Capítulo 06: Transformação no Espaço Imagem
Maximiliano Gobbo
2024-01-12
Ref.: Cap. 10, item: 10.2: transformação por principais componentes - MENESES, P. R.; ALMEIDA, T. D.; ROSA, A. N. D. C. S.; SANO, E. E. et al. Introdução ao Processamento de Imagens de Sensoriamento Remoto. Brasília: UnB-CNPq, 276 p., 2012.
1 Introdução
A análise de componentes principais (PCA, do inglês Principal Component Analysis) é uma técnica estatística que é comumente usada para redução de dimensionalidade em conjuntos de dados multivariados. Ela é útil para identificar padrões nos dados, encontrar relações entre variáveis e reduzir a complexidade dos dados, mantendo a maior quantidade possível de informações.
No contexto de imagens orbitais, a PCA pode ser aplicada para reduzir a dimensionalidade dos dados das imagens, permitindo uma representação mais compacta dos padrões presentes nas imagens. Isso pode ser útil para visualização, compressão de dados ou para extrair características relevantes para análises posteriores.
Podemos aplicar a análise de componentes principais em uma imagem com uma única banda, como uma imagem em escala de cinza. Nesse caso, cada pixel na imagem representa um valor de intensidade em uma escala de cinza, onde valores mais baixos representam tons mais escuros e valores mais altos representam tons mais claros.
A PCA pode ser usada para encontrar os principais modos de variabilidade nos dados da imagem, o que essencialmente significa identificar os padrões dominantes nos valores de intensidade dos pixels. Isso pode ser útil para identificar características importantes na imagem ou para reduzir a dimensionalidade dos dados enquanto se mantém a maior parte da informação relevante.
Ao aplicar a análise de componentes principais (PCA) a uma imagem, é importante notar que a imagem resultante pode parecer diferente da imagem original. Isso ocorre porque a PCA reorganiza os dados da imagem de forma a capturar os principais modos de variabilidade presentes nos dados, o que pode resultar em uma representação diferente da imagem original.
No contexto da PCA aplicada a imagens em escala de cinza, a análise identificará os padrões dominantes nos valores de intensidade dos pixels e reorganizará esses padrões de acordo com sua importância relativa. Isso pode levar a uma nova representação da imagem que ainda mantém as características essenciais, mas pode ter uma aparência diferente da imagem original.
Por exemplo, se a PCA for usada para reduzir a dimensionalidade dos dados da imagem, a imagem resultante pode parecer mais suavizada ou simplificada em comparação com a imagem original. Isso ocorre porque a PCA está tentando capturar a maior parte da variabilidade nos dados com um número menor de componentes principais.
2 Transformação no Espaço Imagem em R
Na aula de hoje iremos precisar dos pacotes a seguir. Então, antes de iniciar, realizem a instalação dos pocotes e o carregamento dos mesmos, como instruído no código a seguir.
Antes de darmos início ao trabalho, vamos conferir se estamos trabalhando no diretório correto (pasta de trabalho).
## [1] "C:/ARQUIVOS COMPUTADOR/DOUTORADO/APOSTILA PROCESSAMENTO DIGITAL DE IMAGENS"Na prática de hoje iremos utilizar um recorte de uma imagem orbital captada da base de dados do INPE, na qual encontra-se a cidade de Franca-SP. O nome do arquivo na pasta de trabalho é franca_pan_banda4.tif.
#Carregamento da imagem orbital
franca <- raster("franca_pan_banda4.tif")
plot(franca, col = gray.colors(256), main = "Recorte de Franca")
Para começar a análise de componentes principais (PCA) na imagem, precisaremos preparar os dados adequadamente. Aqui está um passo a passo básico do que precisamos fazer:
1. Preparação dos dados: Primeiramente, vamos converter a imagem raster em um formato adequado para análise PCA, o que envolve a extração dos valores de intensidades dos pixels da imagem. Após a extração, vamos organizar estas informações em uma matriz para podermos prosseguir com a análise.
# Extraindo os valores de intensidade dos pixels
pixels_franca <- getValues(franca)
# Organizando os valores em uma matriz
matriz_pixels_franca <- matrix(pixels_franca, nrow = ncol(franca), ncol = nrow(franca))
# Transpondo a matriz para que cada linha represente um pixel
matriz_pixels_franca <- t(matriz_pixels_franca)
# Verificando as dimensões da matriz
dim(matriz_pixels_franca)## [1] 1762 1882Temos uma matriz com 1762 linhas e 1882 colunas, o que significa que a imagem “franca” tem 1762 pixels de altura e 1882 pixels de largura.
2. Normalização dos dados (opcional): Dependendo da escala dos valores de intensidade dos pixels, pode ser necessário normalizar os dados para garantir que todas as variáveis tenham a mesma escala. Isso é especialmente importante se houver grandes variações nas intensidades dos pixels. Normalizar os dados pode ser uma boa abordagem para lidar com valores ausentes e/ou infinitos e também pode ajudar a garantir que todas as variáveis tenham a mesma escala, o que é importante para a análise de PCA.Portanto, vamos normalizar os valores da matriz. No caso dos valores ausentes (NAs), faremos a substituição de NA por 0 para não prejudicar nossa análise.
# Normalizando os valores de intensidade dos pixels (0 a 1)
pixels_franca_normalizados <- matriz_pixels_franca / 255
# Substituindo valores NA por 0 na matriz de pixels normalizada
pixels_franca_normalizados[is.na(pixels_franca_normalizados)] <- 03. Aplicação da PCA: Uma vez que os dados estejam preparados e normalizados (se necessário), podemos aplicar a análise de componentes principais para extrair os principais modos de variabilidade presentes na imagem.
# Aplicando a análise de componentes principais (PCA)
pca_resultado_franca <- prcomp(pixels_franca_normalizados)
# Verificando o resumo do resultado da PCA
summary(pca_resultado_franca)## Importance of components:
## PC1 PC2 PC3 PC4 PC5 PC6 PC7
## Standard deviation 2.512 1.49765 1.08677 0.97009 0.86228 0.85892 0.8027
## Proportion of Variance 0.239 0.08493 0.04472 0.03564 0.02815 0.02794 0.0244
## Cumulative Proportion 0.239 0.32397 0.36870 0.40433 0.43249 0.46042 0.4848
## PC8 PC9 PC10 PC11 PC12 PC13 PC14
## Standard deviation 0.72394 0.6701 0.64821 0.60780 0.56693 0.56369 0.53035
## Proportion of Variance 0.01985 0.0170 0.01591 0.01399 0.01217 0.01203 0.01065
## Cumulative Proportion 0.50467 0.5217 0.53758 0.55157 0.56374 0.57577 0.58643
## PC15 PC16 PC17 PC18 PC19 PC20 PC21
## Standard deviation 0.5215 0.50927 0.46600 0.4625 0.44233 0.43163 0.41258
## Proportion of Variance 0.0103 0.00982 0.00822 0.0081 0.00741 0.00705 0.00645
## Cumulative Proportion 0.5967 0.60654 0.61477 0.6229 0.63027 0.63733 0.64378
## PC22 PC23 PC24 PC25 PC26 PC27 PC28
## Standard deviation 0.40766 0.39975 0.39087 0.38676 0.38022 0.37842 0.36908
## Proportion of Variance 0.00629 0.00605 0.00579 0.00566 0.00547 0.00542 0.00516
## Cumulative Proportion 0.65007 0.65612 0.66190 0.66757 0.67304 0.67847 0.68362
## PC29 PC30 PC31 PC32 PC33 PC34 PC35
## Standard deviation 0.3559 0.35045 0.34157 0.32791 0.32729 0.31881 0.31585
## Proportion of Variance 0.0048 0.00465 0.00442 0.00407 0.00406 0.00385 0.00378
## Cumulative Proportion 0.6884 0.69307 0.69749 0.70156 0.70562 0.70946 0.71324
## PC36 PC37 PC38 PC39 PC40 PC41 PC42
## Standard deviation 0.30965 0.30652 0.30446 0.30143 0.29791 0.29257 0.28918
## Proportion of Variance 0.00363 0.00356 0.00351 0.00344 0.00336 0.00324 0.00317
## Cumulative Proportion 0.71687 0.72043 0.72394 0.72738 0.73074 0.73398 0.73715
## PC43 PC44 PC45 PC46 PC47 PC48 PC49
## Standard deviation 0.28742 0.28100 0.2769 0.27009 0.26936 0.26628 0.26136
## Proportion of Variance 0.00313 0.00299 0.0029 0.00276 0.00275 0.00268 0.00259
## Cumulative Proportion 0.74028 0.74327 0.7462 0.74893 0.75168 0.75437 0.75695
## PC50 PC51 PC52 PC53 PC54 PC55 PC56
## Standard deviation 0.26031 0.25773 0.25457 0.25291 0.2463 0.24472 0.2411
## Proportion of Variance 0.00257 0.00252 0.00245 0.00242 0.0023 0.00227 0.0022
## Cumulative Proportion 0.75952 0.76203 0.76449 0.76691 0.7692 0.77147 0.7737
## PC57 PC58 PC59 PC60 PC61 PC62 PC63
## Standard deviation 0.23860 0.23826 0.2357 0.23272 0.23078 0.22750 0.22528
## Proportion of Variance 0.00216 0.00215 0.0021 0.00205 0.00202 0.00196 0.00192
## Cumulative Proportion 0.77583 0.77798 0.7801 0.78213 0.78415 0.78611 0.78803
## PC64 PC65 PC66 PC67 PC68 PC69 PC70
## Standard deviation 0.22473 0.22312 0.22246 0.22138 0.21834 0.21629 0.21438
## Proportion of Variance 0.00191 0.00189 0.00187 0.00186 0.00181 0.00177 0.00174
## Cumulative Proportion 0.78995 0.79183 0.79370 0.79556 0.79737 0.79914 0.80088
## PC71 PC72 PC73 PC74 PC75 PC76 PC77
## Standard deviation 0.2118 0.21081 0.20825 0.20715 0.20521 0.20266 0.20124
## Proportion of Variance 0.0017 0.00168 0.00164 0.00162 0.00159 0.00156 0.00153
## Cumulative Proportion 0.8026 0.80426 0.80590 0.80753 0.80912 0.81068 0.81221
## PC78 PC79 PC80 PC81 PC82 PC83 PC84
## Standard deviation 0.19937 0.19825 0.19812 0.19573 0.19413 0.19289 0.1922
## Proportion of Variance 0.00151 0.00149 0.00149 0.00145 0.00143 0.00141 0.0014
## Cumulative Proportion 0.81371 0.81520 0.81669 0.81814 0.81957 0.82098 0.8224
## PC85 PC86 PC87 PC88 PC89 PC90 PC91
## Standard deviation 0.19116 0.18953 0.18735 0.18619 0.1855 0.18453 0.18420
## Proportion of Variance 0.00138 0.00136 0.00133 0.00131 0.0013 0.00129 0.00128
## Cumulative Proportion 0.82376 0.82512 0.82645 0.82776 0.8291 0.83035 0.83164
## PC92 PC93 PC94 PC95 PC96 PC97 PC98
## Standard deviation 0.18284 0.18142 0.18041 0.17966 0.17936 0.17742 0.17728
## Proportion of Variance 0.00127 0.00125 0.00123 0.00122 0.00122 0.00119 0.00119
## Cumulative Proportion 0.83290 0.83415 0.83538 0.83661 0.83782 0.83902 0.84021
## PC99 PC100 PC101 PC102 PC103 PC104 PC105
## Standard deviation 0.17599 0.17499 0.17281 0.17217 0.17134 0.16966 0.16877
## Proportion of Variance 0.00117 0.00116 0.00113 0.00112 0.00111 0.00109 0.00108
## Cumulative Proportion 0.84138 0.84254 0.84367 0.84479 0.84590 0.84699 0.84807
## PC106 PC107 PC108 PC109 PC110 PC111 PC112
## Standard deviation 0.16752 0.16683 0.16640 0.16523 0.16480 0.16399 0.16352
## Proportion of Variance 0.00106 0.00105 0.00105 0.00103 0.00103 0.00102 0.00101
## Cumulative Proportion 0.84913 0.85019 0.85124 0.85227 0.85330 0.85432 0.85533
## PC113 PC114 PC115 PC116 PC117 PC118 PC119
