin theo cc gi trfi-kimfinh gim dn v ch l a chn cc phn t ln nht, iuny gip xc finh rt nhanh chng c im cc t hp.

Hnh 16: S phn tch qun tnh theo quan h Huygens

Hnh 17: Cht lng tng th ca mt phn hopich

1 Tt nhin, ta s tnh gi trfi trung bnh i vi cc bin finh lng v t l phn trm i vi cc bin finh tnh. 2 Mt gi trfi-kim finh c ngha mc thng thng 5% nu n vt qu gi 1,96: gi thuyt {bng khng} bfi bc b v

gi trfi trung bnh hay t l ca mt bin trn tng th hay trong t khc nhau mt cch r rt.


Trong s cc bin cfln c cc bin khng ng gp vovic hnh thnh cc t hp nhng lpii c th tham gia vovic m t chng theo nguyn tc ging nh nguyn tcp dng i vi cc bin b sung trong phn tch nhnt. Cc bin ny sau cho php xc finh v lm rc tnh cc phn t c la chn v c hnh thnht cc bin ng.

Tnh b sung ln nhau gia phng php nhn t vphng php phn lopii Hai nhm phng php nhn t v phn lopii cho phplm sng t cc d liu mt cch khc nhau. Trong trnghp ny th c th p dng cc k thut lin tc nh vicchiu ln mt tiu khng gian chnh lm cc bin n xuthin, cfln trong trng hp khc l cc k thut ngtqung tpio ra cc nhm c th ng nht v tiu ch lachn m t. a ra cc kt qu ging nhau nhng haiphng php ny c cch thc khai thc d liu, khai thccc yu t thng tin v cch hin thfi kt qu khc nhaumt cch cn bn.

Do vy, tnh b sung cho nhau gia phng php phntch nhn t v phng php phn lopii th hin khi tmhiu kt cu d liu v cc yu t tr gip trong giai opincui cng l gii thch cc kt qu. Rt nn kt hp sdng hai phng php ny c th m t mt cch tondin mt tp hp phc tpip cc d liu.

Chin lc x l d liu cc cuc iu traMc ch ca mc ny l xut mt chin lc khai thcd liu iu tra gm 3 giai opin:- chun bfi bng d liu ch yu gm vic m ho cc

bin v kt cu cc d liu theo cc ch iu tra. - kt hp s dng phng php giai tha v phng

php phn lopii bng cch pht huy tnh b sung lnnhau ca hai phng php ny. i vi cc d liuiu tra kinh t, x hi, ch yu ta s p dng phngphp phn tch cc a tng ng vn rt thch hp chovic phn tch cc bng hi.

- vic gii thch v bnh lun cc kt qu gn nh nhtthit fli hi phi xem xt lpii cc d liu hoc iuchnh m ho hoc xc finh cc ch mt cchtt hn hoc lopii b mt s tc ng ca mt s bin.

M ho y chc chn l giai opin phc tpip nht v c bn nht tpio ra cc kt qu ng b. Tuy nhin, kh c th giithiu cc k thut m ho do ch l cc thao tc thcnghim ph thuc qu nng n vo k lut trin khai chngv vn c x l . i vi vic x l cc d liu iu trakinh t, x hi, chng t i ch c th nhc lpii mt vi quy tclin quan n vic m ho phn tuyn ton din.

Ba nguyn tc chnh finh hng cho giai opin m ha: - Hnh thnh cc t hp c s lng tng i bng

nhau v trnh cc dping thc c s lng hpin ch:

thng th cc dping thc him, do vy t lin quan ncc c th, t mnh tpio ra cc nhn t u tin phntch. Do vy, nhng nhn t ny m t cc hin tngmang tnh finh k v thng c ch khi rt ra cc hintng bao qut hn. i vi cc bin finh lng, rtc li khi tnh n cc ngng c c nh vic xemxt lc hnh trfln (khng nn phn ct thnh t ccbin bng nhau). Tuy nhin, vic la chn cc cncfln ph thuc vo vn cn x l v c th tn tpiimt hay nhiu ngng xem xt khi tpio lp cckhong.

- Phn tch cc bin sao cho c cng mt lng dpingthc: mt bin cng ng gp nhiu vo vic hnhthnh cc trc nu c cng nhiu dping thc. Do vy, mi bin c th tc ng mt cch tng t nhnhau th cc bin phi c phn tch thnh mt slng tng ng vi s lng dping thc. iu nyc ngha l bin {gii tnh} s lun c hai dping thc vkhng phi lc no cng nn gn s lng dping thcny cho cc bin khc.

