Chng 5:

HI QUI A BIN

Phng php hi qui a bin l k thut a bin c dng rng ri trong phng thi nghim ho hc gip gii quyt cc bi ton xc nh ng thi nhiu cu t cng c mt trong hn hp m khng cn tch loi trc khi xc nh. V nguyn tc ch cn xy dng dy dung dch chun c mt tt c cc cu t cn xc nh vi nng bit trc trong hn hp (cc bin c lp x), o tn hiu phn tch ca cc dung dch ny di dng mt hay nhiu bin ph thuc y) v thit lp m hnh ton hc m t quan h gia hm y (tn hiu o) v cc bin c lp x (nng cc cht trong hn hp). Da trn m hnh ny c th tm c nng ca cc cu t trong cng dung dch nh phn khi c tn hiu phn tch ca dung dch . Nu cc cu t c mt trong hn hp cho tn hiu o c tnh cht cng tnh th c th s dng phng php hi qui a bin tuyn tnh thng thng (multiple linear regression- MLR) nh phng php bnh phng ti thiu hoc a dng hn nh bnh phng ti thiu tng phn, phng php hi qui cu t chnh . Nhng nu trong hn hp, cc cu t c s tng tc ln nhau lm mt tnh cht cng tnh tn hiu o th phi s dng m hnh hi qui a bin phi tuyn tnh (ph bin l cc phng php kt hp vi mng nron nhn to). Cc thut ton v hi qui tuyn tnh a s c gii quyt bng phn mm MATLAB, mt s thut ton n gin hn c th s dng MINITAB hoc SPSS hay STATGRAPHICS, Unscrambler...

5.1. Hi qui a bin tuyn tnhGi s hn hp cn phn tch c k cu t (X 1, X2Xk), tn hiu phn tch ca hn hp l y th phng trnh hi qui a bin m t quan h gia y v cc bin X i (i=1,2, k) c dng : y= a+ b1X1 + b2X2 ++ bkXk V mt l thuyt tm nng ca k cu t cn c t nht k phng trnh hi qui. V vy thc t s cn tin hnh m th nghim (m k) vi m dung dch chun hn hp th s lp c m phng trnh hi qui a bin. Dng tng qut ca h phng trnh ny nh sau : y= a+Xb Trong b l vecto cha cc h s ca phng trnh hi qui. y l vecto ct cha m gi tr y1ym cn X l ma trn c m hng (ng vi m quan st) v k ct (ng vi k bin)

1

y1 y 2 y y= 3 . . ym

x1 1 x X = 21 ... xm1

x1 2 x2 2 ... xm 2

... ... .. ...

x1k x2k ... xm k

Nu tn hiu o ng vi mi th nghim c nhiu hn mt gi tr (v d o hp th quang mt dung dch chun hn hp ti p bc sng thay v mt bc sng) th s liu ca Y s l ma trn c m dng v p ct ( ymxp) nh sau:

y1 1 x1 2 x x 21 22 y= ... ... xm1 xm 2

... ... .. ...

x1 p x2 p ... xm p

Cc phng trnh hi qui tuyn tnh thu c s cho bit: - Nhng bin (cu t) no c nh hng ln (nu gi tr tuyt i ca h s hi qui ln) n kt qu th nghim (tn hiu o). - Bit c chiu hng cc nh hng (h s hi qui mang du dng s c nh hng cng chiu n kt qu th nghim v ngc li). - Tm c nng cc cu t trong dung dch cn nh phn khi c tn hiu phn tch y. 5.1.1. Phng php bnh phng ti thiu thng thng (classical least squareCLS)(Phng php ny cn gi l ma trn K (K-matrix)) - T dng tng qut y= XK +e (1) vi y l vecto (mx1) ; X l ma trn (mxk), v e l vecto s d (mx1). K l vecto h s ca phng trnh hi qui dng hng (kx1) nu y l vc t ct biu din tn hiu o ca mt dung dch chun; K l ma trn (kxp) nu y l s liu dng ma trn (mxp) biu din tn hiu ca dung dch chun c o ti nhiu thi im (v d o hp th quang ti p bc sng). - Nu c gi tr nhp vo l bin c lp X v bin ph thuc y s tnh c gi tr h s b. Theo phng php bnh phng ti thiu, ma trn h s K s c tnh nh sau:

K= (XTX)-1 XTy

(2)

vi XT l ma trn chuyn v ca X (transpose to matrix). -Vi mu cha bit cn tm gi tr X0 t gi tr y0 ta s c:

X0 = y0 KT (KKT)-1

(3)2

Phng trnh (1) cho thy c th xem CLS nh l phn tch nhn t v ma trn tn hiu y l tch cu hai ma trn nh X v K. Trong phng php trc quang, phng php CLS ghi tn hiu phn tch dng ma trn c xem l phng php nh lng ph ton phn, do vy t c chnh xc cao so vi cc phng php ch s dng mt s bc sng v cho php tnh ton ng vi tt c cc ph trong hn hp. Nhc im ca CLS l cn phi bit tt c cc ph ca nhng cht gy nh hng n vng ph c o v chng u ng gp vo ng chun. iu ny c th c loi tr ng k bng cch phn tch di ph ti mt thi im sau khi gp kt qu vo php phn tch thng k. N cho php loi b di ph khng tun theo nh lut Lambe-Bia hoc nhng ph c cha tn hiu ca ion cn. V vy cn thit phi xc nh xem trong hn hp c nhng cht no ng gp vo tn hiu ph. Ch : Nhng cu t trong hn hp mun gii c theo phng php ny phi c tnh cht cng tnh. Thut ton CLS trong phn mm Mat lab: Nhp ma trn s liu nng cc cht trong cng hn hp khi xy dng ng chun X (mxk). Nhp tn hiu phn tch di dng vecto ct hoc ma trn. Vit cu lnh tnh h s K ca phng trnh hi qui vi K= inv(X*X)*X*y Nhp tn hiu phn tch y0 ca mu cn nh phn. Tnh X0=y0*K *inv(K*K)

Th d 4.1: Hn hp cn phn tch c 4 cu t, nng tng ng nh sau, tin hnh o 6 dung dch chun ti mt bc sng, tn hiu phn tch l vecto 1 ct, 6 dng >>X=[1 2 3 4; 4 5 6 7; 5 4 3 6; 5 6 7 8 ; 3 5 6 7 ; 8 5 9 5] X= 1 4 5 5 3 8 y= 4 6 2 5 4 6 5 5 3 6 3 7 6 9 4 7 6 8 7 5

>>y=[4;6;7;8;3;7]

3

7 8 3 7 >>K=inv(X'*X)*X'*y K= 1.2120 -2.3145 0.0351 1.7570 Nu s dng thut ton CLS B=regress(y,X) Hoc [b,bint, r,rint, stats]= regress(y,X) Trong trng hp ny y phi l vecto Nu kt qu trong mu phn tch l mt gi tr bng s th Matlab s khng tnh c gi tr ca nng trong mu. V vy CLS thng ch thch hp cho nhng php phn tch ti nhiu bc sng

Th d 4.2: Nu Y l ma trn c 6 dng v 6 ct (vi 6 dung dch chun o ti 6 bc sng) th kt qa tnh h s K s l ma trn (6x4) v lp c 6 phng tnh hi qui: Y= [1 2 3 4 5 9; 3 4 5 6 7 7; 5 6 7 8 9 2; 2 3 4 5 6 8 ;9 8 7 6 5 5 ; 1 3 5 7 8 9] Y= 1 3 5 2 9 1 K= -0.5104 2.2617 -0.0912 0.0694 0.6492 1.2290 0.1062 2.1712 1.6905 0.2329 2.9466 0.2976 2.8174 3.6635 0.5191 -1.2236 -2.9663 -4.4791 -7.3646 0.6629 1.4171 2 4 6 3 8 3 3 5 7 4 7 5 4 6 8 5 6 7 5 7 9 6 5 8 9 7 2 8 5 9