## Standard deviation 0.1623 0.16163 0.16071 0.15988 0.15890 0.15827 0.15738
## Proportion of Variance 0.0010 0.00099 0.00098 0.00097 0.00096 0.00095 0.00094
## Cumulative Proportion 0.8563 0.85732 0.85829 0.85926 0.86022 0.86117 0.86210
## PC120 PC121 PC122 PC123 PC124 PC125 PC126
## Standard deviation 0.15652 0.15594 0.15514 0.15465 0.1541 0.15315 0.15234
## Proportion of Variance 0.00093 0.00092 0.00091 0.00091 0.0009 0.00089 0.00088
## Cumulative Proportion 0.86303 0.86395 0.86486 0.86577 0.8667 0.86756 0.86844
## PC127 PC128 PC129 PC130 PC131 PC132 PC133
## Standard deviation 0.15204 0.15073 0.15048 0.14962 0.14899 0.14814 0.14786
## Proportion of Variance 0.00088 0.00086 0.00086 0.00085 0.00084 0.00083 0.00083
## Cumulative Proportion 0.86931 0.87017 0.87103 0.87188 0.87272 0.87355 0.87438
## PC134 PC135 PC136 PC137 PC138 PC139 PC140
## Standard deviation 0.14661 0.14613 0.1455 0.1452 0.14424 0.14343 0.14318
## Proportion of Variance 0.00081 0.00081 0.0008 0.0008 0.00079 0.00078 0.00078
## Cumulative Proportion 0.87519 0.87600 0.8768 0.8776 0.87839 0.87917 0.87994
## PC141 PC142 PC143 PC144 PC145 PC146 PC147
## Standard deviation 0.14253 0.14224 0.14136 0.14065 0.14018 0.13892 0.13871
## Proportion of Variance 0.00077 0.00077 0.00076 0.00075 0.00074 0.00073 0.00073
## Cumulative Proportion 0.88071 0.88148 0.88223 0.88298 0.88373 0.88446 0.88519
## PC148 PC149 PC150 PC151 PC152 PC153 PC154
## Standard deviation 0.13775 0.13750 0.13679 0.1362 0.1359 0.13503 0.13402
## Proportion of Variance 0.00072 0.00072 0.00071 0.0007 0.0007 0.00069 0.00068
## Cumulative Proportion 0.88591 0.88662 0.88733 0.8880 0.8887 0.88942 0.89010
## PC155 PC156 PC157 PC158 PC159 PC160 PC161
## Standard deviation 0.13367 0.13322 0.13275 0.13221 0.13110 0.13092 0.13046
## Proportion of Variance 0.00068 0.00067 0.00067 0.00066 0.00065 0.00065 0.00064
## Cumulative Proportion 0.89078 0.89145 0.89212 0.89278 0.89343 0.89408 0.89472
## PC162 PC163 PC164 PC165 PC166 PC167 PC168
## Standard deviation 0.12937 0.12906 0.12858 0.12798 0.12744 0.12707 0.12650
## Proportion of Variance 0.00063 0.00063 0.00063 0.00062 0.00062 0.00061 0.00061
## Cumulative Proportion 0.89536 0.89599 0.89661 0.89723 0.89785 0.89846 0.89907
## PC169 PC170 PC171 PC172 PC173 PC174 PC175
## Standard deviation 0.1263 0.1254 0.12502 0.12465 0.12442 0.12353 0.12317
## Proportion of Variance 0.0006 0.0006 0.00059 0.00059 0.00059 0.00058 0.00057
## Cumulative Proportion 0.8997 0.9003 0.90086 0.90145 0.90203 0.90261 0.90319
## PC176 PC177 PC178 PC179 PC180 PC181 PC182
## Standard deviation 0.12204 0.12191 0.12165 0.12104 0.12061 0.12039 0.11984
## Proportion of Variance 0.00056 0.00056 0.00056 0.00055 0.00055 0.00055 0.00054
## Cumulative Proportion 0.90375 0.90431 0.90487 0.90543 0.90598 0.90653 0.90707
## PC183 PC184 PC185 PC186 PC187 PC188 PC189
## Standard deviation 0.11976 0.11929 0.11856 0.11812 0.11795 0.11760 0.11700
## Proportion of Variance 0.00054 0.00054 0.00053 0.00053 0.00053 0.00052 0.00052
## Cumulative Proportion 0.90761 0.90815 0.90869 0.90921 0.90974 0.91026 0.91078
## PC190 PC191 PC192 PC193 PC194 PC195 PC196
## Standard deviation 0.11672 0.11623 0.11560 0.1153 0.1147 0.11425 0.11404
## Proportion of Variance 0.00052 0.00051 0.00051 0.0005 0.0005 0.00049 0.00049
## Cumulative Proportion 0.91130 0.91181 0.91232 0.9128 0.9133 0.91381 0.91430
## PC197 PC198 PC199 PC200 PC201 PC202 PC203
## Standard deviation 0.11353 0.11297 0.11284 0.11242 0.11202 0.11177 0.11147
## Proportion of Variance 0.00049 0.00048 0.00048 0.00048 0.00048 0.00047 0.00047
## Cumulative Proportion 0.91479 0.91528 0.91576 0.91624 0.91671 0.91718 0.91766
## PC204 PC205 PC206 PC207 PC208 PC209 PC210
## Standard deviation 0.11126 0.11065 0.11042 0.10996 0.10957 0.10939 0.10894
## Proportion of Variance 0.00047 0.00046 0.00046 0.00046 0.00045 0.00045 0.00045
## Cumulative Proportion 0.91812 0.91859 0.91905 0.91951 0.91996 0.92041 0.92086
## PC211 PC212 PC213 PC214 PC215 PC216 PC217
## Standard deviation 0.10856 0.10820 0.10793 0.10785 0.10726 0.10684 0.10641
## Proportion of Variance 0.00045 0.00044 0.00044 0.00044 0.00044 0.00043 0.00043
## Cumulative Proportion 0.92131 0.92175 0.92219 0.92264 0.92307 0.92350 0.92393
## PC218 PC219 PC220 PC221 PC222 PC223 PC224
## Standard deviation 0.10603 0.10539 0.10531 0.10468 0.10453 0.10429 0.10404
## Proportion of Variance 0.00043 0.00042 0.00042 0.00041 0.00041 0.00041 0.00041
## Cumulative Proportion 0.92436 0.92478 0.92520 0.92561 0.92603 0.92644 0.92685
## PC225 PC226 PC227 PC228 PC229 PC230 PC231
## Standard deviation 0.10363 0.1033 0.1028 0.1027 0.10208 0.10180 0.10139
## Proportion of Variance 0.00041 0.0004 0.0004 0.0004 0.00039 0.00039 0.00039
## Cumulative Proportion 0.92726 0.9277 0.9281 0.9285 0.92885 0.92925 0.92964
## PC232 PC233 PC234 PC235 PC236 PC237 PC238
## Standard deviation 0.10120 0.10105 0.10072 0.10044 0.09997 0.09960 0.09954
## Proportion of Variance 0.00039 0.00039 0.00038 0.00038 0.00038 0.00038 0.00038
## Cumulative Proportion 0.93002 0.93041 0.93079 0.93118 0.93156 0.93193 0.93231
## PC239 PC240 PC241 PC242 PC243 PC244 PC245
## Standard deviation 0.09936 0.09896 0.09864 0.09840 0.09818 0.09744 0.09706
## Proportion of Variance 0.00037 0.00037 0.00037 0.00037 0.00036 0.00036 0.00036
## Cumulative Proportion 0.93268 0.93305 0.93342 0.93379 0.93415 0.93451 0.93487
## PC246 PC247 PC248 PC249 PC250 PC251 PC252
## Standard deviation 0.09688 0.09676 0.09638 0.09607 0.09564 0.09514 0.09504
## Proportion of Variance 0.00036 0.00035 0.00035 0.00035 0.00035 0.00034 0.00034
## Cumulative Proportion 0.93522 0.93558 0.93593 0.93628 0.93662 0.93697 0.93731
## PC253 PC254 PC255 PC256 PC257 PC258 PC259
## Standard deviation 0.09454 0.09406 0.09370 0.09348 0.09332 0.09322 0.09283
## Proportion of Variance 0.00034 0.00034 0.00033 0.00033 0.00033 0.00033 0.00033
## Cumulative Proportion 0.93765 0.93798 0.93832 0.93865 0.93898 0.93931 0.93963
## PC260 PC261 PC262 PC263 PC264 PC265 PC266
## Standard deviation 0.09275 0.09234 0.09215 0.09156 0.09150 0.09123 0.09082
## Proportion of Variance 0.00033 0.00032 0.00032 0.00032 0.00032 0.00032 0.00031
## Cumulative Proportion 0.93996 0.94028 0.94060 0.94092 0.94124 0.94155 0.94186
## PC267 PC268 PC269 PC270 PC271 PC272 PC273
## Standard deviation 0.09063 0.09003 0.08992 0.08980 0.08944 0.0894 0.08897
## Proportion of Variance 0.00031 0.00031 0.00031 0.00031 0.00030 0.0003 0.00030
## Cumulative Proportion 0.94217 0.94248 0.94279 0.94309 0.94340 0.9437 0.94400
## PC274 PC275 PC276 PC277 PC278 PC279 PC280
## Standard deviation 0.08889 0.08851 0.08821 0.08814 0.08783 0.08745 0.08732
## Proportion of Variance 0.00030 0.00030 0.00029 0.00029 0.00029 0.00029 0.00029
## Cumulative Proportion 0.94430 0.94459 0.94489 0.94518 0.94548 0.94576 0.94605
## PC281 PC282 PC283 PC284 PC285 PC286 PC287
## Standard deviation 0.08704 0.08664 0.08631 0.08612 0.08604 0.08587 0.08537
## Proportion of Variance 0.00029 0.00028 0.00028 0.00028 0.00028 0.00028 0.00028
## Cumulative Proportion 0.94634 0.94662 0.94691 0.94719 0.94747 0.94775 0.94802
## PC288 PC289 PC290 PC291 PC292 PC293 PC294
## Standard deviation 0.08513 0.08505 0.08478 0.08431 0.08412 0.08387 0.08367
## Proportion of Variance 0.00027 0.00027 0.00027 0.00027 0.00027 0.00027 0.00027
## Cumulative Proportion 0.94830 0.94857 0.94884 0.94911 0.94938 0.94965 0.94991
## PC295 PC296 PC297 PC298 PC299 PC300 PC301
## Standard deviation 0.08358 0.08330 0.08300 0.08270 0.08250 0.08222 0.08193
## Proportion of Variance 0.00026 0.00026 0.00026 0.00026 0.00026 0.00026 0.00025
## Cumulative Proportion 0.95018 0.95044 0.95070 0.95096 0.95122 0.95147 0.95173
## PC302 PC303 PC304 PC305 PC306 PC307 PC308
## Standard deviation 0.08172 0.08139 0.08128 0.08118 0.08101 0.08050 0.08039
## Proportion of Variance 0.00025 0.00025 0.00025 0.00025 0.00025 0.00025 0.00024
## Cumulative Proportion 0.95198 0.95223 0.95248 0.95273 0.95298 0.95322 0.95347
## PC309 PC310 PC311 PC312 PC313 PC314 PC315
## Standard deviation 0.08015 0.07959 0.07945 0.07930 0.07914 0.07896 0.07883
## Proportion of Variance 0.00024 0.00024 0.00024 0.00024 0.00024 0.00024 0.00024
## Cumulative Proportion 0.95371 0.95395 0.95419 0.95443 0.95467 0.95490 0.95514
## PC316 PC317 PC318 PC319 PC320 PC321 PC322
## Standard deviation 0.07873 0.07849 0.07840 0.07804 0.07791 0.07755 0.07728
## Proportion of Variance 0.00023 0.00023 0.00023 0.00023 0.00023 0.00023 0.00023
## Cumulative Proportion 0.95537 0.95561 0.95584 0.95607 0.95630 0.95653 0.95675
## PC323 PC324 PC325 PC326 PC327 PC328 PC329
## Standard deviation 0.07714 0.07673 0.07658 0.07609 0.07602 0.07590 0.07577
## Proportion of Variance 0.00023 0.00022 0.00022 0.00022 0.00022 0.00022 0.00022
## Cumulative Proportion 0.95698 0.95720 0.95742 0.95764 0.95786 0.95808 0.95830
## PC330 PC331 PC332 PC333 PC334 PC335 PC336
## Standard deviation 0.07555 0.07532 0.07496 0.07478 0.07453 0.07444 0.07414
## Proportion of Variance 0.00022 0.00021 0.00021 0.00021 0.00021 0.00021 0.00021
## Cumulative Proportion 0.95851 0.95873 0.95894 0.95915 0.95936 0.95957 0.95978
## PC337 PC338 PC339 PC340 PC341 PC342 PC343
## Standard deviation 0.07409 0.07394 0.07373 0.07352 0.0731 0.07294 0.07282
## Proportion of Variance 0.00021 0.00021 0.00021 0.00020 0.0002 0.00020 0.00020
## Cumulative Proportion 0.95999 0.96020 0.96040 0.96061 0.9608 0.96101 0.96121
## PC344 PC345 PC346 PC347 PC348 PC349 PC350
## Standard deviation 0.07256 0.07247 0.07217 0.07211 0.07185 0.07164 0.07147
## Proportion of Variance 0.00020 0.00020 0.00020 0.00020 0.00020 0.00019 0.00019
## Cumulative Proportion 0.96141 0.96161 0.96181 0.96200 0.96220 0.96239 0.96259
## PC351 PC352 PC353 PC354 PC355 PC356 PC357
## Standard deviation 0.07120 0.07111 0.07088 0.07061 0.07045 0.07006 0.06989
## Proportion of Variance 0.00019 0.00019 0.00019 0.00019 0.00019 0.00019 0.00018
## Cumulative Proportion 0.96278 0.96297 0.96316 0.96335 0.96354 0.96372 0.96391
## PC358 PC359 PC360 PC361 PC362 PC363 PC364
## Standard deviation 0.06974 0.06963 0.06953 0.06925 0.06892 0.06879 0.06867
## Proportion of Variance 0.00018 0.00018 0.00018 0.00018 0.00018 0.00018 0.00018
## Cumulative Proportion 0.96409 0.96428 0.96446 0.96464 0.96482 0.96500 0.96518
## PC365 PC366 PC367 PC368 PC369 PC370 PC371
## Standard deviation 0.06832 0.06825 0.06817 0.06788 0.06762 0.06750 0.06720
