T M G D E B U P F R T F, 5-7 08005 B SPAIN E-: @. A: A,,. I, () CA -, (),, CA, (), (), (). K:,,, -,,,,,,,,. T Fó BBVA, M, S.
1. I C (CA) (H 1974),. T, SPSS, M, S, SAS S, R. N,. I I -. A,, CA, - -. T. T CA, CA. A, : CA -, ; ; ;. A,, I /. A (-) CA. M (MCA),,,.. S I CA. CA (PCA) (Bé 1973, G 1984: 3). I, - E,. A - (, -) -,. T
, (G & H 1996; G 1993, 004), S 6. T,,,. S N I J, -. E N,. T I E. E,. D -, E,. I, N, - -, N T N. H,,,. A PCA, -, - -. T G (1984: C A) - (SVD). T, N - P = (1/) N. L P,, D D. T,, P : D 1 P. T CA PCA D 1 P, - D 1 D. T ( ) T, CA D 1 P 1 T,. T,.. P. T CA PCA, D 1 P T, - D 1 D. T T, CA D 1 P T 1 T. 3
I, (-), : I = I J φ = (1) = 1 = 1 T, (),. I (P ) - φ ( - ), P : φ = χ /. T, SVD, : 1. C : S 1/ T 1/ = D ( P ) D (). C SVD: S T = UD V U T U = V T V = I (3) α 3. P : F = D 1/ UDα (4) 4. P : G = D 1/ VDα (5) 1/ 5. S : X = D U (6) 1/ 6. S : Y = D V (7) T (4) (7),,,,,. N T T FD F = GD G = D α,.. -- - (.., ) α, - (, λ ), -- 1: T T XD X = YD Y = I. N D α. A -,,. T, (PCA) - () : 1. S : F G 4
. A : F Y. 3. A : G X. T X Y. T S 6. S,,... T (1) λ 1 +λ +λ 3, -,, λ 1 +λ, : λ 3 +λ 4 +. T, PCA. 3. E : T. T R (R D C T 005). I R MASS, : (MASS) () T 1 6 1, (T 1). T 6,. T. T 8000-10000. T, (T ). T 13 ( 1 11, R1 R), 10 ( 1,,, 10). T (-) N S, 11,, R1 R. T ( ) ( ). T CA F 1. I F 1, (0.0184) 1,. I F, 5
11 4. 4. M I CA,, (1) S.. S. W 1 ( ) 1. I : χ I ( )... W χ ½I(I 1) ( ' ) < I : χ J ( ) W χ ½J(J 1) ( ' ) < D, ( ) ( ). T :,? I,. T,,. T PCA 1,. B CA (,, Pé Bé-B, 006),. 6
A,. F, 6371, ( ) ( ) ( G 00, ). I -, 5, 7, 9 11,,. T, CA, : T: 5 5 7 5 9 5 11 5 T : 0.1389 0.1441 0.146 0.1479 1 : 0.1363 0.139 0.1407 0.1416 (P): (98.1% ) (96.6%) (96.%) (95.8%) A,,. I,, 5 5. I CA {I 1, J 1}, 4. H,. T -,. I,,,. T. N,,, 3 3, 5 5 7 7. T,. T 0.1754, 0.448 0.3333,,. T, 4 6. A C V. I CA, / { I 1, J 1}, : 3 3 : = 0.1754/ = 0.0877, V = 0.0877 = 0. 96 7
5 5 : = 0.448/4 = 0.061, V = 0.061 = 0. 47 7 7 : = 0.3333/6 = 0.0555, V = 0.0555 = 0. 36. T C V,,. I, () : 3 3 : 0.1716 0.0038 97.8%.% 5 5 : 0.069 0.00 0.0158 0.0001 84.5% 9.0% 6.5% 0.0% 7 7 : 0.39 0.056 0.018 0.0188 0.0008 0.000 71.8% 15.8% 6.5% 5.6% 0.3% 0.0% I,. S -,. T : 3 3 : 0.1716 0.1754 5 5 : 0.069 0.89 7 7 : 0.39 0.918 T. I 5 5 7 7, -, 0.448 0.333. R, 3 3 5 5 0.89/0.1754 = 1.305, 30.5%, 5 5 7 7 0.333/0.448 = 1.357, 35.7%. F 3 3 7 7 0.918/0.1754 = 1.664, 66.4%. T, - CA, ( ),. T,. 8
L,. T 11 9, 9 :, 0.01836, 0.3798. S 0.3798/0.01836 = 0.7 0. T,,. E,, -,,. I,. I,, --,. O,,,. 5. T M CA, -,. F, R (1995:.45) -,. L (001:. 71),. M,. I I, CA,,, CA. I,. W CA,. B CA,. T CA I CA. B. F, : (0.07%), (0.08%), (0.08%) (0.1%), 9
