PCA PPGEP
Fagner Sutel de Moura
8/19/2023
Utilizando Principal Component Analysis (PCA) no R
A partir da bibliteca factoextra é possível rodar PCA no R. Essa biblioteca conta com duas funções principais que são a prcomp e princomp.
A função prcomp utiliza a decomposição de valor singuar (SVD) erealiza cálculos a partir da decomposição de valor singular de uma matriz de dados por default centralizada e escalada, sem utilizar autovalores na matriz de covariância. Método preferido para precisão numérica.
A função princomp utiliza a abordagem de decomposição espectral e realiza cálculos utilizando autovalores de uma matriz de correlação ou covariância. Essa abordagem é realizada para compatibilidade com resultados do S-PLUS.
Dados
Para este exercício foi utilizada a base Wine onde os vinhos são classificados em três classes. Como tais classes diferem em termos de intensidade de cor, as classes foram renomeadas como Branco, Rosê e Tinto
library(factoextra)
dadoswine = read.table(file = "wine.csv", header = 0, sep = ",", na.strings = "NA")
names(dadoswine) = c("Classe", "Alcohol", "MalicAcid", "Ash", "Alcalinity", "Magnesium", "Phenols", "Flavanoids",
"Nonflavanoid", "Proanthocyanins", "Colorintensity", "Hue", "OD280OD315", "Proline")
dadoswine$Classe = ifelse(dadoswine$Classe==1, "R", ifelse(dadoswine$Classe ==2, "B", "T"))
base = dadoswine
dadoswine$Classe = paste(dadoswine$Classe, 1:nrow(dadoswine), sep = "-")
rownames(dadoswine) = dadoswine$Classe
dadoswine$Classe = NULL
linhas = nrow(dadoswine)
head(base)## Classe Alcohol MalicAcid Ash Alcalinity Magnesium Phenols Flavanoids
## 1 R 14.23 1.71 2.43 15.6 127 2.80 3.06
## 2 R 13.20 1.78 2.14 11.2 100 2.65 2.76
## 3 R 13.16 2.36 2.67 18.6 101 2.80 3.24
## 4 R 14.37 1.95 2.50 16.8 113 3.85 3.49
## 5 R 13.24 2.59 2.87 21.0 118 2.80 2.69
## 6 R 14.20 1.76 2.45 15.2 112 3.27 3.39
## Nonflavanoid Proanthocyanins Colorintensity Hue OD280OD315 Proline
## 1 0.28 2.29 5.64 1.04 3.92 1065
## 2 0.26 1.28 4.38 1.05 3.40 1050
## 3 0.30 2.81 5.68 1.03 3.17 1185
## 4 0.24 2.18 7.80 0.86 3.45 1480
## 5 0.39 1.82 4.32 1.04 2.93 735
## 6 0.34 1.97 6.75 1.05 2.85 1450PCA
Inicialmente foi aplicado o PCA para o máximo número de componentes possível.
res.pca <- prcomp(dadoswine, scale = TRUE)
res.pca## Standard deviations (1, .., p=13):
## [1] 2.1692972 1.5801816 1.2025273 0.9586313 0.9237035 0.8010350 0.7423128
## [8] 0.5903367 0.5374755 0.5009017 0.4751722 0.4108165 0.3215244
##
## Rotation (n x k) = (13 x 13):
## PC1 PC2 PC3 PC4 PC5
## Alcohol -0.144329395 0.483651548 -0.20738262 0.01785630 -0.26566365
## MalicAcid 0.245187580 0.224930935 0.08901289 -0.53689028 0.03521363
## Ash 0.002051061 0.316068814 0.62622390 0.21417556 -0.14302547
## Alcalinity 0.239320405 -0.010590502 0.61208035 -0.06085941 0.06610294
## Magnesium -0.141992042 0.299634003 0.13075693 0.35179658 0.72704851
## Phenols -0.394660845 0.065039512 0.14617896 -0.19806835 -0.14931841
## Flavanoids -0.422934297 -0.003359812 0.15068190 -0.15229479 -0.10902584
## Nonflavanoid 0.298533103 0.028779488 0.17036816 0.20330102 -0.50070298
## Proanthocyanins -0.313429488 0.039301722 0.14945431 -0.39905653 0.13685982
## Colorintensity 0.088616705 0.529995672 -0.13730621 -0.06592568 -0.07643678
## Hue -0.296714564 -0.279235148 0.08522192 0.42777141 -0.17361452
## OD280OD315 -0.376167411 -0.164496193 0.16600459 -0.18412074 -0.10116099
## Proline -0.286752227 