## Proportion of Variance 0.00018 0.00018 0.00018 0.00017 0.00017 0.00017 0.00017
## Cumulative Proportion 0.96535 0.96553 0.96571 0.96588 0.96605 0.96623 0.96640
## PC372 PC373 PC374 PC375 PC376 PC377 PC378
## Standard deviation 0.06715 0.06701 0.06680 0.06676 0.06662 0.06651 0.06620
## Proportion of Variance 0.00017 0.00017 0.00017 0.00017 0.00017 0.00017 0.00017
## Cumulative Proportion 0.96657 0.96674 0.96691 0.96708 0.96724 0.96741 0.96758
## PC379 PC380 PC381 PC382 PC383 PC384 PC385
## Standard deviation 0.06587 0.06577 0.06566 0.06557 0.06543 0.06517 0.06506
## Proportion of Variance 0.00016 0.00016 0.00016 0.00016 0.00016 0.00016 0.00016
## Cumulative Proportion 0.96774 0.96791 0.96807 0.96823 0.96839 0.96855 0.96872
## PC386 PC387 PC388 PC389 PC390 PC391 PC392
## Standard deviation 0.06474 0.06457 0.06451 0.06442 0.06426 0.06402 0.06380
## Proportion of Variance 0.00016 0.00016 0.00016 0.00016 0.00016 0.00016 0.00015
## Cumulative Proportion 0.96887 0.96903 0.96919 0.96935 0.96950 0.96966 0.96981
## PC393 PC394 PC395 PC396 PC397 PC398 PC399
## Standard deviation 0.06371 0.06353 0.06343 0.06315 0.06311 0.06287 0.06244
## Proportion of Variance 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015 0.00015
## Cumulative Proportion 0.96997 0.97012 0.97027 0.97042 0.97057 0.97072 0.97087
## PC400 PC401 PC402 PC403 PC404 PC405 PC406
## Standard deviation 0.06236 0.06218 0.06216 0.06190 0.06169 0.06160 0.06142
## Proportion of Variance 0.00015 0.00015 0.00015 0.00015 0.00014 0.00014 0.00014
## Cumulative Proportion 0.97102 0.97116 0.97131 0.97146 0.97160 0.97174 0.97189
## PC407 PC408 PC409 PC410 PC411 PC412 PC413
## Standard deviation 0.06134 0.06123 0.06102 0.06084 0.06066 0.06050 0.06045
## Proportion of Variance 0.00014 0.00014 0.00014 0.00014 0.00014 0.00014 0.00014
## Cumulative Proportion 0.97203 0.97217 0.97231 0.97245 0.97259 0.97273 0.97287
## PC414 PC415 PC416 PC417 PC418 PC419 PC420
## Standard deviation 0.06020 0.06015 0.05987 0.05982 0.05951 0.05944 0.05929
## Proportion of Variance 0.00014 0.00014 0.00014 0.00014 0.00013 0.00013 0.00013
## Cumulative Proportion 0.97300 0.97314 0.97328 0.97341 0.97355 0.97368 0.97381
## PC421 PC422 PC423 PC424 PC425 PC426 PC427
## Standard deviation 0.05923 0.05900 0.05874 0.05864 0.05851 0.05826 0.05807
## Proportion of Variance 0.00013 0.00013 0.00013 0.00013 0.00013 0.00013 0.00013
## Cumulative Proportion 0.97395 0.97408 0.97421 0.97434 0.97447 0.97460 0.97473
## PC428 PC429 PC430 PC431 PC432 PC433 PC434
## Standard deviation 0.05806 0.05763 0.05759 0.05756 0.05740 0.05720 0.05703
## Proportion of Variance 0.00013 0.00013 0.00013 0.00013 0.00012 0.00012 0.00012
## Cumulative Proportion 0.97485 0.97498 0.97510 0.97523 0.97535 0.97548 0.97560
## PC435 PC436 PC437 PC438 PC439 PC440 PC441
## Standard deviation 0.05693 0.05681 0.05659 0.05655 0.05643 0.05629 0.05621
## Proportion of Variance 0.00012 0.00012 0.00012 0.00012 0.00012 0.00012 0.00012
## Cumulative Proportion 0.97572 0.97585 0.97597 0.97609 0.97621 0.97633 0.97645
## PC442 PC443 PC444 PC445 PC446 PC447 PC448
## Standard deviation 0.05606 0.05588 0.05575 0.05559 0.05536 0.05528 0.05497
## Proportion of Variance 0.00012 0.00012 0.00012 0.00012 0.00012 0.00012 0.00011
## Cumulative Proportion 0.97657 0.97669 0.97680 0.97692 0.97704 0.97715 0.97727
## PC449 PC450 PC451 PC452 PC453 PC454 PC455
## Standard deviation 0.05489 0.05473 0.05466 0.05458 0.05438 0.05426 0.05413
## Proportion of Variance 0.00011 0.00011 0.00011 0.00011 0.00011 0.00011 0.00011
## Cumulative Proportion 0.97738 0.97749 0.97761 0.97772 0.97783 0.97794 0.97806
## PC456 PC457 PC458 PC459 PC460 PC461 PC462
## Standard deviation 0.05402 0.05389 0.05373 0.05368 0.05349 0.05345 0.05329
## Proportion of Variance 0.00011 0.00011 0.00011 0.00011 0.00011 0.00011 0.00011
## Cumulative Proportion 0.97817 0.97828 0.97839 0.97849 0.97860 0.97871 0.97882
## PC463 PC464 PC465 PC466 PC467 PC468 PC469
## Standard deviation 0.05317 0.05311 0.05294 0.05282 0.05269 0.05254 0.05239
## Proportion of Variance 0.00011 0.00011 0.00011 0.00011 0.00011 0.00010 0.00010
## Cumulative Proportion 0.97893 0.97903 0.97914 0.97924 0.97935 0.97945 0.97956
## PC470 PC471 PC472 PC473 PC474 PC475 PC476
## Standard deviation 0.05225 0.05206 0.05197 0.05184 0.0517 0.05165 0.0515
## Proportion of Variance 0.00010 0.00010 0.00010 0.00010 0.0001 0.00010 0.0001
## Cumulative Proportion 0.97966 0.97976 0.97987 0.97997 0.9801 0.98017 0.9803
## PC477 PC478 PC479 PC480 PC481 PC482 PC483
## Standard deviation 0.05133 0.05115 0.05111 0.0509 0.05072 0.05068 0.05048
## Proportion of Variance 0.00010 0.00010 0.00010 0.0001 0.00010 0.00010 0.00010
## Cumulative Proportion 0.98037 0.98047 0.98057 0.9807 0.98076 0.98086 0.98096
## PC484 PC485 PC486 PC487 PC488 PC489 PC490
## Standard deviation 0.05027 0.05011 0.05009 0.04997 0.04977 0.04967 0.04948
## Proportion of Variance 0.00010 0.00010 0.00010 0.00009 0.00009 0.00009 0.00009
## Cumulative Proportion 0.98105 0.98115 0.98124 0.98134 0.98143 0.98152 0.98162
## PC491 PC492 PC493 PC494 PC495 PC496 PC497
## Standard deviation 0.04939 0.04921 0.04911 0.04904 0.04886 0.04881 0.04877
## Proportion of Variance 0.00009 0.00009 0.00009 0.00009 0.00009 0.00009 0.00009
## Cumulative Proportion 0.98171 0.98180 0.98189 0.98198 0.98207 0.98216 0.98225
## PC498 PC499 PC500 PC501 PC502 PC503 PC504
## Standard deviation 0.04841 0.04831 0.04828 0.04811 0.04805 0.04790 0.04773
## Proportion of Variance 0.00009 0.00009 0.00009 0.00009 0.00009 0.00009 0.00009
## Cumulative Proportion 0.98234 0.98243 0.98252 0.98261 0.98270 0.98278 0.98287
## PC505 PC506 PC507 PC508 PC509 PC510 PC511
## Standard deviation 0.04755 0.04751 0.04739 0.04729 0.04710 0.04694 0.04684
## Proportion of Variance 0.00009 0.00009 0.00009 0.00008 0.00008 0.00008 0.00008
## Cumulative Proportion 0.98295 0.98304 0.98312 0.98321 0.98329 0.98338 0.98346
## PC512 PC513 PC514 PC515 PC516 PC517 PC518
## Standard deviation 0.04672 0.04663 0.04653 0.04641 0.04628 0.04614 0.04603
## Proportion of Variance 0.00008 0.00008 0.00008 0.00008 0.00008 0.00008 0.00008
## Cumulative Proportion 0.98354 0.98362 0.98371 0.98379 0.98387 0.98395 0.98403
## PC519 PC520 PC521 PC522 PC523 PC524 PC525
## Standard deviation 0.04601 0.04578 0.04575 0.04558 0.04549 0.04541 0.04526
## Proportion of Variance 0.00008 0.00008 0.00008 0.00008 0.00008 0.00008 0.00008
## Cumulative Proportion 0.98411 0.98419 0.98427 0.98435 0.98443 0.98450 0.98458
## PC526 PC527 PC528 PC529 PC530 PC531 PC532
## Standard deviation 0.04523 0.04513 0.04496 0.04483 0.04474 0.04462 0.04458
## Proportion of Variance 0.00008 0.00008 0.00008 0.00008 0.00008 0.00008 0.00008
## Cumulative Proportion 0.98466 0.98474 0.98481 0.98489 0.98496 0.98504 0.98512
## PC533 PC534 PC535 PC536 PC537 PC538 PC539
## Standard deviation 0.04452 0.04446 0.04431 0.04423 0.04409 0.04398 0.04388
## Proportion of Variance 0.00008 0.00007 0.00007 0.00007 0.00007 0.00007 0.00007
## Cumulative Proportion 0.98519 0.98527 0.98534 0.98541 0.98549 0.98556 0.98563
## PC540 PC541 PC542 PC543 PC544 PC545 PC546
## Standard deviation 0.04367 0.04354 0.04343 0.04327 0.04316 0.04307 0.04295
## Proportion of Variance 0.00007 0.00007 0.00007 0.00007 0.00007 0.00007 0.00007
## Cumulative Proportion 0.98571 0.98578 0.98585 0.98592 0.98599 0.98606 0.98613
## PC547 PC548 PC549 PC550 PC551 PC552 PC553
## Standard deviation 0.04291 0.04279 0.04274 0.04260 0.04257 0.04238 0.04230
## Proportion of Variance 0.00007 0.00007 0.00007 0.00007 0.00007 0.00007 0.00007
## Cumulative Proportion 0.98620 0.98627 0.98634 0.98641 0.98648 0.98654 0.98661
## PC554 PC555 PC556 PC557 PC558 PC559 PC560
## Standard deviation 0.04222 0.04220 0.04206 0.04198 0.04190 0.04168 0.04163
## Proportion of Variance 0.00007 0.00007 0.00007 0.00007 0.00007 0.00007 0.00007
## Cumulative Proportion 0.98668 0.98675 0.98681 0.98688 0.98695 0.98701 0.98708
## PC561 PC562 PC563 PC564 PC565 PC566 PC567
## Standard deviation 0.04158 0.04144 0.04137 0.04128 0.04121 0.04114 0.04102
## Proportion of Variance 0.00007 0.00007 0.00006 0.00006 0.00006 0.00006 0.00006
## Cumulative Proportion 0.98714 0.98721 0.98727 0.98734 0.98740 0.98747 0.98753
## PC568 PC569 PC570 PC571 PC572 PC573 PC574
## Standard deviation 0.04089 0.04071 0.04056 0.04051 0.04042 0.04034 0.04020
## Proportion of Variance 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006
## Cumulative Proportion 0.98759 0.98766 0.98772 0.98778 0.98784 0.98790 0.98797
## PC575 PC576 PC577 PC578 PC579 PC580 PC581
## Standard deviation 0.04011 0.03995 0.03992 0.03983 0.03976 0.03962 0.03956
## Proportion of Variance 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006
## Cumulative Proportion 0.98803 0.98809 0.98815 0.98821 0.98827 0.98833 0.98839
## PC582 PC583 PC584 PC585 PC586 PC587 PC588
## Standard deviation 0.03944 0.03928 0.03924 0.03919 0.03908 0.03898 0.03893
## Proportion of Variance 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006
## Cumulative Proportion 0.98844 0.98850 0.98856 0.98862 0.98868 0.98873 0.98879
## PC589 PC590 PC591 PC592 PC593 PC594 PC595
## Standard deviation 0.03873 0.03869 0.03860 0.03842 0.03836 0.03834 0.03820
## Proportion of Variance 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006 0.00006
## Cumulative Proportion 0.98885 0.98891 0.98896 0.98902 0.98907 0.98913 0.98918
## PC596 PC597 PC598 PC599 PC600 PC601 PC602
## Standard deviation 0.03807 0.03795 0.03787 0.03780 0.03768 0.03764 0.03753
## Proportion of Variance 0.00005 0.00005 0.00005 0.00005 0.00005 0.00005 0.00005
## Cumulative Proportion 0.98924 0.98929 0.98935 0.98940 0.98946 0.98951 0.98956
## PC603 PC604 PC605 PC606 PC607 PC608 PC609
## Standard deviation 0.03744 0.03736 0.03728 0.03723 0.03717 0.03692 0.03690
## Proportion of Variance 0.00005 0.00005 0.00005 0.00005 0.00005 0.00005 0.00005
## Cumulative Proportion 0.98962 0.98967 0.98972 0.98977 0.98983 0.98988 0.98993
## PC610 PC611 PC612 PC613 PC614 PC615 PC616
## Standard deviation 0.03672 0.03667 0.03662 0.03651 0.03643 0.03631 0.03621
## Proportion of Variance 0.00005 0.00005 0.00005 0.00005 0.00005 0.00005 0.00005
## Cumulative Proportion 0.98998 0.99003 0.99008 0.99013 0.99018 0.99023 0.99028
## PC617 PC618 PC619 PC620 PC621 PC622 PC623
## Standard deviation 0.03618 0.03612 0.03602 0.03583 0.03574 0.03565 0.03562
## Proportion of