-0.7060 -0.4353 -0.1645

4

(4 hng trong ma trn K ch 4 gi tr h s ca 4 bin l 4 cu t cn phn tch trong hn hp). Gi s mt mu phn tch c tn hiu o ti 6 bc sng nh sau y0 = 2 4 6 8 9 3 Th nng ca 4 cu t trong mu s l : >> X0=y0*K'*inv(K*K') X0 = 10.8832 6.4111 9.0823 5.8384

Ngoi ra, c th s dng phn mm Minitab xy dng hm hi qui t ma trn nng ca cc dung dh chun v vect tn hiu phn tch (th d 4.1) : Vo: Stat-> Regresion-> regresssion The regression equation is y = - 20,3 + 3,62 x1 - 17,1 x2 + 2,96 x3 + 11,5 x4 Predictor Constant x1 x2 x3 x4 Coef -20,308 3,6154 -17,135 2,962 11,481 SE Coef 7,456 0,9231 5,567 1,117 3,617 T -2,72 3,92 -3,08 2,65 3,17 P 0,224 0,159 0,200 0,230 0,194

S = 0,784465

R-Sq = 96,7%

R-Sq(adj) = 83,7%

Analysis of Variance Source Regression Residual Error Total DF 4 1 5 SS 18,2179 0,6154 18,8333 MS 4,5545 0,6154 F 7,40 P 0,268

5.1.2. Phng php bnh phng ti thiu nghch o (inverse least square- ILS) (Phng php ma trn P ( P- matrix)) Phng php ny gi thit rng nng cht phn tch l hm ca tn hiu phn tch theo phng trnh: X=y.P+e

5

Trong phng php ny, h s P trong phng trnh hi qui l thnh phn ca ma trn (mxk) c tnh theo phng php bnh phng ti thiu suy rng (generalized): P= (yTy)-1 yTX Vic phn tch nng cht cha bit (X0) c thc hin bng cch nhn trc tip ga tr tn hiu o y0 ca dung dch cn phn tch vi P. X0= y0.P Nhc im ca phng php ILS: tn hiu mu phn tch phi c ghi s t nht thi im chnh xc nht (v d trong trc quang phi chn c s t nht cc bc sng phn nh y tn hiu ca tt c cc cht trong hn hp). V ma trn h s P tnh theo phng trnh trn l ma trn nghch o, do kch thc ca ma trn ny phi bng s bc sng s dng v phi nh hn s dung dch chun em dng. Mt vn khc l tnh cng tnh ca tn hiu o v ng chun khi c nhiu bc sng c s dng s xy ra lm cho chnh xc gim. Th d: Vi tp s liu X v y trn dng cu lnh ca matlab s tm c cc gi tr b theo vecto hng b nh sau: X=[1 2 3 4; 4 5 6 7; 5 4 3 6; 5 6 7 8 ; 3 5 6 7 ; 8 5 9 5] X= 1 4 5 5 3 8 y= 4 6 7 8 3 7 b = 0.7534 0.7354 0.9238 Cho y0= 86

2 5 4 6 5 5

3 6 3 7 6 9

4 7 6 8 7 5

>>y=[4;6;7;8;3;7]

0.9854

s tnh c X0 = 6.0269 5.8834 7.3901 7.8924 Nu c nhiu mu cn phn tch, cc gi tr y0 s c nhp vo di dang vc t ct v kt qu nh sau: >> y0=[3;5;7;8] y0 = 3 5 7 8 >> X0=y0*b X0 = 2.2601 3.7668 5.2735 6.0269 2.2063 3.6771 5.1480 5.8834 2.7713 4.6188 6.4664 7.3901 2.9596 4.9327 6.9058 7.8924