0.364902832 -0.12674592 0.23207086 -0.15786880
## PC6 PC7 PC8 PC9 PC10
## Alcohol 0.21353865 -0.05639636 0.39613926 -0.50861912 0.21160473
## MalicAcid 0.53681385 0.42052391 0.06582674 0.07528304 -0.30907994
## Ash 0.15447466 -0.14917061 -0.17026002 0.30769445 -0.02712539
## Alcalinity -0.10082451 -0.28696914 0.42797018 -0.20044931 0.05279942
## Magnesium 0.03814394 0.32288330 -0.15636143 -0.27140257 0.06787022
## Phenols -0.08412230 -0.02792498 -0.40593409 -0.28603452 -0.32013135
## Flavanoids -0.01892002 -0.06068521 -0.18724536 -0.04957849 -0.16315051
## Nonflavanoid -0.25859401 0.59544729 -0.23328465 -0.19550132 0.21553507
## Proanthocyanins -0.53379539 0.37213935 0.36822675 0.20914487 0.13418390
## Colorintensity -0.41864414 -0.22771214 -0.03379692 -0.05621752 -0.29077518
## Hue 0.10598274 0.23207564 0.43662362 -0.08582839 -0.52239889
## OD280OD315 0.26585107 -0.04476370 -0.07810789 -0.13722690 0.52370587
## Proline 0.11972557 0.07680450 0.12002267 0.57578611 0.16211600
## PC11 PC12 PC13
## Alcohol 0.22591696 -0.26628645 0.01496997
## MalicAcid -0.07648554 0.12169604 0.02596375
## Ash 0.49869142 -0.04962237 -0.14121803
## Alcalinity -0.47931378 -0.05574287 0.09168285
## Magnesium -0.07128891 0.06222011 0.05677422
## Phenols -0.30434119 -0.30388245 -0.46390791
## Flavanoids 0.02569409 -0.04289883 0.83225706
## Nonflavanoid -0.11689586 0.04235219 0.11403985
## Proanthocyanins 0.23736257 -0.09555303 -0.11691707
## Colorintensity -0.03183880 0.60422163 -0.01199280
## Hue 0.04821201 0.25921400 -0.08988884
## OD280OD315 -0.04642330 0.60095872 -0.15671813
## Proline -0.53926983 -0.07940162 0.01444734PAreto
Com auxílio do Gráfico de Pareto foram avaliados os principais componentas a explicar a maior parte da variação dos dados.
fviz_eig(res.pca)
Corte
PAra utilização de componentes proncipis foram utilizadas as combinações do número máximo de componentes admitidos e critério de Kaiser.
Rank
Com uso do parÂmetro rank. é determinado o número máximo de fatores a ser adotado na análise
res.pca <- prcomp(dadoswine, scale = TRUE, rank. = 4)
res.pca## Standard deviations (1, .., p=13):
## [1] 2.1692972 1.5801816 1.2025273 0.9586313 0.9237035 0.8010350 0.7423128
## [8] 0.5903367 0.5374755 0.5009017 0.4751722 0.4108165 0.3215244
##
## Rotation (n x k) = (13 x 4):
## PC1 PC2 PC3 PC4
## Alcohol -0.144329395 0.483651548 -0.20738262 0.01785630
## MalicAcid 0.245187580 0.224930935 0.08901289 -0.53689028
## Ash 0.002051061 0.316068814 0.62622390 0.21417556
## Alcalinity 0.239320405 -0.010590502 0.61208035 -0.06085941
## Magnesium -0.141992042 0.299634003 0.13075693 0.35179658
## Phenols -0.394660845 0.065039512 0.14617896 -0.19806835
## Flavanoids -0.422934297 -0.003359812 0.15068190 -0.15229479
## Nonflavanoid 0.298533103 0.028779488 0.17036816 0.20330102
## Proanthocyanins -0.313429488 0.039301722 0.14945431 -0.39905653
## Colorintensity 0.088616705 0.529995672 -0.13730621 -0.06592568
## Hue -0.296714564 -0.279235148 0.08522192 0.42777141
## OD280OD315 -0.376167411 -0.164496193 0.16600459 -0.18412074
## Proline -0.286752227 0.364902832 -0.12674592 0.23207086Kaiser
Com o parâmetro tol é definido o indice de corte para o parâmetro de Kaiser
res.pca <- prcomp(dadoswine, scale = TRUE, tol = 0.6)
res.pca## Standard deviations (1, .., p=13):