Variance 0.00005 0.00005 0.00005 0.00005 0.00005 0.00005 0.00005
## Cumulative Proportion 0.99033 0.99038 0.99043 0.99048 0.99053 0.99058 0.99062
## PC624 PC625 PC626 PC627 PC628 PC629 PC630
## Standard deviation 0.03558 0.03551 0.03539 0.03525 0.03523 0.03518 0.03511
## Proportion of Variance 0.00005 0.00005 0.00005 0.00005 0.00005 0.00005 0.00005
## Cumulative Proportion 0.99067 0.99072 0.99077 0.99081 0.99086 0.99091 0.99095
## PC631 PC632 PC633 PC634 PC635 PC636 PC637
## Standard deviation 0.03501 0.03490 0.03478 0.03459 0.03458 0.03451 0.03437
## Proportion of Variance 0.00005 0.00005 0.00005 0.00005 0.00005 0.00005 0.00004
## Cumulative Proportion 0.99100 0.99105 0.99109 0.99114 0.99118 0.99123 0.99127
## PC638 PC639 PC640 PC641 PC642 PC643 PC644
## Standard deviation 0.03425 0.03420 0.03413 0.03402 0.03395 0.03383 0.03381
## Proportion of Variance 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004
## Cumulative Proportion 0.99132 0.99136 0.99141 0.99145 0.99149 0.99154 0.99158
## PC645 PC646 PC647 PC648 PC649 PC650 PC651
## Standard deviation 0.03379 0.03357 0.03353 0.03345 0.03340 0.03332 0.03325
## Proportion of Variance 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004
## Cumulative Proportion 0.99162 0.99167 0.99171 0.99175 0.99179 0.99184 0.99188
## PC652 PC653 PC654 PC655 PC656 PC657 PC658
## Standard deviation 0.03318 0.03311 0.03307 0.03296 0.03285 0.03282 0.03268
## Proportion of Variance 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004
## Cumulative Proportion 0.99192 0.99196 0.99200 0.99204 0.99208 0.99212 0.99217
## PC659 PC660 PC661 PC662 PC663 PC664 PC665
## Standard deviation 0.03256 0.03250 0.03237 0.03229 0.03227 0.03216 0.03208
## Proportion of Variance 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004
## Cumulative Proportion 0.99221 0.99225 0.99229 0.99232 0.99236 0.99240 0.99244
## PC666 PC667 PC668 PC669 PC670 PC671 PC672
## Standard deviation 0.03198 0.03187 0.03180 0.03178 0.03170 0.03161 0.03153
## Proportion of Variance 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004
## Cumulative Proportion 0.99248 0.99252 0.99256 0.99260 0.99263 0.99267 0.99271
## PC673 PC674 PC675 PC676 PC677 PC678 PC679
## Standard deviation 0.03144 0.03139 0.03136 0.03123 0.03114 0.03114 0.03095
## Proportion of Variance 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004
## Cumulative Proportion 0.99275 0.99278 0.99282 0.99286 0.99290 0.99293 0.99297
## PC680 PC681 PC682 PC683 PC684 PC685 PC686
## Standard deviation 0.03090 0.03088 0.03078 0.03069 0.03067 0.03064 0.03054
## Proportion of Variance 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004 0.00004
## Cumulative Proportion 0.99300 0.99304 0.99308 0.99311 0.99315 0.99318 0.99322
## PC687 PC688 PC689 PC690 PC691 PC692 PC693
## Standard deviation 0.03041 0.03036 0.03028 0.03023 0.03016 0.03003 0.02993
## Proportion of Variance 0.00004 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003
## Cumulative Proportion 0.99325 0.99329 0.99332 0.99336 0.99339 0.99343 0.99346
## PC694 PC695 PC696 PC697 PC698 PC699 PC700
## Standard deviation 0.02987 0.02982 0.02974 0.02967 0.02966 0.02961 0.02955
## Proportion of Variance 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003
## Cumulative Proportion 0.99349 0.99353 0.99356 0.99359 0.99363 0.99366 0.99369
## PC701 PC702 PC703 PC704 PC705 PC706 PC707
## Standard deviation 0.02943 0.02937 0.02931 0.02917 0.02907 0.02899 0.02898
## Proportion of Variance 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003
## Cumulative Proportion 0.99373 0.99376 0.99379 0.99382 0.99386 0.99389 0.99392
## PC708 PC709 PC710 PC711 PC712 PC713 PC714
## Standard deviation 0.02878 0.02871 0.02866 0.02863 0.02854 0.02853 0.02849
## Proportion of Variance 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003
## Cumulative Proportion 0.99395 0.99398 0.99401 0.99404 0.99408 0.99411 0.99414
## PC715 PC716 PC717 PC718 PC719 PC720 PC721
## Standard deviation 0.02846 0.02840 0.02828 0.02823 0.02815 0.02807 0.02806
## Proportion of Variance 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003
## Cumulative Proportion 0.99417 0.99420 0.99423 0.99426 0.99429 0.99432 0.99435
## PC722 PC723 PC724 PC725 PC726 PC727 PC728
## Standard deviation 0.02798 0.02783 0.02776 0.02770 0.02765 0.02754 0.02752
## Proportion of Variance 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003
## Cumulative Proportion 0.99438 0.99441 0.99444 0.99447 0.99449 0.99452 0.99455
## PC729 PC730 PC731 PC732 PC733 PC734 PC735
## Standard deviation 0.02749 0.02738 0.02731 0.02722 0.02719 0.02713 0.02709
## Proportion of Variance 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003
## Cumulative Proportion 0.99458 0.99461 0.99464 0.99467 0.99469 0.99472 0.99475
## PC736 PC737 PC738 PC739 PC740 PC741 PC742
## Standard deviation 0.02696 0.02693 0.02688 0.02683 0.02671 0.02671 0.02659
## Proportion of Variance 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003
## Cumulative Proportion 0.99478 0.99480 0.99483 0.99486 0.99489 0.99491 0.99494
## PC743 PC744 PC745 PC746 PC747 PC748 PC749
## Standard deviation 0.02650 0.02645 0.02641 0.02632 0.02625 0.02618 0.02613
## Proportion of Variance 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003 0.00003
## Cumulative Proportion 0.99497 0.99499 0.99502 0.99505 0.99507 0.99510 0.99512
## PC750 PC751 PC752 PC753 PC754 PC755 PC756
## Standard deviation 0.02602 0.02598 0.02592 0.02579 0.02578 0.02563 0.02558
## Proportion of Variance 0.00003 0.00003 0.00003 0.00003 0.00003 0.00002 0.00002
## Cumulative Proportion 0.99515 0.99517 0.99520 0.99522 0.99525 0.99527 0.99530
## PC757 PC758 PC759 PC760 PC761 PC762 PC763
## Standard deviation 0.02552 0.02547 0.02540 0.02538 0.02535 0.02532 0.02525
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99532 0.99535 0.99537 0.99540 0.99542 0.99545 0.99547
## PC764 PC765 PC766 PC767 PC768 PC769 PC770
## Standard deviation 0.02507 0.02503 0.02498 0.02493 0.02485 0.02478 0.02474
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99549 0.99552 0.99554 0.99557 0.99559 0.99561 0.99563
## PC771 PC772 PC773 PC774 PC775 PC776 PC777
## Standard deviation 0.02470 0.02467 0.02458 0.02455 0.02443 0.02438 0.02433
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99566 0.99568 0.99570 0.99573 0.99575 0.99577 0.99579
## PC778 PC779 PC780 PC781 PC782 PC783 PC784
## Standard deviation 0.02426 0.02417 0.02411 0.02408 0.02402 0.02398 0.02395
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99582 0.99584 0.99586 0.99588 0.99590 0.99593 0.99595
## PC785 PC786 PC787 PC788 PC789 PC790 PC791
## Standard deviation 0.02390 0.02384 0.02379 0.02371 0.02361 0.02356 0.02350
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99597 0.99599 0.99601 0.99603 0.99606 0.99608 0.99610
## PC792 PC793 PC794 PC795 PC796 PC797 PC798
## Standard deviation 0.02346 0.02338 0.02331 0.02328 0.02317 0.02309 0.02308
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99612 0.99614 0.99616 0.99618 0.99620 0.99622 0.99624
## PC799 PC800 PC801 PC802 PC803 PC804 PC805
## Standard deviation 0.02304 0.02301 0.02298 0.02290 0.02282 0.02280 0.02268
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99626 0.99628 0.99630 0.99632 0.99634 0.99636 0.99638
## PC806 PC807 PC808 PC809 PC810 PC811 PC812
## Standard deviation 0.02258 0.02258 0.02255 0.02247 0.02240 0.02238 0.02233
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99640 0.99642 0.99644 0.99646 0.99648 0.99649 0.99651
## PC813 PC814 PC815 PC816 PC817 PC818 PC819
## Standard deviation 0.02223 0.02215 0.02209 0.02205 0.02198 0.02192 0.02190
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99653 0.99655 0.99657 0.99659 0.99661 0.99662 0.99664
## PC820 PC821 PC822 PC823 PC824 PC825 PC826
## Standard deviation 0.02189 0.02186 0.02182 0.02173 0.02168 0.02165 0.02154
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99666 0.99668 0.99670 0.99671 0.99673 0.99675 0.99677
## PC827 PC828 PC829 PC830 PC831 PC832 PC833
## Standard deviation 0.02151 0.02146 0.02138 0.02134 0.02125 0.02117 0.02113
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99678 0.99680 0.99682 0.99684 0.99685 0.99687 0.99689
## PC834 PC835 PC836 PC837 PC838 PC839 PC840
## Standard deviation 0.02108 0.02103 0.02099 0.02091 0.02083 0.02080 0.02077
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99690 0.99692 0.99694 0.99695 0.99697 0.99699 0.99700
## PC841 PC842 PC843 PC844 PC845 PC846 PC847
## Standard deviation 0.02069 0.02067 0.02060 0.02057 0.02050 0.02047 0.02038
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99702 0.99704 0.99705 0.99707 0.99708 0.99710 0.99712
## PC848 PC849 PC850 PC851 PC852 PC853 PC854
## Standard deviation 0.02034 0.02030 0.02028 0.02023 0.02013 0.02010 0.02003
## Proportion of Variance 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002 0.00002
## Cumulative Proportion 0.99713 0.99715 0.99716 0.99718 0.99719 0.99721 0.99722
## PC855 PC856 PC857 PC858 PC859 PC860 PC861
## Standard deviation 0.01999 0.01989 0.01983 0.01979 0.01977 0.01970 0.01965
## Proportion of Variance 0.00002 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99724 0.99725 0.99727 0.99728 0.99730 0.99731 0.99733
## PC862 PC863 PC864 PC865 PC866 PC867 PC868
## Standard deviation 0.01963 0.01953 0.01952 0.01947 0.01939 0.01938 0.01935
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99734 0.99736 0.99737 0.99739 0.99740 0.99741 0.99743
## PC869 PC870 PC871 PC872 PC873 PC874 PC875
## Standard deviation 0.01931 0.01925 0.01919 0.01913 0.01910 0.01906 0.01899
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99744 0.99746 0.99747 0.99748 0.99750 0.99751 0.99753
## PC876 PC877 PC878 PC879 PC880 PC881 PC882
## Standard deviation 0.01894 0.01888 0.01884 0.01877 0.01870 0.01868 0.01862
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99754 0.99755 0.99757 0.99758 0.99759 0.99761 0.99762
## PC883 PC884 PC885 PC886 PC887 PC888 PC889
## Standard deviation 0.01859 0.01853 0.01847 0.01844 0.01842 0.01834 0.01832
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99763 0.99764 0.99766 0.99767 0.99768 0.99770 0.99771
## PC890 PC891 PC892 PC893 PC894 PC895 PC896
## Standard deviation 0.01827 0.01823 0.01817 0.01814 0.01804 0.01799 0.01795
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99772 0.99773 0.99775 0.99776 0.99777 0.99778 0.99780