1%. O F 1,,. H, 1.1%, 3.7% 1.3% 0.%, 1.0%.1%. T : (17.0%), (16.1%), (14.6%), (10.%), (48.5%) (,.%, F ). T,,,,. T -. I F 1 I (H) P F (C),. W - 0.100,, 0.0077, 7.6%. I. T. T 93.5%, (6 10) 6.5%. T 6.% 1.5%,. T CA,. 6. T CA T CA,. I M (I J) AB T, : M AB T. U - M: M = UD σ V T, U, V D σ, σ 1, σ, σ 3,..., σ R, R M. T - M, -. F - ( -), A (I ) ( B (J ) U V,,, D σ. I, - : 10
1 1 + = σ 1 1 1 + σ (8) T [ 1, ] [ 1, ], σ 1 σ. I : 1 = σ γ 1 1 = σ γ 1 γ 1 γ 1 = σ 1 1 = σ.., γ (1 γ). G (006) γ-. I : () γ = 1,.. ( S ), - (RMP) G (1971); () γ = 0,.., -- (CMP): (RMP): [ 1, ] = [σ 1 1,σ ] [ 1, ] = [ 1, ] (CMP): [ 1, ] = [ 1, ] [ 1, ] = [σ 1 1,σ ] I E M ( RMP ), ( CMP ). W, (A G 00). A,, (.., γ=½), RMP CMP. I,, RMP CMP γ-,, : (RMP & CMP): [ 1, ] = [σ 1 1,σ ] [ 1, ] = [σ 1 1,σ ] T, -- --, : ( σ ) ( ) = σ = σ. W,, --, (,, R ). I, (.., ),, (.., ),. A,,, 11
( ). T ( G O 1990, G 1993, G H 1996). T CA,. T SVD CA, () (7) S, (8), : α +α 1 1 1 (9) O (9) /( ) 1; (3) ( = 1,) X Y (6) (7). H, X, F (4), CA, RMP -. O, Y,, CMP -. I, F 1, -,. C, SPSS C, I, F Bé Bé F. N G (00),,. T CA. T CA, ( ): [ 1 0 0... 0 ], [ 0 1 0... 0 ],. F,,. T CA. T α CA 1, (,, G, 1984). A, 1
(9). L, α. F 3,. I F (- - ), ( F 3 F 1, 0. 45 0. 073 ). T F 3. T,,. I F 4,, 1,. I F 4, 1. B ( ),,. T, F 4 ( F 3). T CA,, (9). W (9) : ( α 1 1) 1 + ( α ) (10),,. I,. S F 4,. T,,,. T, : (10), (=6). I 13
,, (10) : ( α 11)( 1) + ( α )( ) (11) ( - SVD). T (11) [α 1 1, α ] [ 1, ]. T F 5. N, (),,. T CA,, G & O (1990). B F 5,,, (11),. A (10) (11) : 1/ ( )( 1/ ) ( )( 1/ α 11 1 + α ) (1),. T F 6. M, F 6,,, ( - - ). T - (G 1993, 1993, A G 00),. I F 7,, (1): 1/ ( 1/ )( ) ( 1/ 1 α 1 1 + )( α ) (13) I F 6 7. S, CA. I 14
() F 6, () F 7. I, CA -. H. N : F 6 F 6 ( ), F 7 F 7 ( ). A,,,,,... 7. T T,?. R CA,, : ()? () CA, CA? F,? T,,. T,. I CA,. T,,,. T PCA/ CA. A,, CA, [1... ] : Σ = 1,. R, PCA/,. F - 15
. I ( F 3 6). H,,,, MCA. F, F 8 MCA 10. A,. S, -. T,,,? V V (000) V K (005),. I. I (..,, ),,. T (. PCA/ ). T, (). A,, :. T (,, A, 004), - PCA,. A CA, - -. T, :, J : 1 ( ~ ~ ) (14) J 16
~ ~, (, )- Y = YQ, Q. N 1/. S ~ = ( ~ ),, : () 1 /, CA S 6. T. 8. S CA,. I,,, (L 1976, G 1984: S 8.1 ). I, (9), (G H 1986). I,, G (1984). I,,,. H. W ( ),? S. T CA. T λ = α -,,. I,. O :, - S 5. G (1984),. 17
E,. I,,. I,,. L,,. M (198) G (1984), N,, N 100 500. T. H N,. G (1984), - N ; L (006). T, M (198) - CA,, P,, P. F 9 100, 100,. R, :. F 10. S,,. F 11 8.7. I F 11 91.3%. T 95%, 5% (, ). T,. C 95% ( ), ( S R 1981:. 504 599, M C, 1996). F 1 95%. T,. W, (,, G (1993)), 18