5.1.3. Phng php bnh phng ti thiu thng thng (ordinary least squareOLS) Gi s c tp s liu (y,X) trong y l cc ga tr hm mc tiu (bin ph thuc) v X l gi tr cc bin c lp. Bi ton t ra l cn tm phng trnh hi qui k chiu ph hp sao cho tng bnh phng sai s QB gia gi tr thc nghim yi v ga tr y i tnh theo phng trnh hi qui y= X l nh nht. Q( ) =(1/T) e( ) e( ) = (1/T) (y-X ) (y-X )

i vi h phng trnh hi qui a bin tuyn tnh cc h s l vec to hoc ma trn c k hiu di dng

7

Sai s gia gi tr tnh c v gi tr thc nghim c gi li phn d ei (residue)

V tng bnh phng ca n ca m hnh

cng c dng nh ga tnh thch ng

Khi c gia tr y bit trc c th tnh c gi tr X 5.1.4. Cc phng php a bin s dng tp s liu o hm

5.2. Phng php hi qui cu t chnh (principal component regression -PCR) y l phng php m rng v phng trnh hi qui s dng phn tch a bin p dng cho tp s liu c rt nhiu bin. PCR gm 2 qu trnh: - Phn tch cu t chnh chuyn sang tp d liu mi, cha mt s t cc yu t quan trng, cn thit. Sau s dng phng php bnh phng ti thiu nghch o (ILS) phn tch tp d liu mi ny. Trc tin, chiu tp s liu ln khng gian c t chiu hn theo PCA m khng lm mt i cc thng tin quan trng v tin hnh phn tch hi qui a bin trn khng gian mi ny. N gi thit rng mi thnh phn trong tp s liu c th c gn mt gi tr nh lng u tin cn to m hnh PCA cho tp s liu v s dng ga tr ring ca cc bin o (score) xy dng phng trnh hi qui a bin tuyn tnh trong gi tr y l gi tr hm mc tiu. u im ca PCA so vi PLS:

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- Gi tr nhiu nn c chuyn vo trong sai s d v loi ra khi m hnh hi qui v trong phng php ny cc vector ring c tr ring thp ch chim phn phng sai thp - T hn hp c rt nhiu cu t, bng phng php PCA c th gim s chiu trong tp hp v do vy ch lm vic vi s t bin. Cng cn lu rng, do phng php ny pht trin trn c s ca phng php ILS nn s dng c cc phng php ny trong phn tch trc quang chng ta cn s mu chun ti thiu phi bng s thi im s dng trong ng chun m ha, tc l s mu chun khng nh hn s PC la chn. Ly mt v d c th, khi o ph ca 15 dung dch chun ti 100 bc sng, s dng phng php ILS, chng ta cn phi gim kch thc ph xung s bc sng khng qu 15. Cch n gin nht l chn t hn 15 bc sng o hp th nhng sai s s ln nu khng chn c cc bc sng c trng cho ph cc cht. Vi m hnh PCR ta c th s dng ton ph tnh cc PC, sau chn s PC nh hn 15 tnh ton tip. Thng thng, vi mt tp s liu c mc tp trung tt th ch c mt s t cc PC u tin l c ngha (c tng phng sai tch ly ln coi rng chng cha ton b thng tin hu ch c trng ca tp s liu). Nh vy, s dng m hnh PCR c th gim c kch thc tp s liu m khng lm mt thng tin ng thi c th loi c tn hiu nhiu ca d liu gc. Hn ch ca PCR: Vic gim kch thc ca tp s liu i khi c th loi b nhm tn hiu v gi li sai s trong cc PC. Cch tin hnh: Bc 1: Nhp s liu v x l ban u tp s liu Gi thit c m dung dch hn hp phn tch cha n cu t. Nng ca n cu t trong hn hp c biu din di dng ma trn C(mxn). Tn hiu phn tch l hp th quang A o ti p bc sng v c vit di dng ma trn A(mxp). Vi mt tp s liu chun ha hoc cha chun ha, trc khi s dng u cn bc bnh phng ton tp d liu - y l yu cu bt buc i vi hu ht cc hm tnh vect ring. D = AT . A Trong A l ma trn s liu biu din hp th quang theo cc thi im o ca cc dung dch chun v AT l ma trn chuyn v ca ma trn A. Bc 2:Xc nh cc vect ring hay cc PC: Dng phng php PCA cho hai tp s liu A v C tm cc bin o PC c tr s P (score- gi tr eigenvector) v trng s Q (loading). Nhng PC no c eigenvector>1 mi thc s c ngha. Bng cch ny s gim c s bin tng quan t n bin xung thnh k bin khng tng quan (k> [theta, w, cw, ssqdif, yres]=plsr(Xreg, yreg,ninput, lv, plotopt) Percent Variance Captured by PLS Model ----X-Block------ ----Y-Block-----LV# 2.0000 This LV Total This LV Total 1.0000 92.9100 92.9100 96.4797 96.4797 3.8378 96.7478 2.0157 98.4954