## PC897 PC898 PC899 PC900 PC901 PC902 PC903
## Standard deviation 0.01793 0.01788 0.01782 0.01775 0.01773 0.01766 0.01765
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99781 0.99782 0.99783 0.99784 0.99786 0.99787 0.99788
## PC904 PC905 PC906 PC907 PC908 PC909 PC910
## Standard deviation 0.01760 0.01753 0.01750 0.01749 0.01747 0.01742 0.01739
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99789 0.99790 0.99791 0.99793 0.99794 0.99795 0.99796
## PC911 PC912 PC913 PC914 PC915 PC916 PC917
## Standard deviation 0.01734 0.01724 0.01720 0.01718 0.01714 0.01712 0.01707
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99797 0.99798 0.99799 0.99801 0.99802 0.99803 0.99804
## PC918 PC919 PC920 PC921 PC922 PC923 PC924
## Standard deviation 0.01705 0.01701 0.01699 0.01693 0.01685 0.01682 0.01679
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99805 0.99806 0.99807 0.99808 0.99809 0.99810 0.99811
## PC925 PC926 PC927 PC928 PC929 PC930 PC931
## Standard deviation 0.01670 0.01666 0.01665 0.01662 0.01658 0.01652 0.01646
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99813 0.99814 0.99815 0.99816 0.99817 0.99818 0.99819
## PC932 PC933 PC934 PC935 PC936 PC937 PC938
## Standard deviation 0.01643 0.01637 0.01634 0.01629 0.01626 0.01622 0.01619
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99820 0.99821 0.99822 0.99823 0.99824 0.99825 0.99826
## PC939 PC940 PC941 PC942 PC943 PC944 PC945
## Standard deviation 0.01616 0.01606 0.01603 0.01594 0.01592 0.01590 0.01587
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99827 0.99828 0.99829 0.99830 0.99831 0.99832 0.99833
## PC946 PC947 PC948 PC949 PC950 PC951 PC952
## Standard deviation 0.01581 0.01576 0.01572 0.01566 0.01562 0.01556 0.01549
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99834 0.99834 0.99835 0.99836 0.99837 0.99838 0.99839
## PC953 PC954 PC955 PC956 PC957 PC958 PC959
## Standard deviation 0.01549 0.01547 0.01542 0.01535 0.01533 0.01529 0.01525
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99840 0.99841 0.99842 0.99843 0.99844 0.99844 0.99845
## PC960 PC961 PC962 PC963 PC964 PC965 PC966
## Standard deviation 0.01521 0.01520 0.01518 0.01515 0.01513 0.01507 0.01500
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99846 0.99847 0.99848 0.99849 0.99850 0.99851 0.99851
## PC967 PC968 PC969 PC970 PC971 PC972 PC973
## Standard deviation 0.01498 0.01493 0.01488 0.01485 0.01482 0.01480 0.01474
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99852 0.99853 0.99854 0.99855 0.99856 0.99856 0.99857
## PC974 PC975 PC976 PC977 PC978 PC979 PC980
## Standard deviation 0.01471 0.01468 0.01461 0.01459 0.01454 0.01451 0.01448
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99858 0.99859 0.99860 0.99861 0.99861 0.99862 0.99863
## PC981 PC982 PC983 PC984 PC985 PC986 PC987
## Standard deviation 0.01441 0.01439 0.01436 0.01432 0.01426 0.01420 0.01419
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99864 0.99865 0.99865 0.99866 0.99867 0.99868 0.99868
## PC988 PC989 PC990 PC991 PC992 PC993 PC994
## Standard deviation 0.01414 0.01410 0.01407 0.01405 0.01402 0.01400 0.01392
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99869 0.99870 0.99871 0.99871 0.99872 0.99873 0.99874
## PC995 PC996 PC997 PC998 PC999 PC1000 PC1001
## Standard deviation 0.01384 0.01380 0.01374 0.01373 0.01372 0.01366 0.01365
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99874 0.99875 0.99876 0.99876 0.99877 0.99878 0.99879
## PC1002 PC1003 PC1004 PC1005 PC1006 PC1007 PC1008
## Standard deviation 0.01363 0.01361 0.01355 0.01351 0.01345 0.01344 0.01342
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99879 0.99880 0.99881 0.99881 0.99882 0.99883 0.99883
## PC1009 PC1010 PC1011 PC1012 PC1013 PC1014 PC1015
## Standard deviation 0.01337 0.01334 0.01333 0.01327 0.01324 0.01322 0.01318
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99884 0.99885 0.99885 0.99886 0.99887 0.99887 0.99888
## PC1016 PC1017 PC1018 PC1019 PC1020 PC1021 PC1022
## Standard deviation 0.01317 0.01309 0.01309 0.01305 0.01301 0.01295 0.01292
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99889 0.99889 0.99890 0.99891 0.99891 0.99892 0.99893
## PC1023 PC1024 PC1025 PC1026 PC1027 PC1028 PC1029
## Standard deviation 0.01288 0.01287 0.01283 0.01281 0.01280 0.01277 0.01273
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99893 0.99894 0.99894 0.99895 0.99896 0.99896 0.99897
## PC1030 PC1031 PC1032 PC1033 PC1034 PC1035 PC1036
## Standard deviation 0.01269 0.01262 0.01257 0.01255 0.01253 0.01247 0.01246
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99898 0.99898 0.99899 0.99899 0.99900 0.99901 0.99901
## PC1037 PC1038 PC1039 PC1040 PC1041 PC1042 PC1043
## Standard deviation 0.01244 0.01241 0.01233 0.01232 0.01228 0.01224 0.01218
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99902 0.99902 0.99903 0.99903 0.99904 0.99905 0.99905
## PC1044 PC1045 PC1046 PC1047 PC1048 PC1049 PC1050
## Standard deviation 0.01217 0.01211 0.01208 0.01206 0.01199 0.01195 0.01193
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99906 0.99906 0.99907 0.99907 0.99908 0.99908 0.99909
## PC1051 PC1052 PC1053 PC1054 PC1055 PC1056 PC1057
## Standard deviation 0.01191 0.01189 0.01184 0.01181 0.01180 0.01175 0.01172
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99910 0.99910 0.99911 0.99911 0.99912 0.99912 0.99913
## PC1058 PC1059 PC1060 PC1061 PC1062 PC1063 PC1064
## Standard deviation 0.01169 0.01169 0.01167 0.01164 0.01160 0.01158 0.01152
## Proportion of Variance 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001 0.00001
## Cumulative Proportion 0.99913 0.99914 0.99914 0.99915 0.99915 0.99916 0.99916
## PC1065 PC1066 PC1067 PC1068 PC1069 PC1070 PC1071
## Standard deviation 0.01151 0.01149 0.01143 0.01139 0.01138 0.01136 0.01132
## Proportion of Variance 0.00001 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
## Cumulative Proportion 0.99917 0.99917 0.99918 0.99918 0.99919 0.99919 0.99920
## PC1072 PC1073 PC1074 PC1075 PC1076 PC1077 PC1078
## Standard deviation 0.01126 0.01125 0.01123 0.01116 0.01115 0.01114 0.01109
## Proportion of Variance 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
## Cumulative Proportion 0.99920 0.99921 0.99921 0.99922 0.99922 0.99923 0.99923
## PC1079 PC1080 PC1081 PC1082 PC1083 PC1084 PC1085
## Standard deviation 0.01108 0.01105 0.01102 0.01099 0.01096 0.01092 0.0109
## Proportion of Variance 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.0000
## Cumulative Proportion 0.99924 0.99924 0.99924 0.99925 0.99925 0.99926 0.9993
## PC1086 PC1087 PC1088 PC1089 PC1090 PC1091 PC1092
## Standard deviation 0.01088 0.01083 0.01082 0.01079 0.01075 0.01073 0.01067
## Proportion of Variance 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
## Cumulative Proportion 0.99927 0.99927 0.99928 0.99928 0.99928 0.99929 0.99929
## PC1093 PC1094 PC1095 PC1096 PC1097 PC1098 PC1099
## Standard deviation 0.01064 0.01061 0.01058 0.01056 0.01054 0.01049 0.01049
## Proportion of Variance 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000 0.00000
## Cumulative Proportion 0.99930 0.99930 0.99931 0.99931 0.99931 0.99932 0.99932
## PC1100 PC1101 PC1102 PC1103 PC1104 PC1105 PC1106
## Standard deviation 0.01042 0.01041 0.01038 0.01036 0.01035 0.0103 0.01028
## Proportion of Variance 0.00000 0.00000 0.00000 0.00000 0.00000 0.0000 0.00000
## Cumulative Proportion 0.99933 0.99933 0.99934 0.99934 0.99934 0.9993 0.99935
## PC1107 PC1108 PC1109 PC1110 PC1111 PC1112 PC1113
## Standard deviation 0.01026 0.01025 0.01018 0.01015 0.01011 0.0101 0.01008
## Proportion of Variance 0.00000 0.00000 0.00000 0.00000 0.00000 0.0000 0.00000
## Cumulative Proportion 0.99936 0.99936 0.99936 0.99937 0.99937 0.9994 0.99938
## PC1114 PC1115 PC1116 PC1117 PC1118 PC1119
## Standard deviation 0.01006 0.01004 0.01001 0.009958 0.009925 0.009901
## Proportion of Variance 0.00000 0.00000 0.00000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.99938 0.99939 0.99939 0.999390 0.999400 0.999400
## PC1120 PC1121 PC1122 PC1123 PC1124 PC1125
## Standard deviation 0.009872 0.009847 0.009819 0.009789 0.009776 0.009741
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999410 0.999410 0.999410 0.999420 0.999420 0.999420
## PC1126 PC1127 PC1128 PC1129 PC1130 PC1131
## Standard deviation 0.009724 0.009695 0.009663 0.009639 0.009607 0.009586
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999430 0.999430 0.999430 0.999440 0.999440 0.999440
## PC1132 PC1133 PC1134 PC1135 PC1136 PC1137
## Standard deviation 0.009534 0.009525 0.009511 0.009473 0.009426 0.009392
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999450 0.999450 0.999450 0.999460 0.999460 0.999460
## PC1138 PC1139 PC1140 PC1141 PC1142 PC1143
## Standard deviation 0.009368 0.009359 0.009327 0.009305 0.009291 0.009272
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999470 0.999470 0.999470 0.999480 0.999480 0.999480
## PC1144 PC1145 PC1146 PC1147 PC1148 PC1149
## Standard deviation 0.009235 0.009225 0.009172 0.009145 0.009116 0.00907
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.00000
## Cumulative Proportion 0.999490 0.999490 0.999490 0.999500 0.999500 0.99950
## PC1150 PC1151 PC1152 PC1153 PC1154 PC1155
## Standard deviation 0.009068 0.009062 0.009034 0.00902 0.008996 0.008968
## Proportion of Variance 0.000000 0.000000 0.000000 0.00000 0.000000 0.000000
## Cumulative Proportion 0.999510 0.999510 0.999510 0.99952 0.999520 0.999520
## PC1156 PC1157 PC1158 PC1159 PC1160 PC1161
## Standard deviation 0.008934 0.008924 0.008893 0.008867 0.00884 0.008822
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.00000 0.000000
## Cumulative Proportion 0.999530 0.999530 0.999530 0.999530 0.99954 0.999540
## PC1162 PC1163 PC1164 PC1165 PC1166 PC1167
## Standard deviation 0.008784 0.008753 0.008725 0.008722 0.008699 0.00866
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.00000
## Cumulative Proportion 0.999540 0.999550 0.999550 0.999550 0.999550 0.99956
## PC1168 PC1169 PC1170 PC1171 PC1172 PC1173
## Standard deviation 0.008645 0.008618 0.008582 0.008572 0.008542 0.008525
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999560 0.999560 0.999570 0.999570 0.999570 0.999570
## PC1174 PC1175 PC1176 PC1177 PC1178 PC1179
## Standard deviation 0.008495 0.008457 0.008435 0.008403 0.008374 0.008354
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999580 0.999580 0.999580 0.999580 0.999590 0.999590