- V mt lng khng qu ln cc dping thc: ci mngi ta ngh rng c c v mt thng tin khi tinhnh phn tch khng nht thit c th hin trongphn tch. Vic phn tch nh vy tpio iu kin thunli cho vic xut hin cc nhm c s lng thp vnh chng ta bit, c th c tc ng gy ri chovic phn tch.

Do vy, nn xy dng cc bin khng c qu nhiu dpingthc c th c c thng tin chnh ngay trn ccnhn t u tin.

Cc hopit ng phn tch nm trong qu trnh lp i lplpii nhm hng ti vic bit c thng tin c bn. fli hica ngi s dng tng ln khi ngi ta bit c cngnhiu v ch ca mnh. Cn phi cho cc bin c bngiao nhau, tp hp cc dping thc ca cc bin khc, chimt s bin lin tc thnh cc t, tc l chun bfi cc dliu c th tin hnh phn tch mt cch k cng hn.

Lm vic theo ch Cc cu hi ca mt cuc iu tra kinh t, x hi c thc nhm theo t nht l hai ch . Cng trnh nghincu c th cp mt ch , thm ch l nhiu ch nu cuc iu tra nhm nhiu mc ch v cc c imkinh t x hi ca cc i tng iu tra c thu thp(nh gii tnh, tui, trnh hc vn) hnh thnh nn {hs nhn dping}.

Mt nguyn tc a ra l lm vic theo ch chkhng ch theo cc bin, mt ch c finh ngha nhmt b ng nht cc bin v mt ni dung.

Thc vy, khong cch gia cc c th hay cc quanst thc s c mt ngha, cc bin ng dng tnhton cc mt phng nhn t, phi tpio thnh mt tp hpng nht v mt ni dung. S l vng v nu nh v d


trn ln cc thng tin v kinh t-x hi (tui, gii tnh, nghnghip...) vi cc quan im v cc hnh vi ng x. Lmth no gii thch mc ln cn gia hai c th? Nuhai c th cch nhau rt xa, liu c phi do quan imca chng khc nhau hay do chng c cc c im kinht-x hi i lp nhau?

Cn lu rng vic phn tch khai ph ch gip xcfinh vfi tr ca cc d liu trn c s la chn cc phnt ng.

Vic finh vfi cc bin b sung gip lm phong phthm kt qu gii thch cc lopii thfi do cc bin ngxc finh nn.

Vfi tr u tin ca mt bin khng tham gia vo vic phntch ch c ngha bng chng: do khng gp phn vovic xy dng trc nn ta c th chc chn gii thch mitng quan ca bin vi trc . Tp hp cc bin bsung hon ton khng nht thit phi ng nht. Thmch nu tp hp ny cng rng th cng tt. Nh tngkh nng pht hin cc bin c th gip gii thch cc trc. Trong thc t, iu kin b sung ny s dn ti vic xemxt nhiu nhm ng nht cc bin, mi nhm thuc vcng mt ch ca cuc iu tra nhm m t cc cth xut pht t mt quan im duy nht.

Kt hp cc phng php Tnh b sung ln nhau gia phng php phn tch nhnt v phn lopii theo trt t tng dn hon ton c gi trfii vi vic khai thc k nhng bng d liu c nhn s nh cc bng kt qu cc cuc iu tra. Phng phpphn tch nhn t rt ph hp vi bi cnh ny, nht lphn tch cc a tng ng, lpii khng phi lc no cng em lpii mt ci nhn ton din v cc d liu v ikhi cc kt qu qu phc tpip nn khng d dng giithch. xc finh hnh th cc im c c fli hi phitng hp su hn. Khi cc k thut phn lopii gip bsung v cng c thm cc phn tch nhn t trc . Sdng ng thi hai k thut ny c tin hnh nh sau(xem hnh 18)

Giai opin 1: Phn tch nhn t v la chn mt ch {ng}Phn tch nhn t c s dng nh mt giai opin tinquyt khng th thiu cho vic phn lopii v hai l do sau:th nht phng php ny cho php t chc v xc finhkt cu ca c s thng tin bng cch la chn nhngmi quan h mang tnh quyt finh gia cc bin gc vt chc thng tin theo th bc, th hai phng php nys h tr cho vic phn lopii.

Ngoi ra, cn phi la chn mt ch , tc l mt bng nht cc bin ng, xc finh cch nhn nhn c thkhi tin hnh m t. Ta c th m t cc c th xut phtt cc c im c bn ca chng hay t mt ch cth tu theo ni dung cuc iu tra nh thi quen tiu

dng, quan im chnh trfi... Vic la chn u phi c ldo. Cc bin khc c coi l cc phn t b sung.