21

theta = 0.3237 0.0252 -0.0689 0.1584 0.0757 0.0857 0.2112 0.0665 0.1174 0.2020 0.0983 0.1492

w= 0.2810 0.6563

0.2908 -0.3310 0.1808 -0.4817 0.2346 0.1931 0.3128 0.2493 0.3837 0.3055 0.1832 0.0051 0.2443 0.0288 0.1136 0.0525 0.2517 -0.1107

0.3226 -0.2414

0.3788 -0.2178

cw = 0.4357 0.3067

ssqdif =

22

92.9100 96.4797 3.8378 2.0157

yres = 1.4340 -0.7358 -0.3543

nh gi phng trnh hi qui tm c cn dng tp s liu mi ca cc dung dch chun. Cu lnh: yres = validmod(xreg,yreg,theta,plotopt)

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* PLS- DA. y l dngdc bit ca m hnh PLS tm ra cc bin v hng trong khng gian a bin, m phn bit c nhng loi bit trong tp hp ng chun. Trong PLS-DA, ma trn ch th Y ca cc bin c xy dng sao cho cha nhiu ct nh trong xy dng ng chun, c ngha l mi loi c mt ct trong Y. Mi loi bin cha gi tr 0 hoc 1 tu thuc bin l loi no. thu c s ph hp phng php cross- validation c dng chn kch thc ca m hnh PLS. H s cross- validation ca php xc nh Q2 c dng nh gi s ph hp. Gi tr ca h s xc nh R2 ch ra phng sai thu c trong cc . Cc bc tin hnh : Vid d phn tch hn hp c nhiu cu t theo phng php trc quang. Ma tran s liu xy dng phng trnh hi qui s l ma trn hp th quang A0 v ma trn nng Co Thut ton PLS trc giao gm cc bc sau: - Tnh vector ti trng (weight) w: - Tnh score v loading: t1= A0 w P1 = A0Tt1 / t1T t1 q1 = C0T t1 / t1T t1 Ma trn v vc t s d trong A0 v C0 l : A1 = A0- t1P1T ; C1 =C0- t1q1T T phng trnh tuyn tnh tng qut h s hi qui c tnh l : b= w(PTw)-1q v a= Cmean-ATmean b Phng trnh ny s c dng tnh cc cu t trong mu

A C w = 0T 0 C0 Co

T

5.4. Hi qui a bin phi tuyn tnhTt c cc phng trnh hi qui tuyn tnh v tuyn tnh a bin u c th m rng cho trng hp cc bin phi tuyn tnh bng cch chuyn thnh dng tuyn tnh, ph hp ho cho hm phi tuyn, hoc s dng cu t chnh. 5.4.1. Phng php mng nron nhn to (artificial neuron network- ANN) : ANN l khi nim tng i mi trong qu trnh x l s liu. Tuy nhin s cng trnh khoa hc s dng ANN trong Ho phn tch ngay cng nhiu c bit trong lnh vc du o v phn tch hi qui a bin phi tuyn tnh gii quyt bi ton nh lng ng thi nhiu cu t trong hn hp.