## PC1180 PC1181 PC1182 PC1183 PC1184 PC1185
## Standard deviation 0.008305 0.008297 0.008281 0.008256 0.008224 0.008199
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999590 0.999600 0.999600 0.999600 0.999600 0.999610
## PC1186 PC1187 PC1188 PC1189 PC1190 PC1191
## Standard deviation 0.008169 0.008169 0.008152 0.00813 0.008107 0.008096
## Proportion of Variance 0.000000 0.000000 0.000000 0.00000 0.000000 0.000000
## Cumulative Proportion 0.999610 0.999610 0.999610 0.99962 0.999620 0.999620
## PC1192 PC1193 PC1194 PC1195 PC1196 PC1197
## Standard deviation 0.00805 0.00804 0.008008 0.007984 0.007967 0.007952
## Proportion of Variance 0.00000 0.00000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.99962 0.99963 0.999630 0.999630 0.999630 0.999640
## PC1198 PC1199 PC1200 PC1201 PC1202 PC1203
## Standard deviation 0.007907 0.00788 0.007867 0.007848 0.007842 0.00782
## Proportion of Variance 0.000000 0.00000 0.000000 0.000000 0.000000 0.00000
## Cumulative Proportion 0.999640 0.99964 0.999640 0.999640 0.999650 0.99965
## PC1204 PC1205 PC1206 PC1207 PC1208 PC1209
## Standard deviation 0.007791 0.007771 0.007735 0.007724 0.007718 0.007668
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999650 0.999650 0.999660 0.999660 0.999660 0.999660
## PC1210 PC1211 PC1212 PC1213 PC1214 PC1215
## Standard deviation 0.007638 0.007629 0.007588 0.007578 0.007553 0.007526
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999670 0.999670 0.999670 0.999670 0.999670 0.999680
## PC1216 PC1217 PC1218 PC1219 PC1220 PC1221
## Standard deviation 0.007499 0.007465 0.007436 0.007413 0.007394 0.007383
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999680 0.999680 0.999680 0.999680 0.999690 0.999690
## PC1222 PC1223 PC1224 PC1225 PC1226 PC1227
## Standard deviation 0.007336 0.007331 0.007307 0.007287 0.00728 0.00727
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.00000 0.00000
## Cumulative Proportion 0.999690 0.999690 0.999690 0.999700 0.99970 0.99970
## PC1228 PC1229 PC1230 PC1231 PC1232 PC1233
## Standard deviation 0.00725 0.007224 0.0072 0.007186 0.007163 0.007135
## Proportion of Variance 0.00000 0.000000 0.0000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.99970 0.999700 0.9997 0.999710 0.999710 0.999710
## PC1234 PC1235 PC1236 PC1237 PC1238 PC1239
## Standard deviation 0.007113 0.007096 0.00707 0.007058 0.007036 0.007019
## Proportion of Variance 0.000000 0.000000 0.00000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999710 0.999720 0.99972 0.999720 0.999720 0.999720
## PC1240 PC1241 PC1242 PC1243 PC1244 PC1245
## Standard deviation 0.006979 0.006967 0.006939 0.006933 0.006913 0.006875
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999730 0.999730 0.999730 0.999730 0.999730 0.999730
## PC1246 PC1247 PC1248 PC1249 PC1250 PC1251
## Standard deviation 0.006858 0.006844 0.006832 0.006823 0.006786 0.006774
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999740 0.999740 0.999740 0.999740 0.999740 0.999750
## PC1252 PC1253 PC1254 PC1255 PC1256 PC1257
## Standard deviation 0.006763 0.00674 0.006718 0.006695 0.006667 0.006643
## Proportion of Variance 0.000000 0.00000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999750 0.99975 0.999750 0.999750 0.999750 0.999760
## PC1258 PC1259 PC1260 PC1261 PC1262 PC1263
## Standard deviation 0.006623 0.006608 0.006598 0.00657 0.006556 0.006536
## Proportion of Variance 0.000000 0.000000 0.000000 0.00000 0.000000 0.000000
## Cumulative Proportion 0.999760 0.999760 0.999760 0.99976 0.999760 0.999770
## PC1264 PC1265 PC1266 PC1267 PC1268 PC1269
## Standard deviation 0.006524 0.006513 0.006499 0.006485 0.006466 0.006439
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999770 0.999770 0.999770 0.999770 0.999770 0.999770
## PC1270 PC1271 PC1272 PC1273 PC1274 PC1275
## Standard deviation 0.006424 0.006406 0.006378 0.00636 0.006326 0.006307
## Proportion of Variance 0.000000 0.000000 0.000000 0.00000 0.000000 0.000000
## Cumulative Proportion 0.999780 0.999780 0.999780 0.99978 0.999780 0.999780
## PC1276 PC1277 PC1278 PC1279 PC1280 PC1281
## Standard deviation 0.006287 0.006277 0.006265 0.006254 0.006223 0.006213
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999790 0.999790 0.999790 0.999790 0.999790 0.999790
## PC1282 PC1283 PC1284 PC1285 PC1286 PC1287
## Standard deviation 0.00621 0.006188 0.00615 0.00612 0.006116 0.006111
## Proportion of Variance 0.00000 0.000000 0.00000 0.00000 0.000000 0.000000
## Cumulative Proportion 0.99979 0.999800 0.99980 0.99980 0.999800 0.999800
## PC1288 PC1289 PC1290 PC1291 PC1292 PC1293
## Standard deviation 0.006076 0.006071 0.006059 0.005996 0.005993 0.00598
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.00000
## Cumulative Proportion 0.999800 0.999800 0.999810 0.999810 0.999810 0.99981
## PC1294 PC1295 PC1296 PC1297 PC1298 PC1299
## Standard deviation 0.005967 0.005952 0.005934 0.00591 0.005898 0.005866
## Proportion of Variance 0.000000 0.000000 0.000000 0.00000 0.000000 0.000000
## Cumulative Proportion 0.999810 0.999810 0.999810 0.99982 0.999820 0.999820
## PC1300 PC1301 PC1302 PC1303 PC1304 PC1305
## Standard deviation 0.005863 0.005837 0.005815 0.005802 0.005788 0.005774
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999820 0.999820 0.999820 0.999820 0.999820 0.999830
## PC1306 PC1307 PC1308 PC1309 PC1310 PC1311
## Standard deviation 0.005752 0.005744 0.00573 0.005718 0.005698 0.005689
## Proportion of Variance 0.000000 0.000000 0.00000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999830 0.999830 0.99983 0.999830 0.999830 0.999830
## PC1312 PC1313 PC1314 PC1315 PC1316 PC1317
## Standard deviation 0.005665 0.005631 0.005623 0.005611 0.005579 0.005559
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999830 0.999840 0.999840 0.999840 0.999840 0.999840
## PC1318 PC1319 PC1320 PC1321 PC1322 PC1323
## Standard deviation 0.005542 0.005526 0.005509 0.005491 0.005473 0.005455
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999840 0.999840 0.999840 0.999840 0.999850 0.999850
## PC1324 PC1325 PC1326 PC1327 PC1328 PC1329
## Standard deviation 0.005444 0.005404 0.005399 0.005392 0.005366 0.005352
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999850 0.999850 0.999850 0.999850 0.999850 0.999850
## PC1330 PC1331 PC1332 PC1333 PC1334 PC1335
## Standard deviation 0.005331 0.005325 0.005305 0.005296 0.005279 0.005269
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999850 0.999860 0.999860 0.999860 0.999860 0.999860
## PC1336 PC1337 PC1338 PC1339 PC1340 PC1341
## Standard deviation 0.005255 0.005229 0.005227 0.005204 0.005181 0.005175
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999860 0.999860 0.999860 0.999860 0.999870 0.999870
## PC1342 PC1343 PC1344 PC1345 PC1346 PC1347
## Standard deviation 0.005171 0.005144 0.005131 0.005116 0.005112 0.005075
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999870 0.999870 0.999870 0.999870 0.999870 0.999870
## PC1348 PC1349 PC1350 PC1351 PC1352 PC1353
## Standard deviation 0.00506 0.005057 0.005045 0.005028 0.005005 0.004996
## Proportion of Variance 0.00000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.99987 0.999870 0.999870 0.999880 0.999880 0.999880
## PC1354 PC1355 PC1356 PC1357 PC1358 PC1359
## Standard deviation 0.004973 0.004955 0.004931 0.004916 0.004904 0.004895
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999880 0.999880 0.999880 0.999880 0.999880 0.999880
## PC1360 PC1361 PC1362 PC1363 PC1364 PC1365
## Standard deviation 0.004881 0.00487 0.004859 0.004832 0.004818 0.004803
## Proportion of Variance 0.000000 0.00000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999880 0.99989 0.999890 0.999890 0.999890 0.999890
## PC1366 PC1367 PC1368 PC1369 PC1370 PC1371
## Standard deviation 0.004795 0.004787 0.004772 0.004739 0.004731 0.004713
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999890 0.999890 0.999890 0.999890 0.999890 0.999890
## PC1372 PC1373 PC1374 PC1375 PC1376 PC1377
## Standard deviation 0.004699 0.004697 0.004676 0.004662 0.004647 0.004634
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999890 0.999900 0.999900 0.999900 0.999900 0.999900
## PC1378 PC1379 PC1380 PC1381 PC1382 PC1383
## Standard deviation 0.00463 0.004597 0.004593 0.004592 0.004578 0.004549
## Proportion of Variance 0.00000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.99990 0.999900 0.999900 0.999900 0.999900 0.999900
## PC1384 PC1385 PC1386 PC1387 PC1388 PC1389
## Standard deviation 0.004536 0.004527 0.004511 0.00449 0.004477 0.004453
## Proportion of Variance 0.000000 0.000000 0.000000 0.00000 0.000000 0.000000
## Cumulative Proportion 0.999900 0.999910 0.999910 0.99991 0.999910 0.999910
## PC1390 PC1391 PC1392 PC1393 PC1394 PC1395
## Standard deviation 0.004445 0.004434 0.00443 0.004425 0.004405 0.004397
## Proportion of Variance 0.000000 0.000000 0.00000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999910 0.999910 0.99991 0.999910 0.999910 0.999910
## PC1396 PC1397 PC1398 PC1399 PC1400 PC1401
## Standard deviation 0.00437 0.004346 0.004334 0.004311 0.004304 0.004287
## Proportion of Variance 0.00000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.99991 0.999910 0.999910 0.999920 0.999920 0.999920
## PC1402 PC1403 PC1404 PC1405 PC1406 PC1407
## Standard deviation 0.004269 0.004259 0.00425 0.004236 0.004231 0.00421
## Proportion of Variance 0.000000 0.000000 0.00000 0.000000 0.000000 0.00000
## Cumulative Proportion 0.999920 0.999920 0.99992 0.999920 0.999920 0.99992
## PC1408 PC1409 PC1410 PC1411 PC1412 PC1413
## Standard deviation 0.004202 0.004182 0.004174 0.004158 0.00415 0.004139
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.00000 0.000000
## Cumulative Proportion 0.999920 0.999920 0.999920 0.999920 0.99992 0.999920
## PC1414 PC1415 PC1416 PC1417 PC1418 PC1419
## Standard deviation 0.004106 0.004089 0.004083 0.004071 0.004055 0.004047
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999930 0.999930 0.999930 0.999930 0.999930 0.999930
## PC1420 PC1421 PC1422 PC1423 PC1424 PC1425
## Standard deviation 0.004032 0.004012 0.004008 0.003992 0.003973 0.003969
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999930 0.999930 0.999930 0.999930 0.999930 0.999930