,. I,. C. A - S T (1980),. G (1990: 408 417),. T,,. A, (F 13). C F 1,,. T,,. F,, ( ) (). F, F 1,? O 1 1 F 1,,. I, 10000, ( F 1) --,, P<0.00001. 9. S I CA,,. I I. () C :,, - CA. 19
() O: CA,. () S :,, F,. W,,,,,,, CA : (), -, () -. T. () R:, CA;, - ( () ),... () S :, ;,, / CA,,,,. 0
R ADACHI, K. (004). O P. B 31, 1 1. AITCHISON, J. GREENACRE, M.J. (00). B. A S 51, 375 39. GABRIEL, K.R. (1971). T -. B 58, 453 467. GABRIEL, K.R. (00). G. B 89, 43 436. GABRIEL, K.R. ODOROFF, C.L. (1990). B, S M 9, 43-436. GIFI, A. (1990). N M A. C, UK: W GILULA, Z. HABERMAN, S J. (1986). C. J A S A 81, 780 788. GOWER, J.C. HAND, D.J. (1996). B. L: C H. GOWER, J.C. (006). D : -. I M.J. G J. B (), M C A R M, L: C H,. GREENACRE, M.J. (1984). T A C A. L: A P. GREENACRE, M.J. (1993). B. J A S 0, 51 69. GREENACRE, M.J. (1993). C A P. L: A P. GREENACRE, M.J. (00). C S. G S 16, 160-170. GREENACRE, M.J. (004). W. W 777, D E E, U P F, B. HILL, M.O. (1974) C :. A S 3, 340 354. 1
LEBART, L. (1976). T. I J. G P. N (), P C S, P V, V,. 38 45. LEBART, L. (006). V. I M.J. G J. B (), M C A R M, L: C H,. LEGENDRE, P. (001). E. O 19, 71-80 MEULMAN, J. (198). H A I D. L, T N: DSWO P. MURDOCH, D.J. CHOW, E.D. (1996). A. A S 50, 178 180. PAGÈS, J. BÉCUE-BERTAUT, M. (006). M. I M.J. G J. B (), M C A R M. L: C H,. R DEVELOPMENT CORE TEAM (005). R: A L E S C. R F S C, V, A. ://.R-. RAO, C.R. (1995). A H. Qüó 19, 3 63. SILVERMAN, B.W. TITTERINGTON, D.M. (1980). M. SIAM J. S. S. C. 1, 401 409. SOKAL, R. R. ROHLF, F.J. (1981). B: T P P S B R. E. N Y:W.H. F C. VAN DE VELDEN, M. (000). S T C A. PD T, U A. VAN DE VELDEN, M. KIERS, H.A.L. (005). R. J C, 51 71.
T 1 D : 1 (R D C T 005). A. TD-B 550 116 147 374 1015 131 131 493 44 5 30 159 EW-B 557 19 18 343 996 158 19 571 555 4 76 91 47 D-M 515 109 17 311 87 167 136 376 43 8 61 80 146 A-M 554 108 06 43 797 164 100 38 471 4 34 93 149 LW-C 590 11 181 65 940 137 119 419 514 6 46 335 176 PF-C 59 151 51 38 985 168 15 381 544 7 39 416 36 FA-H 589 7 19 339 866 108 159 449 47 7 59 64 158 I-H 576 10 136 404 873 1 156 593 406 3 90 81 14 SF7-F 541 109 136 8 763 16 19 401 50 5 7 80 09 SF6-F 517 96 17 356 771 115 189 478 558 6 80 3 163 P3-H 557 97 145 354 909 97 11 479 431 10 94 40 154 P-H 541 93 149 390 887 133 154 463 518 4 65 65 194 A. TD-B 534 516 115 4 409 467 63 174 66 155 5 150 3 EW-B 479 509 9 3 413 533 63 181 68 187 10 184 4 D-M 470 561 140 4 368 387 63 195 