24

ANN l cng c phn tch s liu da trn m hnh tnh ton gii quyt nhng vn phc tp. ANN gm nhng n v x l s liu dy c lin quan mt thit vi nhau. Mi n v c ni vi n v bn cnh bng lc (weight). Vic xem xt c kt hp bng cch chun ho nhng lc ny to ra mng c kt qu thch hp. S d phng php ny c tn gi l ANN v m hnh x l thng tin tng t nh no ngi trong cc nron truyn ti d liu bng cch tnh hay d on u ra (output) d trn cc d liu u vo (input), trng lng (weight) v lch (bias). Phng php ny rt thch hp mo hnh ho g h phi tuyn tnh. - m hnh ANN a lp lin h xui ( feed-forward) cso dng nhu sau: X1

Input X1 X2 X3 . . Xi . . Xn n Incident arc n+m i n+2 S output 1 2 3 W1, n+1 n+1 Wn+1,s

25

Trong m hnh trn, gi N l tp hp cc nt mng th c th xem N gm 3 tp hp con l NI ( nt nhp- input node), NH ( nt n- hidden node) v NO ( nt xutoutput node) Nu gi thit trong hm thu c c n bin x1xn m chng ta mun tm ( v d nh lng ng thi n cu t trong hn hp) ta s c N I =n. Mng nron c m nron n N H = m vi lch trong mi nron n v xut. Trong hnn mt mng nron c dng NI={1,2,n} v NH= {n+1, n+2n+m}. Gi su c mu phn tch vi cc gi tr u vo l x={x1..xn} th amngj nron cung cp thng tin u ra NN(x,w) l hm ca trng lng w. Mi nt i trong lp nhp nhn tn hiu xi c gi qua tt cc cc cung ti cc nt trong lp n. Mi nt j trong lp n nhn tin hiu u vo input(j) theo phng trnh: Input(j)=j +

x wi =1 i

n

ijj

Tron wj l lch ca nt j; wij l gi tr trng lng trn cung t nt i trong lop nhp n nt i trong lp xut. Mi nt n chuyn gi tr nhp ca n bng trung bnh ca hm phi tuyn sigmoid Output(j)= sig(input(j)). Hm ny c dng sau:sig ( x) = 1 1 + ex

Mi nt n j s gi tng tn hiu output(j) qua cung (j,s). Nt s trong lp xut nhn tng trng lng ca ga tr n t lp n. Tng ny NN(x,w) l gi tr xut ca mng theo phng trnh

N N( x, w) = ws + output n + j ) wn + j , s (j =1

m

trong qu trnh training mng ( supervisor training)vn t ra l tm gi tr trng lng (gm cc yu t lch) m ti thiu ho sai s (RMSE theo tp training E. Mtnkhhi qu trnhf ti u ho c trnh by v trng lng c lp (w=w*)th mng sn sng tnh ga tr u ra khi c bt k ga tr ua vo no. Sai s kim tra ( testing error-TE) tinhd RMSE theo thnh vin trong tp kim tra TS= {y1 , y2..ys }

TE =

error ( y , wi i =1

s

*

)

s

Ba m hnh ph bin ca ANN l: - liene h (lan truyn) xui ( feed-forward) - Hm c bn radial (radial basic function) - hybrid fuzzy system system) (cn gi l adaptive-network- base fuzzy inference