## [1] 2.1692972 1.5801816 1.2025273 0.9586313 0.9237035 0.8010350 0.7423128
## [8] 0.5903367 0.5374755 0.5009017 0.4751722 0.4108165 0.3215244
##
## Rotation (n x k) = (13 x 2):
## PC1 PC2
## Alcohol -0.144329395 0.483651548
## MalicAcid 0.245187580 0.224930935
## Ash 0.002051061 0.316068814
## Alcalinity 0.239320405 -0.010590502
## Magnesium -0.141992042 0.299634003
## Phenols -0.394660845 0.065039512
## Flavanoids -0.422934297 -0.003359812
## Nonflavanoid 0.298533103 0.028779488
## Proanthocyanins -0.313429488 0.039301722
## Colorintensity 0.088616705 0.529995672
## Hue -0.296714564 -0.279235148
## OD280OD315 -0.376167411 -0.164496193
## Proline -0.286752227 0.364902832Combinação de modelos de corte
Por fim são aplicados os parâmetros rank. e tol para definir o número máximo de componentes prioncipais adotados
res.pca <- prcomp(dadoswine, scale = TRUE, rank. = 3, tol = 0.3)
res.pca## Standard deviations (1, .., p=13):
## [1] 2.1692972 1.5801816 1.2025273 0.9586313 0.9237035 0.8010350 0.7423128
## [8] 0.5903367 0.5374755 0.5009017 0.4751722 0.4108165 0.3215244
##
## Rotation (n x k) = (13 x 3):
## PC1 PC2 PC3
## Alcohol -0.144329395 0.483651548 -0.20738262
## MalicAcid 0.245187580 0.224930935 0.08901289
## Ash 0.002051061 0.316068814 0.62622390
## Alcalinity 0.239320405 -0.010590502 0.61208035
## Magnesium -0.141992042 0.299634003 0.13075693
## Phenols -0.394660845 0.065039512 0.14617896
## Flavanoids -0.422934297 -0.003359812 0.15068190
## Nonflavanoid 0.298533103 0.028779488 0.17036816
## Proanthocyanins -0.313429488 0.039301722 0.14945431
## Colorintensity 0.088616705 0.529995672 -0.13730621
## Hue -0.296714564 -0.279235148 0.08522192
## OD280OD315 -0.376167411 -0.164496193 0.16600459
## Proline -0.286752227 0.364902832 -0.12674592Obtidos os componentes proncipais são obtidas as estatísticas dos mesmos
summary(res.pca)## Importance of first k=3 (out of 13) components:
## PC1 PC2 PC3
## Standard deviation 2.169 1.5802 1.2025
## Proportion of Variance 0.362 0.1921 0.1112
## Cumulative Proportion 0.362 0.5541 0.6653Variancia explicada
Demonstração do cálculo da variância explicada
eigs <- res.pca$sdev^2
eigs[1] / sum(eigs)## [1] 0.3619885rbind(
SD = sqrt(eigs),
"Explicação (%)" = (eigs/sum(eigs))*100,
"Cumulativo (%)" = (cumsum(eigs)/sum(eigs))*100)## [,1] [,2] [,3] [,4] [,5] [,6]
## SD 2.169297 1.580182 1.202527 0.9586313 0.9237035 0.801035
## Explicação (%) 36.198848 19.207490 11.123631 7.0690302 6.5632937 4.935823
## Cumulativo (%) 36.198848 55.406338 66.529969 73.5989991 80.1622928 85.098116
## [,7] [,8] [,9] [,10] [,11]
## SD 0.7423128 0.5903367 0.5374755 0.5009017 0.4751722
## Explicação (%) 4.2386793 2.6807489 2.2221534 1.9300191 1.7368357
## Cumulativo (%) 89.3367954 92.0175443 94.2396978 96.1697168 97.9065525
## [,12] [,13]
## SD 0.4108165 0.3215244
## Explicação (%) 1.2982326 0.7952149
## Cumulativo (%) 99.2047851 100.0000000Resultados
Obtenção dos resultados iniciais dos PCAs
fviz_pca_ind(res.pca,
col.ind = "cos2",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE
)
Variáveis
Obtenção da contribuição de cada variável em relação ao componente
fviz_pca_var(res.pca,
col.var = "contrib",
gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
repel = TRUE # Evite sobreposição de texto
)
Variáveis
Obtenção da contribui~ção de cada variável na classificação das unidades de análise.
fviz_pca_biplot(res.pca, repel = TRUE,
col.var = "#2E9FDF", # Cor das variáveis
col.ind = "#696969" # Cor dos vinhos
)
Autovalores
Onbtenção dos autovalores.