Giai opin 2: Phn lopii kt hp t cc nhn t Phn lopii cc c th trn mt tp hp p bin hay trn tphp cc p nhn t l tng t nh nhau. Trong c haitrng hp, ta u thc hin trong khng gian a chiu.Nhng ta cng c th ch xt n mt tiu khng giannhn t chiu q (q


Giai opin 4: finh vfi cc t hp trong mt phng nhn tNh vy, mi kt qu phn tch nhn t u c b sungbng cc phn lopii v cc t hp c xc finh t ngnh vic lm r cc c im thng k trn cc bin gc.Nhng i khi vic xy dng cc t hp dn n vic phntch tu tin mt khng gian lin tc. Khi vic phn tchcc tng ng cho php lm r vfi trfi tng i ca cc thp trong khng gian v lm ni bt trong khng gian nymt s bin thin lin tc c th bfi n i do cc t hpkhng lin tc. Do vy, s c li khi a cc trng tm cct gm cc c th c c vo cc bin hay cc dpingthc ng trn mt phng nhn t u tin. Nh vy,phng tin h tr hin thfi ny cho php nh gi khongcch gia cc t. Ngoi ra, vfi tr ca mi c th c nhdu bng s ca t hp cho php biu din mt v phn tn ca cc t trn mt phng. minh hopi vfi trca cc t hp trn mt phng nhn t, y chng taxem xt mt phn hopich ca tp hp cc c th gm 3t hp.

Giai opin 5: Gii thch, bnh lun v quay tr lpii xem xtcc d liu v m ho Gii thch cc kt qu pit c tc tm ra ngha ca cc thfi c c, nh gi gi trfi ca chng v t chng votrong mt bi cnh c th. Nh vy, khi nim kt qu phic nhn nhn nh mt thng tin mi.

Vic ng thi s dng phng php phn tch nhn tv phng php phn lopii khng ch cho php nh gihin trping cc t hp m cfln nh gi vfi tr tng i, mt v phn tn ca chng.

Cht lng thng tin v gi trfi cc kt qu Phn tch d liu l mt cng c in hnh gip kimsot cht lng cc cuc iu tra v ca thng tin nichung. Cc phng php ny trc ht cho php png d dng cho cc vn quan trng nh pht hincc sai s ca c s d liu, nhng sai st mang tnhh thng do iu tra vin gy ra hay vic x l cc phnkhng c cu tr li, nhng vn m cc cn bthng k thng gp phi v cng kh gii quyt theomt cch khc. - Pht hin sai s: Pht hin cc gi trfi sai lch hay

nhm ln l mt kt qu ph rt quen thuc vi cccn b thng k c s dng cc k thut phn tchnhn t: nhng bt thng n du trong cc con sthng d dng pht hin c trn cc mt phngnhn t vn l cc kim finh v s ng b tng th.Nhng kt qu phn tch nhn t u tin thng pht hin cc sai s trong c s d liu.

- finh vfi cc bin k thut: ta cng c th bnh lun vcc d liu bng cch cho xut hin vi t cch l ccphn t b sung, trn cc mt phng nhn t haytrong cc t ca mt phn hopich, cc {bin k thut}nh: s th t hay tn ca iu tra vin, cc c imca iu tra vin, fia im v thi gian phng vn,nh gi ca iu tra vin hay ngi tham gia iu trav cuc phng vn... Hnh di y xc finh thi imdin ra phng vn v tui ca cn b iu tra. V d,im {phng vn vo ban ti} l trng tm ca nhngngi c phng vn vo ban ti. Nh ta cc bc tranh ton cnh v qu trnh sn xut thngtin, cho php kt hp bi cnh cc cuc phng vnvi c im nhng ngi tr li phng vn.

Ngoi vic gip kim sot cht lng cc d liu v cccuc iu tra, nhng phng php kho st ny chophp nh gi gi trfi ca cc d liu c s v lm susc thm vic gii thch cc kt qu. Cc phng phpthc chng khc (v d phng php Bootstrap), thngqua vic tnh ton n finh v nhpiy, cng cho phpxc nhn gi trfi kt qu ca cc phn tch nhn t vcc kt qu phn lopii.

Ti liu tham kho Greenacre M. (1993) - Correspondence Analysis in

Practice. Academic Press, London. Lebart L., Piron M., Morineau A., (2006) - Statistique

exploratoire multidimensionnelle. Dunod, Paris. Saporta G. (1990) - Probabilits, analyse des

donnes et statistiques. Technip, Paris.

Hnh 19: finh vfi cc bin k thut


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