社会学部紀要 １１８号☆／３．中山
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1 Mrh Multiple Ftor AnlysisMFA PCA Prinipl Component Anlysis PCA MFA Esofier nd Pges 9 R Pkge FtoMineR MFA MFA weight glol tle MFA quntittive tegoril PCA Prinipl Component Anlysis, CA Correspondene Anlysis, MFA Multiple Ftor Anlysis FtoMineR pkge MFA R FtoMineR n p p numeril vriles tegoril vriles PCA MCA MFA MFA PCA MFA J Multiple ftor nlysis, R, FtoMineR
2 set vriles K j Kj J individuls i I Xij J MFA MFA Singulr vlue deomposition α X!λ ; X!λ ; ; XJ!λ J Z, Z,, ZJ MFA PCA weighted PCA svd Zj MFA Generlized singulr vlue deomposition GSVD GSVD Singulr vlue deomposition SVD X UΛV T U T U V T V I P M / U Q W / V X PΔQ T P T MP Q T WQ I X M / XW / X M / XW / M W GSVD SVD GSVD P M / U Q W / V M X row row m M dig /m,,/m W W dig α dig α α α J GSVD P T U T M / Q T V T W / P T MP U T M / MM / U U T U I Q T WQ V T W / WW / V V T V I SVD X PΔQ T F PΔ X FQ T P M / U F M / UΔ F Sore Q W / V G W / VΔ G lodings F G Biplot X λ λ α SVD GSVD
3 !j Mrh tegoril dt J!j pijt pi.!i p.jt row weight pi.. ol weight p.jt orrespondene nlysis φ pijt pi..p.jt n pi..p.jt pijt pi.t row weight pi.t p.t!i p.jt pi.. ol weight p.jt p..t Internl orrespondene nlysis ICA pijt pijt p..t pi.t p.jt pi.t pi.. p.jt p..t pi.. p.it ICA ontingeny tle MFA MFA R MFA progrmming wine tste wines wine wine wine wine wine wine Expert Expert Expert fruity woody offe redfruit rosted vnillin woody fruity uttery woody progrm progrming
4 Exel Yred.tlelipordheder TRUE,row.nmes #Exel Expert Yred.tlelipordheder TRUE,row.nmes #Expert Yred.tlelipordheder TRUE,row.nmes #Expert nnrow Y #n sdpply Y,,sd sdpsqrtn n *sd #sdp XXsle Y,pply Y,,mensdp X /sqrt n*xx #Y nnrow Y sdpply Y,,sd sdpsqrtn n *sd XXsle Y,pply Y,,mensdp X /sqrt n*xx #Y nnrow Y sdpply Y,,sd sdpsqrtn n *sd XXsle Y,pply Y,,mensdp X /sqrt n*xx #Y ZX/svd X $d #X ZX/svd X $d #X ZX/svd X $d #X Zind Z,Z,Z # Z # X α /!λ wine wine wine wine wine wine wine wine wine wine wine wine fruity woody offe redfruit rosted vnillin woody fruity uttery woody ZZ, Z, ZUΔV T Singulr Vlue Deomposition U T U V T V I GSVD Z Z PΔQ T P M / U Q W / V P T MP Q T WQ I M W M W row olumn
5 Mrh /n nnrow Z #n M rep /n,n M Z PΔQ T F PΔ Z FQ T P M / U F M / UΔ Pdig /sqrt M%*% svd Z $u Fdig /sqrt M%*% svd Z $u %*% dig svd Z $d F # sore, dim., dim., dim. wine wine wine wine wine wine individul lodings W inerti ol.wpply Zˆ,,sum Wol.w W fruity woody offe redfruit rosted vnillin woody fruity uttery woody Z T QΔP T G QΔ Qdig /sqrt W%*% svd Z $v Q,,,,,,,, 9,, Dim. Dim. Dim
6 Gdig /sqrt W%*%svd Z $v%*%dig svd Z $d G #individuls loding,,,,,,,, 9,, Dim. Dim. Dim ZZ, Z, ZPΔQ T QQ, Q, QZPΔQ T,PΔQ T,PΔQ T Z PΔQ T Z WQ PΔQWQ PΔ F F ZWQZ, Z, Z WQ Q T Q, Q, Q T Fk ΣZkWkQk Σα kzkqk GK k Fk k ontingeny tles p. dt tle A, B tle A A A A tle B B B B R R R R R R Tle A, B tle C tle C A A A B B B R R R ICA C A A A B B B R R R MFA Tle C row.mpply C,,sum.,.,.ol.mpply C,,sum.,.,.,.,.,. ICA
7 Mrh row.w.,.,.row.m ol.wol.m*rep svd A $d ˆ /svd B $d ˆ / row.w,ol.w svd.triplet C,row.w,ol.w R Pkge R Pkge FtoMineR MFA FtoMineR MFA pkge mnul wine MFA wine res.mfmfa wine,group,,type reps nme.group Exp Exp Exp grph FALSE res.mf progrm wine Exp, Exp, Exp,, type s MFA type seprte nlysis s PCA seprte nlysis n MCA fca PCA glol nlysis glol.p group glol.p$ll$x GSVD FoMineR svd.triplet dt,row.w,ol.wgsvd wine Z ol.wpply Zˆ,,sumres.mf$glol.p$ll$ol.w ol.w fruity woody offe redfruit rosted vnillin woody fruity uttery woody row.w rep /, $ll$row.w svd.triplet X,row.w,ol.w $vs svd.trplet FtoMineR MFA grph FALSE