26

5.2.1. Thut ton lan truyn ngc ( backpropogation) Thut ton ny c to ra bng cch tng qut ho qui lut ph bin ( learning) Widrow- Hoff vi mng a lp v hm chuyn vi phn khng tuyn tnh, Vc t nhp v vc t mc tiu tng ng c dng to mng cho n khi n c th xp x ho mt hm lin quan ti vc t nhp v vect xut c bit hoc phn loi vc t nhp thnh cc cch tng ng c m t trc. Mng vi lch (bias), lp nhp l hm tng ( sigmoid) v lp xut tuyn tnh (linear) c xem l c kh nng xp x ho bt k hm no vi s hu hn cc gin on. Thut ton lan truyn ngc chun l l thut ton gim graient trong trng lng khi ( network weight) c dch chuyn dc theo trc m ( negative) ca graient ca hm biu din. Thut ng lan truyn ngc ni ln cch tnh graient i vi mng a lp khng tuyn tnh. C rt nhiu dao ng (variation) trn thut ton c bn da trn nhng k thut ti u chun khc nhau nh graient lin hp hay thut ton newton. Thng thng mt gi tr u vo mi s cho gi tr u ra tng t vi u ra ng i vi vec t u ra dng trong training m tng t vi gi tr u ra mi c trnh by. S mng BP ANN gm 4 lp nh sau: Wjj H Wij h h1 X1 X2 X3 . Xi . . Xn Bin nhp In hn+1 Hn+1 Lp n n+1nron Lp xut 1nron Ii I1 h2 I2 h3 I3 hj Hj . O H3 H2 Wij O H1

Lp nhp Lp n n nron Hm sigmoid n+1 nron

Nu c n bin u vo ta s c tn hiu vo ng thi cc nt nhp v c lan truyn thng qua cc nron ri xut hin ti im ra cui cng ca mng nh tn hiu ra. Tng tn hiu vo ti mt nron c tnh l hm ca cc tnhiu vo vf lin quan27

n synaptic weight ng dng cho mt nron no . Nron ny s chuyn tng tn hiu nhp thnh tn hiu ra ( outgoing) s dng hm chuyn i ( transfering function) v pht i n cc nron khc. trong khi mt tn hieu sai s xut pht ti mt nron ra ca mng v truyn ngc li theo tng lp n cc nt mng pha trc. Mi qu trnh truyn i ca tn hiu v truyn ngc ca sai s c gi l mt bc lp (epoch). Tn hiu sai s v graient sai s ti mi nron c tnh cho mt weight optimizato sao cho sai s u ra l nh nht. Hm chuyn: ( transfer function) 5.2.2. Hm c bn radial: (radial basic function- RBF). Phng php ny c s dng rng ri nh c tnh ph bin (robust) v nhy cao c bit vi nhng s liu nhiu so vi phng php ANN_BP. M hnh RBF gm 3 lp: lp nhp xuyn qua ( pass-through input layer), lp n v lp xut theo phng php lin h xui. Mi nron ca lp n i din cho mt ht nhn ( hm chuyn trong lp n gi l kernel)hay hm c bn c kch thc nh tp s liu nhp vo. Lp nhp v lp n c ni vi nhau bng n v trng lng. V d nu tp s liu c kch thc l 20 th RBF s c 20 chiu. Mng RBF thng s dng hm kernel l hm gaussian tnh v s khng tuyn tnh. Hm Gaussian c c trng bi hai thng s l gi tr trung tm (centroid- Cj) v rng ( j). u ra te nron Gaussian th j vi i lng nhp vo xi c tnh theo phng trnh sauout j = j ( x i C j ) = exp( xi C j ( j ) 22

y xi C j l khong cch Eucledean gia xi v Cj gi tr j xc nh phn nhp ca FBF th j v tn hiu mc tiu ca mi nt xut hin c tnh bi hm tuyn tnh ca u ra ( gm lch ca u ra w kj y chnh l u ra ca lp n (outk) . quan h gia gi tr outk v bin nhp xi c biu din nh sau: outk= wKo +

wj

kj

j ( xi C j

Trng lng wkj c iu chnh n gi tr sai s bnh phng trung bnh nh nht. Trong m hnh RBF-ANN neuron trong lp n khng s dng weighted sum ca input v hm chuyn sigmoid., thay vo u ra ca mi nron trong lp n i din cho mt hm c bn c xc nh bi khong cch Eucledean gia gi tr input v trung tm ca hm c bn. Khi nt chuyn ng ra khi trung tma khi trung tm nron u ra s gim nhanh n khng. Hm newrb trong Matlab c dng to ra hm c bn radial . N s to ra mt nron radial c bn ti mt rhi im v thm nron vo mng cho n khi tng bnh phng sai s gim ti gradient hoc t s nron ln nht (ga tr ny ph