## PC1426 PC1427 PC1428 PC1429 PC1430 PC1431
## Standard deviation 0.003952 0.003946 0.003944 0.00392 0.003893 0.003885
## Proportion of Variance 0.000000 0.000000 0.000000 0.00000 0.000000 0.000000
## Cumulative Proportion 0.999930 0.999930 0.999930 0.99993 0.999940 0.999940
## PC1432 PC1433 PC1434 PC1435 PC1436 PC1437
## Standard deviation 0.003872 0.003863 0.003845 0.003839 0.003825 0.003809
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999940 0.999940 0.999940 0.999940 0.999940 0.999940
## PC1438 PC1439 PC1440 PC1441 PC1442 PC1443
## Standard deviation 0.003799 0.00377 0.003761 0.00375 0.003744 0.003729
## Proportion of Variance 0.000000 0.00000 0.000000 0.00000 0.000000 0.000000
## Cumulative Proportion 0.999940 0.99994 0.999940 0.99994 0.999940 0.999940
## PC1444 PC1445 PC1446 PC1447 PC1448 PC1449
## Standard deviation 0.003716 0.003701 0.003694 0.003686 0.003666 0.003661
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999940 0.999940 0.999940 0.999940 0.999940 0.999950
## PC1450 PC1451 PC1452 PC1453 PC1454 PC1455
## Standard deviation 0.003628 0.003625 0.003616 0.003608 0.003579 0.003574
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999950 0.999950 0.999950 0.999950 0.999950 0.999950
## PC1456 PC1457 PC1458 PC1459 PC1460 PC1461
## Standard deviation 0.003574 0.003551 0.003547 0.003528 0.003513 0.003509
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999950 0.999950 0.999950 0.999950 0.999950 0.999950
## PC1462 PC1463 PC1464 PC1465 PC1466 PC1467
## Standard deviation 0.003486 0.003481 0.003475 0.00346 0.003434 0.00343
## Proportion of Variance 0.000000 0.000000 0.000000 0.00000 0.000000 0.00000
## Cumulative Proportion 0.999950 0.999950 0.999950 0.99995 0.999950 0.99995
## PC1468 PC1469 PC1470 PC1471 PC1472 PC1473
## Standard deviation 0.003414 0.003399 0.003386 0.003372 0.003352 0.003346
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999950 0.999950 0.999960 0.999960 0.999960 0.999960
## PC1474 PC1475 PC1476 PC1477 PC1478 PC1479
## Standard deviation 0.003334 0.003326 0.003305 0.003302 0.003294 0.003279
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999960 0.999960 0.999960 0.999960 0.999960 0.999960
## PC1480 PC1481 PC1482 PC1483 PC1484 PC1485
## Standard deviation 0.003265 0.003262 0.003244 0.003227 0.003218 0.003202
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999960 0.999960 0.999960 0.999960 0.999960 0.999960
## PC1486 PC1487 PC1488 PC1489 PC1490 PC1491
## Standard deviation 0.003192 0.00318 0.003165 0.003158 0.00315 0.003146
## Proportion of Variance 0.000000 0.00000 0.000000 0.000000 0.00000 0.000000
## Cumulative Proportion 0.999960 0.99996 0.999960 0.999960 0.99996 0.999960
## PC1492 PC1493 PC1494 PC1495 PC1496 PC1497
## Standard deviation 0.003128 0.003117 0.003105 0.003089 0.003081 0.003066
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999960 0.999960 0.999960 0.999970 0.999970 0.999970
## PC1498 PC1499 PC1500 PC1501 PC1502 PC1503
## Standard deviation 0.003058 0.003047 0.003045 0.003014 0.00301 0.003006
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.00000 0.000000
## Cumulative Proportion 0.999970 0.999970 0.999970 0.999970 0.99997 0.999970
## PC1504 PC1505 PC1506 PC1507 PC1508 PC1509
## Standard deviation 0.002987 0.002981 0.002973 0.002949 0.002939 0.002925
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999970 0.999970 0.999970 0.999970 0.999970 0.999970
## PC1510 PC1511 PC1512 PC1513 PC1514 PC1515
## Standard deviation 0.002912 0.002908 0.0029 0.002881 0.002874 0.002865
## Proportion of Variance 0.000000 0.000000 0.0000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999970 0.999970 1.0000 0.999970 0.999970 0.999970
## PC1516 PC1517 PC1518 PC1519 PC1520 PC1521
## Standard deviation 0.002851 0.00284 0.00282 0.002807 0.002794 0.002784
## Proportion of Variance 0.000000 0.00000 0.00000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999970 0.99997 0.99997 0.999970 0.999970 0.999970
## PC1522 PC1523 PC1524 PC1525 PC1526 PC1527
## Standard deviation 0.002774 0.002767 0.002759 0.002748 0.002738 0.00273
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.00000
## Cumulative Proportion 0.999970 0.999970 0.999970 0.999970 0.999980 0.99998
## PC1528 PC1529 PC1530 PC1531 PC1532 PC1533
## Standard deviation 0.002724 0.002708 0.002689 0.00267 0.002663 0.002652
## Proportion of Variance 0.000000 0.000000 0.000000 0.00000 0.000000 0.000000
## Cumulative Proportion 0.999980 0.999980 0.999980 0.99998 0.999980 0.999980
## PC1534 PC1535 PC1536 PC1537 PC1538 PC1539
## Standard deviation 0.002643 0.002636 0.002628 0.002615 0.0026 0.002578
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.0000 0.000000
## Cumulative Proportion 0.999980 0.999980 0.999980 0.999980 1.0000 0.999980
## PC1540 PC1541 PC1542 PC1543 PC1544 PC1545
## Standard deviation 0.002576 0.00257 0.002559 0.002548 0.002536 0.00253
## Proportion of Variance 0.000000 0.00000 0.000000 0.000000 0.000000 0.00000
## Cumulative Proportion 0.999980 0.99998 0.999980 0.999980 0.999980 0.99998
## PC1546 PC1547 PC1548 PC1549 PC1550 PC1551
## Standard deviation 0.002523 0.002511 0.002502 0.002482 0.002468 0.002457
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999980 0.999980 0.999980 0.999980 0.999980 0.999980
## PC1552 PC1553 PC1554 PC1555 PC1556 PC1557
## Standard deviation 0.002447 0.002439 0.002422 0.002418 0.002405 0.002389
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999980 0.999980 0.999980 0.999980 0.999980 0.999980
## PC1558 PC1559 PC1560 PC1561 PC1562 PC1563
## Standard deviation 0.002376 0.002369 0.002366 0.002361 0.002345 0.002343
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999980 0.999980 0.999980 0.999980 0.999980 0.999980
## PC1564 PC1565 PC1566 PC1567 PC1568 PC1569
## Standard deviation 0.002329 0.002303 0.002294 0.002291 0.002286 0.002275
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999980 0.999980 0.999980 0.999980 0.999980 0.999990
## PC1570 PC1571 PC1572 PC1573 PC1574 PC1575
## Standard deviation 0.00226 0.002258 0.002241 0.002232 0.002227 0.002208
## Proportion of Variance 0.00000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.99999 0.999990 0.999990 0.999990 0.999990 0.999990
## PC1576 PC1577 PC1578 PC1579 PC1580 PC1581
## Standard deviation 0.002189 0.002186 0.002178 0.002166 0.002149 0.002142
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999990 0.999990 0.999990 0.999990 0.999990 0.999990
## PC1582 PC1583 PC1584 PC1585 PC1586 PC1587
## Standard deviation 0.002128 0.002123 0.002112 0.002101 0.002094 0.002083
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999990 0.999990 0.999990 0.999990 0.999990 0.999990
## PC1588 PC1589 PC1590 PC1591 PC1592 PC1593
## Standard deviation 0.002076 0.002067 0.002053 0.002036 0.002029 0.002015
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999990 0.999990 0.999990 0.999990 0.999990 0.999990
## PC1594 PC1595 PC1596 PC1597 PC1598 PC1599
## Standard deviation 0.002005 0.001991 0.001986 0.001977 0.001964 0.001959
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999990 0.999990 0.999990 0.999990 0.999990 0.999990
## PC1600 PC1601 PC1602 PC1603 PC1604 PC1605
## Standard deviation 0.001951 0.001944 0.001932 0.001926 0.001912 0.001901
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999990 0.999990 0.999990 0.999990 0.999990 0.999990
## PC1606 PC1607 PC1608 PC1609 PC1610 PC1611
## Standard deviation 0.001895 0.001883 0.001869 0.001845 0.00184 0.001837
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.00000 0.000000
## Cumulative Proportion 0.999990 0.999990 0.999990 0.999990 0.99999 0.999990
## PC1612 PC1613 PC1614 PC1615 PC1616 PC1617
## Standard deviation 0.001831 0.001813 0.001807 0.001794 0.001787 0.001785
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999990 0.999990 0.999990 0.999990 0.999990 0.999990
## PC1618 PC1619 PC1620 PC1621 PC1622 PC1623
## Standard deviation 0.001771 0.001756 0.001752 0.001744 0.001738 0.001731
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999990 0.999990 0.999990 0.999990 0.999990 0.999990
## PC1624 PC1625 PC1626 PC1627 PC1628 PC1629
## Standard deviation 0.001722 0.001709 0.001703 0.001694 0.001683 0.00168
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.00000
## Cumulative Proportion 0.999990 0.999990 0.999990 0.999990 0.999990 0.99999
## PC1630 PC1631 PC1632 PC1633 PC1634 PC1635
## Standard deviation 0.001655 0.00164 0.001635 0.001623 0.001612 0.001609
## Proportion of Variance 0.000000 0.00000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999990 0.99999 0.999990 0.999990 0.999990 0.999990
## PC1636 PC1637 PC1638 PC1639 PC1640 PC1641
## Standard deviation 0.001599 0.001587 0.001575 0.001569 0.001563 0.001558
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 0.999990 0.999990 0.999990 0.999990 1.000000 1.000000
## PC1642 PC1643 PC1644 PC1645 PC1646 PC1647
## Standard deviation 0.001547 0.001525 0.001518 0.001512 0.00151 0.001498
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.00000 0.000000
## Cumulative Proportion 1.000000 1.000000 1.000000 1.000000 1.00000 1.000000
## PC1648 PC1649 PC1650 PC1651 PC1652 PC1653
## Standard deviation 0.001487 0.001478 0.001457 0.001453 0.001435 0.001426
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
## PC1654 PC1655 PC1656 PC1657 PC1658 PC1659
## Standard deviation 0.00142 0.001416 0.001411 0.001395 0.001389 0.001375
## Proportion of Variance 0.00000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 1.00000 1.000000 1.000000 1.000000 1.000000 1.000000
## PC1660 PC1661 PC1662 PC1663 PC1664 PC1665
## Standard deviation 0.001364 0.001358 0.001347 0.001341 0.00132 0.001311
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.00000 0.000000
## Cumulative Proportion 1.000000 1.000000 1.000000 1.000000 1.00000 1.000000
## PC1666 PC1667 PC1668 PC1669 PC1670 PC1671
## Standard deviation 0.001299 0.001295 0.001291 0.001281 0.001275 0.001263
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
## PC1672 PC1673 PC1674 PC1675 PC1676 PC1677
## Standard deviation 0.001252 0.001235 0.001232 0.001217 0.001216 0.001207
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