8 $U,,,,,,,,,,, $V,,,,,,,, 9,,,,,,, MFA group res.mfmfa wine.dt,group,,type reps nme.group Exp Exp Exp res.mf.group Group j Lg ν, KjLg ν, Kjνi i dimension K Lg ν, Kj λ j!k Kj ov x.k, ν group Group Kk KJ Kj!k Lg Kk, KJ λ k i λ i j res.mf$group$lg EXp Exp Exp MFA Kj!k λ j k λ j EXp Exp Exp MFA Lg s Lg Lg RV RV Lg RV
9 Mrh plot res.mf,hoixgroup res.mf$group$oord, : EXp Exp Exp Dim Dim RV MFA ontriution res.mf$group$rv, res.mf$group$ontri plot res.mf,hoixvrhgroup Exp dim
10 plot res.mf,hoixindhillgegroup plot res.mf,hoixind MFA wine res.mf$ind$oord, : wine wine wine wine wine wine Dim Dim Group plot res.mf,hoixvrhgroup
11 Mrh res.mf$glol.p$vr$or, : fruity woody offe red.fruit rosted vnillin woody. fruity. utter woody. Dim Dim plot res.mf,hoixindprtilllhillgegroup res.mf$ind$oord.prtiel, : wine.exp wine.exp wine.exp wine.exp wine.exp wine.exp wine.exp wine.exp wine.exp Dim. Dim. Dim. Dim wine.exp wine.exp wine.exp wine.exp wine.exp wine.exp wine.exp wine.exp wine.exp MFA MFA
12 seiseki group res.mfmfa seiseki,group,type s s nme.group A B A B A. B. A. B A. B. A. B. A. B. A. B plot res.mf,hoixgroup res.mf$group # $Lg $oord MFA Dim. Dim. MFA $RV $ontri MFA Dim. Dim. MFA
13 Mrh res.mfmfa SEISEKI,group,,,type reps nme.group
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15 Mrh res.hmfhmfa seiseki,h hierr,type repsgrph FALSE plot res.hmf,hoixgroup res.ppca seiseki 9,quli.sup plot.pca res.p,hoixindhillge plot.pca res.p,hoixindhillge,lelnone MFA Q j QA J MFA HMFA FtoMineR mnul seiseki
16 dtind JD,DD #JD,DD res.mfmfa dt,group,type f f nme.group Q Q
17 Mrh vriles individuls res.mf$group $Lg MFA MFA $RV MFA MFA $oord Dim. Dim. Dim. Dim. Dim $ontri Dim. Dim. Dim. Dim. Dim MFA dtind JD,DD hierrlist,,,,,,,, res.hmfhmfa dt,h hierr,type reps
18 HMFA LG Dim, MFA res.mfmfa dt,group,,,,,,, type repf nme.group J J J J G G G G
19 Mrh Multiple Ftor Anlysis Prinipl Component Anlysis Contingeny Tle Anlysis R pkge FtoMineR MFA Correspondene Anysis Multiple Correspondene Anlysis MFA R FtoMineR, pkge MFA quntittive tegoril pkge prmeter MFA PCA ontingeny tle MCA ontingeny tle MFA Pges nd Beue-Bertut, Multiple Ftor Anlysis for Contingeny Tles, from, Multiple Correspondene Anlysis nd Relted Methods, Chpmn & Hll/CRC pp 99. Adi & Willims & Vlentin, Multiple Ftor Anlysis : Prinipl Component Anlysis for Multi-Tle nd Multi-Blok Dt Sets Computtionl Sttistis vol / / Wiely Interdisiplinry Reviews J. Pges, Multiple Ftor Anlysis : Min Fetures nd Applition to Sensory Dt, Revist Colomin de Estdisti,
20 vol / / Adi & Vlentin. Multiple Ftor Anlysis, in Enylopedi of Mesurement Sttists. Thousnd Oks CASge H. Adi, Singulr Vlue Deonposition SVD nd Generlized Singulr Vlue Domposition GSVD, Enylopedi of Mesurement nd Sttistis, Thousnd Orks CASge H. Adi, L. I. Willims nd D. Vlentin, Multiple ftor nlysis : prinipl omponent nlysis for multitle nd multilok dt sets, Wiley Periodils, in A. Zrrg nd B. Goitisolo, Simultneous Anlysis : A Joint Study of Severl Contingeny Tles with Different Mrgins. from Multiple Correspondene Anlysis nd Relted Methods, Chpmn & Hll/CRC pp. E. Asl, I. G. Lutre, nd M. I. Lndlue, Multiple Ftor Anlysis of Mixed Tles of Metri nd Ctegoril Dt. From Multiple Correspondene Anlysis nd elted Methods, Chpmn & Hll/CRC pp. 9 H. Adi, RV Coeffiient nd Congruene Coeffiient Enylopedi