60 156 14 137 5 A-M 48 53 145 8 361 40 630 196 66 149 80 6 LW-C 403 505 147 8 395 464 670 4 113 146 13 16 10 PF-C 56 54 107 9 418 508 655 6 89 106 15 14 0 FA-H 504 54 95 0 416 314 691 197 64 5 1 155 I-H 516 488 91 3 339 349 640 194 40 50 3 104 5 SF7-F 471 589 84 34 454 67 47 71 160 11 80 1 SF6-F 483 617 8 8 94 358 685 5 37 16 1 171 5 P3-H 417 477 100 3 305 415 597 37 64 194 9 140 4 P-H 484 545 70 4 99 43 644 193 66 18 17 A: TD (T D), EW (E W) B (P S. B) D (D), A (A) M (J M) LW (L W), PF (P F) C (A C. C) FA (F A), I (I) H (E H) SF7 SF6 (S F, 7 6) F (W F) P3 P (B P, 3 ) H (V H) 3
T D : 10 N S 13 ( 1 11, R1 R ). S S 1 3 4 5 6 7 8 9 10 11 R1 R 1 193 79 150 7 141 30 114 136 67 71 99 5 1 49 30 57 34 39 63 58 71 39 68 76 5 48 3 19 39 11 38 18 0 11 30 40 3 55 65 4 9 6 5 30 35 11 13 5 63 1 0 1 5 17 7 15 8 10 13 1 10 8 18 5 8 3 6 1 4 1 6 7 3 10 8 1 4 6 7 4 0 3 4 11 8 1 3 3 9 3 8 7 1 6 1 3 4 1 8 6 6 4 6 9 4 5 11 1 3 3 3 1 10 1 5 7 1 5 4 0 1 0 4 0 0 0 4
.00369 (19.69 %) 0. 0.1 0-0.1 () () () 3 () () () 6 () () () () ().00766 (40.91 %) -0. 7 () -0.3-0.3-0. -0.1 0 0.1 0. 0.3 0.4 0.5 0.6 F 1: S CA : ; =0.01874 5
1 0.073 (19.1 %) R R1 0.5 8 3 0-0.5 11 1 7 6 9 1 3 7 8 10 5 5 6 4 9 0.45 (64.5 %) 10-1 4-1.5-1 -0.5 0 0.5 1 1.5 F : S CA : ; =0.380 6
0.073 (19.1 %) 8 3 7 1 R R1 11 9 6 1 1 0 3 0.45 (64.5 %) -1 0 8 1 3 7 10 4 5 5-1 6 9-10 -3-4 4 F 3: C CA :, () () ;. 7
4.00369 (19.69 %) 0.00766 (40.91 %) - -4-6 -4-0 4 6 8 10 F 4: R CA :, () () ;. 8
.00369 (19.69 %) 0. 0.1 0-0.1 () () () () 3 () () () () () () 6 ().00766 (40.91 %) -0. 7 () -0.3-0.3-0. -0.1 0 0.1 0. 0.3 0.4 0.5 0.6 F 5: G CA :, () (). 9
0..00369 (19.69 %) 0.1 0-0.1 () () () () 3 () () () ().00766 (40.91 %) () () 6 () 7 () -0. -0.3-0.4-0.5-0.6-0.7-0.5-0.4-0.3-0. -0.1 0 0.1 0. 0.3 0.4 F 6: S CA :, (), (). 30
0.073 (19.1 %) R R1 0.5 3 11 9 6 7 1 1 0 3 10 8 0.45 (64.5 %) 7 8 9 5 6-1 -0.5 0 0.5 1 1.5-0.5 10 4 5 4-1 F 7: S :, () (). 31
0.71 (9.07 %) CX BX GX IX 1 B- C- EX KX JX DX FX AX 0-1 E- I- HX D- B? J- K- C? H+ A+ F+ J? G+ K? E? K+ G? D? F? I? H? F- J+ G- B+ A? C+ E+ D+ 0.3143 (10.48 %) H- A- I+ -1 0 1 3 F 8: M 11, A B, C,..., K, + (),? (), - () X (). T ( ). 3
33 F 9: (P) 6, 100. T, ( ). -0. 0.0 0. 0.4 0.6 0.8-0.4-0. 0.0 0. 0.4 1
-0.4-0. 0.0 0. 0.4-0. 0.0 0. 0.4 0.6 0.8 1 F 10: C F 10,. 34
-0.4-0. 0.0 0. 0.4-0. 0.0 0. 0.4 0.6 0.8 1 F 11: P F 10, 8.7 ( 100 ) F 11. 35
-0.6-0.4-0. 0.0 0. 0.4-0. 0.0 0. 0.4 0.6 0.8 1.0 1 F 1: C 95%,. 36
-0.6-0.4-0. 0.0 0. 0.4-0. 0.0 0. 0.4 0.6 0.8 1.0 1 F 13: 95% (G 1990). 37