Exemple de calcul d'une ACP avec MATLAB. |
MATLAB |
Résultats |
x= [38.01 ---------43.78 ];
[nligne ncol] =size(x); |
Lecture du tableau et calcul des dimensions
nligne =25
ncol =5
|
| moy = mean(x)' |
vecteur des moyennes
moy =
40.9544
108.0376
42.0076
268.3640
91.5688 |
| ect=std(x)' |
vecteur des ecarts-types
ect =
12.1300
170.7207
33.5872
151.5456
19.2988 |
vunit=linspace(1,1,nligne)'
y=x-vunit*moy'; |
Centrage des données
y =
-2.9444 -103.5476 -14.4576 -97.8140 -0.3588
-3.0644 -96.3076 32.2624 -119.2740 15.2712
-1.2844 -95.2076 -9.2476 -83.7340 7.1612
-4.3744 -81.9476 0.7624 -96.1740 -13.3988
-7.4944 -104.1776 3.0724 -85.2540 3.2412
-10.2744 -101.2376 -1.4576 -59.6040 -2.0888
-10.3744 395.1424 -16.3776 -98.0940 -14.8188
-6.3944 -105.3776 26.0224 -38.8840 7.3512
-11.4144 -101.4676 0.2024 -81.6040 -3.8888
-7.8744 -98.4076 -30.6576 -29.1540 -27.9988
-3.4244 -96.7576 120.3724 -81.3240 40.3812
-7.7144 175.0824 -7.6776 -114.3440 -2.3688
0.9656 -88.0376 -36.0576 -85.3540 -26.7388
-4.5744 -76.8876 6.0624 -40.3640 6.3212
-9.5844 191.4324 8.5824 -45.1140 24.6712
10.2756 -80.2776 -27.0176 -31.5240 9.7812
25.3656 -52.4976 68.8924 63.7860 29.3012
-4.3144 -52.4976 -9.7776 1.7660 -10.3188
23.6556 -70.1376 -25.8576 222.5860 0.0412
13.7056 13.6024 -24.4276 386.7760 -12.2888
4.7756 283.7924 -14.4476 150.6360 14.3812
11.4656 -72.9876 -6.9076 426.1660 -12.5688
26.7456 507.1724 -8.2676 92.4360 22.2712
-1.3944 -21.8176 -7.9576 25.9360 -5.5488
-20.4544 -66.6476 -25.6376 -182.4740 -47.7888
|
ds=diag(ect)^-1 |
Matrice diagonale des 1/ect
ds =
0.0824 0 0 0 0
0 0.0059 0 0 0
0 0 0.0298 0 0
0 0 0 0.0066 0
0 0 0 0 0.0518 |
| z=y*ds |
Matrice des données centrées et reduites
z =
-0.2427 -0.6065 -0.4305 -0.6454 -0.0186
-0.2526 -0.5641 0.9606 -0.7871 0.7913
-0.1059 -0.5577 -0.2753 -0.5525 0.3711
-0.3606 -0.4800 0.0227 -0.6346 -0.6943
-0.6178 -0.6102 0.0915 -0.5626 0.1679
-0.8470 -0.5930 -0.0434 -0.3933 -0.1082
-0.8553 2.3146 -0.4876 -0.6473 -0.7679
-0.5272 -0.6173 0.7748 -0.2566 0.3809
-0.9410 -0.5943 0.0060 -0.5385 -0.2015
-0.6492 -0.5764 -0.9128 -0.1924 -1.4508
-0.2823 -0.5668 3.5839 -0.5366 2.0924
-0.6360 1.0255 -0.2286 -0.7545 -0.1227
0.0796 -0.5157 -1.0736 -0.5632 -1.3855
-0.3771 -0.4504 0.1805 -0.2663 0.3275
-0.7901 1.1213 0.2555 -0.2977 1.2784
0.8471 -0.4702 -0.8044 -0.2080 0.5068
2.0911 -0.3075 2.0512 0.4209 1.5183
-0.3557 -0.3075 -0.2911 0.0117 -0.5347
1.9502 -0.4108 -0.7699 1.4688 0.0021
1.1299 0.0797 -0.7273 2.5522 -0.6368
0.3937 1.6623 -0.4302 0.9940 0.7452
0.9452 -0.4275 -0.2057 2.8121 -0.6513
2.2049 2.9708 -0.2462 0.6100 1.1540
-0.1150 -0.1278 -0.2369 0.1711 -0.2875
-1.6863 -0.3904 -0.7633 -1.2041 -2.4763 |
| v=(z'*z)/nligne |
Matrice des corrélations
v =
0.9600 0.2105 0.0413 0.6568 0.3738
0.2105 0.9600 -0.1478 0.1199 0.1857
0.0413 -0.1478 0.9600 -0.1437 0.6750
0.6568 0.1199 -0.1437 0.9600 0.0437
0.3738 0.1857 0.6750 0.0437 0.9600 |
| [f h] = eig(v) |
Vecteurs propres :
f =
0.5657 -0.4505 -0.1819 -0.2948 0.5976
-0.2261 -0.1674 0.8987 -0.2246 0.2506
-0.4433 -0.5125 -0.1319 0.6516 0.3145
-0.6158 0.2641 -0.3493 -0.4911 0.4334
0.2307 0.6607 0.1410 0.4438 0.5416
Valeurs propres :
h =
0.2809 0 0 0 0
0 0.1520 0 0 0
0 0 0.9216 0 0
0 0 0 1.5603 0
0 0 0 0 1.8852
|
| coord=z*f |
Coordonnées des individus sur les axes
coord =
0.5838 0.2488 -0.2213 0.2360 -0.7222
0.2261 0.0309 -0.2012 1.5647 0.0973
0.6141 0.3814 -0.2003 0.4131 -0.3281
0.1251 -0.3952 -0.2450 0.2324 -0.9797
0.1331 0.2960 -0.2279 0.7296 -0.6462
-0.1086 0.3277 -0.2510 0.4997 -0.8975
-0.5695 -0.4306 2.4178 -0.6082 -0.7809
-0.2562 0.1276 -0.4177 1.0939 -0.1309
-0.1155 0.2450 -0.2041 0.5898 -1.0519
-0.0485 -0.1526 -0.4169 -0.8233 -1.6886
-0.8069 -0.3740 -0.4481 3.7378 1.7172
-0.0540 -0.0484 1.3137 0.1243 -0.5884
0.6647 -0.4635 -0.3350 -0.9454 -1.4138
0.0481 0.2989 -0.2207 0.6061 -0.2195
-0.3355 0.8033 1.4020 0.8612 0.4526
1.1871 0.3893 -0.3265 -0.3412 0.3198
0.4343 -0.8275 -0.8602 1.2561 2.8224
-0.1332 0.0107 -0.2527 -0.2588 -0.6657
0.6332 -0.0259 -1.1352 -1.7047 1.4580
-0.7751 0.1037 -1.0193 -2.3608 1.2277
-0.4027 0.5197 1.2369 -0.9271 1.3510
-1.1595 0.0635 -1.6031 -1.9867 1.2591
0.5753 -0.4409 2.2508 -1.2650 2.8740
-0.1028 0.0498 -0.1630 -0.3034 -0.2568
-0.3570 -0.7379 0.1280 -0.4202 -3.2086 |
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