of Mesurement nd Sttistis, Thousnd Orks CASge B. Kostov, M. Berue-Bertut nd F. Husson, Multiple Ftor Anlytsis for Contingeny Tles in the FtoMineR Pkge, The R Journl vol / C. E. Prdo, M Beue-Bertut, J. E. Ortiz. Correspondene Anlysis of Contingeny Tles with Suprtitions on Rows nd Columns. Revist Colomin de Estdisti. vol / A. Zrrge B. Goitisolo, Simultneous Anlysis in S-PLUS : The SimultAn Pkge. Journl of Sttistil Softwre. / vol, Issue. B. Everitt, T. Hthorn, An Introdution to Applied Multivrite Anlysis with R, Springer,. wines Expert Expert Expert fruity woody offe redfruit rosted vnillin woody fruity uttery woody wine wine wine wine wine wine
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24 Q Q Q Qd Qe Qf Qg Qh Qi Qj QA QB QC QD QE QF QG QH QI QJ d e f g h i j A B C D E F G H I J Demogrphi Vriles Q Q D q, D Q Qj, QA QJ JD Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Qd Qd Qd Qd Qd Qe Qe Qe Qe Qe Qf Qf Qf Qf Qf Qg Qg Qg Qg Qg Qh Qh Qh Qh Qh Qi Qi
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26 Explortory Multivrite Sttistil Dt Anlysis Multiple Ftor Anlysis ABSTRACT Multiple ftor nlysis dels with multiple tle, omposed of quntittive or tegoril vriles lning the influene of the different sets on the first prinipl xes. Reently MFA funtion hs een extended to the ontingeny tles. I explin this nlysis using R nd pkge FtoMineR, nd demonstrte some Jpnese pplitions. Key Words: Multiple ftor nlysis, R, FtoMineR
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![Σ A Σ B r Σ A (Σ A ): A r = [ A r A x r A y r z ] T Σ B : B r = [ B r B x r B y r z ] T A r = A x B B r x + A y B B r y + A z B B r z A r = A R B B r](/thumbs/91/105412327.jpg "Σ A Σ B r Σ A (Σ A ): A r = [ A r A x r A y r z ] T Σ B : B r = [ B r B x r B y r z ] T A r = A x B B r x + A y B B r y + A z B B r z A r = A R B B r")
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R = Ar l B r l. A, B A, B.. r 2 R r = r2 [lar r l B r l2 ]=larl l B r l.2 r 2 R = [lar l l Br ] r r r = ll Ar l ll B = ll R rl.3 sin θ Θ = ll.4 Θsinθ
![R = Ar l B r l. A, B A, B.. r 2 R r = r2 [lar r l B r l2 ]=larl l B r l.2 r 2 R = [lar l l Br ] r r r = ll Ar l ll B = ll R rl.3 sin θ Θ = ll.4 Θsinθ](/thumbs/80/82073891.jpg "R = Ar l B r l. A, B A, B.. r 2 R r = r2 [lar r l B r l2 ]=larl l B r l.2 r 2 R = [lar l l Br ] r r r = ll Ar l ll B = ll R rl.3 sin θ Θ = ll.4 Θsinθ")
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A 2 3. m S m = {x R m+1 x = 1} U + k = {x S m x k > 0}, U k = {x S m x k < 0}, ϕ ± k (x) = (x 0,..., ˆx k,... x m ) 1. {(U ± k, ϕ± k ) 0 k m} S m 1.2.
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18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α
18 I ( ) (1) I-1,I-2,I-3 (2) (3) I-1 ( ) (100 ) θ ϕ θ ϕ m m l l θ ϕ θ ϕ 2 g (1) (2) 0 (3) θ ϕ (4) (3) θ(t) = A 1 cos(ω 1 t + α 1 ) + A 2 cos(ω 2 t + α 2 ), ϕ(t) = B 1 cos(ω 1 t + α 1 ) + B 2 cos(ω 2 t
24 I ( ) 1. R 3 (i) C : x 2 + y 2 1 = 0 (ii) C : y = ± 1 x 2 ( 1 x 1) (iii) C : x = cos t, y = sin t (0 t 2π) 1.1. γ : [a, b] R n ; t γ(t) = (x
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II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2
![II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2](/thumbs/101/149159646.jpg "II No.01 [n/2] [1]H n (x) H n (x) = ( 1) r n! r!(n 2r)! (2x)n 2r. r=0 [2]H n (x) n,, H n ( x) = ( 1) n H n (x). [3] H n (x) = ( 1) n dn x2 e dx n e x2")
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