## PC1678 PC1679 PC1680 PC1681 PC1682 PC1683
## Standard deviation 0.001202 0.001198 0.001186 0.00118 0.001172 0.001163
## Proportion of Variance 0.000000 0.000000 0.000000 0.00000 0.000000 0.000000
## Cumulative Proportion 1.000000 1.000000 1.000000 1.00000 1.000000 1.000000
## PC1684 PC1685 PC1686 PC1687 PC1688 PC1689
## Standard deviation 0.001152 0.001146 0.00113 0.001115 0.001112 0.001107
## Proportion of Variance 0.000000 0.000000 0.00000 0.000000 0.000000 0.000000
## Cumulative Proportion 1.000000 1.000000 1.00000 1.000000 1.000000 1.000000
## PC1690 PC1691 PC1692 PC1693 PC1694 PC1695
## Standard deviation 0.001088 0.001084 0.001083 0.001076 0.001066 0.001061
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.000000
## Cumulative Proportion 1.000000 1.000000 1.000000 1.000000 1.000000 1.000000
## PC1696 PC1697 PC1698 PC1699 PC1700 PC1701
## Standard deviation 0.001054 0.001036 0.001024 0.001013 0.001008 0.0009983
## Proportion of Variance 0.000000 0.000000 0.000000 0.000000 0.000000 0.0000000
## Cumulative Proportion 1.000000 1.000000 1.000000 1.000000 1.000000 1.0000000
## PC1702 PC1703 PC1704 PC1705 PC1706
## Standard deviation 0.0009853 0.0009824 0.0009771 0.000953 0.0009517
## Proportion of Variance 0.0000000 0.0000000 0.0000000 0.000000 0.0000000
## Cumulative Proportion 1.0000000 1.0000000 1.0000000 1.000000 1.0000000
## PC1707 PC1708 PC1709 PC1710 PC1711
## Standard deviation 0.0009364 0.0009353 0.0009265 0.000918 0.000912
## Proportion of Variance 0.0000000 0.0000000 0.0000000 0.000000 0.000000
## Cumulative Proportion 1.0000000 1.0000000 1.0000000 1.000000 1.000000
## PC1712 PC1713 PC1714 PC1715 PC1716
## Standard deviation 0.0008928 0.0008869 0.0008827 0.0008778 0.0008608
## Proportion of Variance 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## Cumulative Proportion 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## PC1717 PC1718 PC1719 PC1720 PC1721
## Standard deviation 0.0008581 0.000841 0.0008242 0.0008173 0.0008107
## Proportion of Variance 0.0000000 0.000000 0.0000000 0.0000000 0.0000000
## Cumulative Proportion 1.0000000 1.000000 1.0000000 1.0000000 1.0000000
## PC1722 PC1723 PC1724 PC1725 PC1726
## Standard deviation 0.000799 0.0007922 0.0007884 0.0007742 0.0007631
## Proportion of Variance 0.000000 0.0000000 0.0000000 0.0000000 0.0000000
## Cumulative Proportion 1.000000 1.0000000 1.0000000 1.0000000 1.0000000
## PC1727 PC1728 PC1729 PC1730 PC1731
## Standard deviation 0.0007601 0.0007483 0.0007339 0.0007274 0.0007142
## Proportion of Variance 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## Cumulative Proportion 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## PC1732 PC1733 PC1734 PC1735 PC1736
## Standard deviation 0.0007044 0.0007011 0.0006929 0.000684 0.000674
## Proportion of Variance 0.0000000 0.0000000 0.0000000 0.000000 0.000000
## Cumulative Proportion 1.0000000 1.0000000 1.0000000 1.000000 1.000000
## PC1737 PC1738 PC1739 PC1740 PC1741
## Standard deviation 0.0006701 0.0006565 0.0006511 0.0006283 0.0006177
## Proportion of Variance 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## Cumulative Proportion 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## PC1742 PC1743 PC1744 PC1745 PC1746
## Standard deviation 0.0006129 0.0005976 0.0005742 0.0005711 0.0005678
## Proportion of Variance 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## Cumulative Proportion 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## PC1747 PC1748 PC1749 PC1750 PC1751
## Standard deviation 0.0005453 0.0005404 0.0005195 0.0005116 0.0004966
## Proportion of Variance 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## Cumulative Proportion 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## PC1752 PC1753 PC1754 PC1755 PC1756
## Standard deviation 0.0004839 0.0004722 0.000456 0.0004392 0.0004354
## Proportion of Variance 0.0000000 0.0000000 0.000000 0.0000000 0.0000000
## Cumulative Proportion 1.0000000 1.0000000 1.000000 1.0000000 1.0000000
## PC1757 PC1758 PC1759 PC1760 PC1761
## Standard deviation 0.0004314 0.0004173 0.0003785 0.0003657 0.0003095
## Proportion of Variance 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000
## Cumulative Proportion 1.0000000 1.0000000 1.0000000 1.0000000 1.0000000
## PC1762
## Standard deviation 1.116e-15
## Proportion of Variance 0.000e+00
## Cumulative Proportion 1.000e+00O resumo apresentado pela função summary() é muito extenso, mas ele mostra a importância das componentes princiais (PCs) na explicação da variância dos dados. Cada PC tem um valor associado, que indica quanto da variância total dos dados ele explica. Neste contexto, podemos selecionar um número adequado de PCs com base na quantidade de variância que desejamos reter nos dados. Por exemplo, se quisermos reter 95% da variância total, podemos escolher as primeiras PCs que acumulam 95% da variância.
Para reter 95% da variância total na análise, podemos calcular a proporção da variância explicada por cada componente principal e selecionar as primeiras PCs que acumulam 95% da variância. Seguiremos os seguintes passos:
- Calcularemos os autovalores resultantes da análise PCA;
- Dividiremos cada autovalor pelo total da soma dos autovalores para obter a proporção da variância explicada por cada PC;
- Calcularemos a proporção cumulativa de variância acumulada;
- Determinaremos quantas PCs são necessárias para acumluar pelo menos 95% da variância total.
# Calcula a proporção de variância explicada por cada PC
variance_proportion <- pca_resultado_franca$sdev^2 / sum(pca_resultado_franca$sdev^2)
# Calcula a proporção cumulativa de variância explicada
cumulative_variance <- cumsum(variance_proportion)
# Determina quantas PCs são necessárias para reter 95% da variância
n_components <- which(cumulative_variance >= 0.95)[1]
# Exibe o resultado
print(paste("Numero de componentes necessarias para reter 95% da variancia:", n_components))## [1] "Numero de componentes necessarias para reter 95% da variancia: 295"De acordo com o resultado, sabemos que precisamos de 295 componentes principais para reter 95% da variância. Assim, podemos proceder com a redução da dimensionalidade, mantendo apenas esses componentes; isso nos ajudará a simplificar a representação dos dados, mantendo a maior parte da informação relevante. Vamos prosseguir com o código para realizar a redução da dimensionalidade.
# Reduzindo a dimensionalidade mantendo os 295 primeiros componentes principais
pca_reduzido_franca <- pca_resultado_franca$x[, 1:295]Após reduzir a dimensionalidade, o próximo passo é reconstruir a imagem usando os componentes principais reduzidos. Podemos fazer isso multiplicando a matriz dos componentes principais reduzidos pelos vetores próprios correspondentes e adicionando a média, se a média dos dados foi subtraída durante o processo de PCA. Essa ação nos dará uma aproximação da imagem original, mas com uma dimensionalidade reduzida. O código a seguir demonstra essa operação.
# Reconstruindo a imagem usando os componentes principais reduzidos
imagem_reconstruida <- pca_reduzido_franca %*% t(pca_resultado_franca$rotation[, 1:295])No código acima, a reconstrução da imagem é feita utilizando os componentes principais reduzidos (pca_reduzido_franca) e a matriz de rotação dos componentes principais (pca_resultado_franca$rotation[, 1:295]). Detalhando cada um dos aspectos:
pca_reduzido_franca: Esta é a matriz contendo os dados reduzidos para as dimensões escolhidas (neste caso, os 295 primeiros componentes principais). Cada linha dessa matriz representa um ponto de dados, e cada coluna representa uma dimensão reduzida.
pca_resultado_franca$rotation[, 1:295]: Esta é a matriz de rotação dos componentes principais. Ela contém os vetores de peso que são usados para transformar os dados originais em dados nos novos espaços de características definidos pelos componentes principais. Aqui, estamos selecionando apenas as primeiras 295 colunas, que correspondem aos primeiros 295 componentes principais.
%*%: Este é o operador de multiplicação de matrizes em R. Ele realiza a multiplicação matricial entre pca_reduzido_franca e a transposta da matriz de rotação.
t(pca_resultado_franca$rotation[, 1:295]): Este trecho transpõe a matriz de rotação para garantir que as dimensões estejam alinhadas corretamente para a multiplicação.
imagem_reconstruida: Esta é a matriz resultante da multiplicação, que representa a imagem reconstruída no novo espaço de características definido pelos componentes principais.
Basicamente, multiplicamos os dados reduzidos pelos componentes principais pela transposta da matriz de rotação para reconstruir a imagem original a partir dos componentes principais reduzidos. Isso nos permite visualizar como a imagem se parece quando projetada no espaço de características definido pelos primeiros 295 componentes principais.
Agora vamos conferir se a matriz de imagem_reconstruida possui as mesmas dimensões da nossa matriz_pixels_franca, utilizando a função dim().
## [1] 1762 1882## [1] 1762 1882Os resultados demonstraram que a imagem_reconstruida possui a mesma dimensão de matriz_pixels_franca. Diante disso, podemos prosseguir com a reconstrução de fato da nossa imagem orbital, agora com os componentes principais reduzidos. Para reconstrução podemos usar a função raster(), criando uma imagem a partir da matriz imagem_reconstruida.
# Criando uma imagem raster a partir da matriz reconstruída
imagem_reconstruida_raster <- raster(matrix(imagem_reconstruida, ncol = ncol(imagem_reconstruida)))Após a reconstrução da nossa imagem, vamos comparar nossa imagem original de Franca e a imagem com componentes principais reduzidos.
# Plotar comparativamente a imagem original de Franca e a imagem com componentes principais reduzidos
par(mfrow=c(1,2))
plot(franca, col = gray.colors(256), main = "Recorte de Franca")
plot(imagem_reconstruida_raster, col = gray.colors(256), main = "Imagem PCA")
Comparativamente, observamos que a imagem com os componentes principais reduzidos mostra-se mais suavizada frente a imagem original de Franca, ou seja, verificamos que houve uma redução das intensidades colorimétricas que definem limites na área da imagem original.
Com isso, encerramos a prática de hoje sobre Transformação no Espaço Imagem, demonstrando a construção do código para a análise de principais componentes, reduzindo os valores colorimétricos através desta estrutura analítica e gerando uma imagem com os componentes principais reduzidos. Nos vemos na próxima aula.
Capítulo 05 - Morfologia Matemática
Capítulo 07 - Aritmética de Bandas: soma, subtração, multiplicação e divisão
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