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thuc vo phn tn ca hm c bn raial. Nu phn tn ln th dc ca hm c bn radial gim. nu phn tn nh th hmcbn radial s rt dc n mc nron c trng lng gn nht vi ga tr nhp s cho gi tr u ra ln hn nhng nron khc. Th d: Phn tch ng thi maltol, ethyl maltol, vanilin v ethyl vanilin bng phng php UV. Ma trn s liu trc giao l ga tr ph ghi trong khong bc sng 200-350 nm vi 16 dung dch ( ngun: Yongnian N. et al., 2005. Analytical, nutrial and clinic methods. Food Chemistry, 89 , 465-473 5.2.2. Phng php hi qui cu t chnh kt hpvi mng nron nhn to (PCA-ANN) Trc khi thc hin ANN, cc s liu v bin ph thuc trong phn tch ng chun c thc hin theo ph\ng php PCA tm cc gi tr ring score v ti trng loading. Trong m hnh ny cc ga tr ring (score) khi thc hin PCA vi tp s liu ng chun c dng lm lp nhp . phng php PCA-ANN c xy dng da trn vic s dng gi tr khc ca cc PC. Lp n cha cc nron vi hm sigmoid v lp xut vi hm tuyn tnh linear. Thut ton lan truyn ngc c p dng cho mng PCA-ANN a lp feed-forward. Cc bin ca PCA-ANN c ti u sao cho t c sai s nh nht khi so snh vi nng bit trc. Cc dung dch dng xy dng m hnh theophng php ng chun cn trnh c tng quan nng v s gy ra tnh xen ph ( overfitting) trong m hnh. Th d: ( ngun thng tin: K. Zarei et al., Il Farmaco 60(1), (2005), 37-42) Xc nh ng thi Fe(II) v Fe(III) bng hn hp thuc th 1,10- phenaltrolin 0,005 M v thioxianat 0.05M pH=1 ( m HCl-NH2CH2COOH) trong dung dch mu cha 30% (v/v) axeton. hp th quang ca dung dch phc mu hn hp c o trong khong 380600 nm vi tc qut 3000 nm/pht , khong cch ghi l 1.29 nm. xy dng ng chun pha 18 dung dch hn hp cha ng thi Fe(II) trong khong 1-8 mg/l v Fe(III) 0.4-9 mg/l sao cho cc dung dch khng c s tng quan v nng trnh s xen ph m hnh. Ma trn s liu hp th quang l ma trn A c kch thc 18 x170 (18 mu v 170 bc sng) M hnh PC-ANN 3 lp vi thut ton lan truyn ngc c s dng. u tin, dng PCA tm cc ga tr ring (score) ca cc cu t chnh (PCs) v dng n lm nt nhp ca lp nhp. Lp n cha cc nron vi hm chuyn thng tin l hm sigmoid. Lp xut cha hai ga tr u ra l nng Fe(II) v Fe(III). trnh s chng cho m hnh (overfitting), m hnh hi qui c chn ( s PC, s nt trong lp n, s bc- epoch, learning rate, momenttum), phi c sai s bnh phng trung bnh ca tp s liu d on (MSEP) nh nht.

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Trong cc phng php kim tra tnh ng n cu m hnh, phng php kim tra cho (loi b mt) thgn c dng xc nh s PC da trn vic tnh gi tr PRESS theo s PC. -----------------

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