# Autovalores
eig.val <- get_eigenvalue(res.pca)
eig.val## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 4.7058503 36.1988481 36.19885
## Dim.2 2.4969737 19.2074903 55.40634
## Dim.3 1.4460720 11.1236305 66.52997
## Dim.4 0.9189739 7.0690302 73.59900
## Dim.5 0.8532282 6.5632937 80.16229
## Dim.6 0.6416570 4.9358233 85.09812
## Dim.7 0.5510283 4.2386793 89.33680
## Dim.8 0.3484974 2.6807489 92.01754
## Dim.9 0.2888799 2.2221534 94.23970
## Dim.10 0.2509025 1.9300191 96.16972
## Dim.11 0.2257886 1.7368357 97.90655
## Dim.12 0.1687702 1.2982326 99.20479
## Dim.13 0.1033779 0.7952149 100.00000# Resultados para variáveis
res.var <- get_pca_var(res.pca)
res.var$coord # Coordenadas## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Alcohol -0.313093350 0.764257253 -0.2493833 -0.138358673 0.446750633
## MalicAcid 0.531884726 0.355431713 0.1070404 0.235044483 0.207769494
## Ash 0.004449362 0.499446109 0.7530514 0.001966212 0.291953874
## Alcalinity 0.519157081 -0.016734916 0.7360433 0.229420026 -0.009782484
## Magnesium -0.308022936 0.473476124 0.1572388 -0.136118012 0.276772981
## Phenols -0.856136658 0.102774237 0.1757842 -0.378334230 0.060077225
## Flavanoids -0.917470177 -0.005309113 0.1811991 -0.405438045 -0.003103470
## Nonflavanoid 0.647607018 0.045476816 0.2048724 0.286183169 0.026583714
## Proanthocyanins -0.679921705 0.062103856 0.1797229 -0.300463310 0.036303139
## Colorintensity 0.192235968 0.837489383 -0.1651145 0.084950745 0.489558864
## Hue -0.643662066 -0.441242229 0.1024817 -0.284439861 -0.257930487
## OD280OD315 -0.816018903 -0.259933849 0.1996251 -0.360605845 -0.151945711
## Proline -0.622050797 0.576612723 -0.1524154 -0.274889653 0.337062027
## Dim.6 Dim.7 Dim.8 Dim.9 Dim.10
## Alcohol -0.16612074 -0.107137559 0.285517236 -0.11146309 -0.07229484
## MalicAcid 0.07130243 0.182005882 0.132784975 0.04784225 0.12281487
## Ash 0.50162725 0.001522529 0.186587006 0.33658002 0.00102738
## Alcalinity 0.49029777 0.177650603 -0.006251962 0.32897821 0.11987599
## Magnesium 0.10474088 -0.105402512 0.176884934 0.07027865 -0.07112405
## Phenols 0.11709446 -0.292961802 0.038395208 0.07856762 -0.19768628
## Flavanoids 0.12070147 -0.313949547 -0.001983420 0.08098783 -0.21184850
## Nonflavanoid 0.13647086 0.221604947 0.016989587 0.09156872 0.14953573
## Proanthocyanins 0.11971813 -0.232662725 0.023201247 0.08032803 -0.15699735
## Colorintensity -0.10998708 0.065781315 0.312875871 -0.07379873 0.04438826
## Hue 0.06826574 -0.220255022 -0.164842742 0.04580470 -0.14862482
## OD280OD315 0.13297548 -0.279233889 -0.097108132 0.08922340 -0.18842288
## Proline -0.10152791 -0.212859852 0.215415516 -0.06812283 -0.14363467
## Dim.11 Dim.12 Dim.13
## Alcohol 0.229817780 -0.08519621 -0.0464054213
## MalicAcid 0.106880932 0.03656797 0.0788337881
## Ash 0.150187120 0.25726314 0.0006594663
## Alcalinity -0.005032312 0.25145274 0.0769473483
## Magnesium 0.142377755 0.05371711 -0.0456539052
## Phenols 0.030904969 0.06005274 -0.1268930889
## Flavanoids -0.001596489 0.06190262 -0.1359836933
## Nonflavanoid 0.013675213 0.06999006 0.0959856749
## Proanthocyanins 0.018675087 0.06139830 -0.1007752262
## Colorintensity 0.251839221 -0.05640766 0.0284924323
## Hue -0.132684785 0.03501058 -0.0954009701
## OD280OD315 -0.078164021 0.06819743 -0.1209469986
## Proline 0.173391689 -0.05206932 -0.0921978359res.var$contrib # Contribuições para os PCs## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Alcohol 2.083097e+00 23.391881971 4.3007553 2.083097e+00 23.391881971
## MalicAcid 6.011695e+00 5.059392535 0.7923294 6.011695e+00 5.059392535
## Ash 4.206853e-04 9.989949520 39.2156374 4.206853e-04 9.989949520
## Alcalinity 5.727426e+00 0.011215874 37.4642355 5.727426e+00 0.011215874
## Magnesium 2.016174e+00 8.978053590 1.7097376 2.016174e+00 8.978053590
## Phenols 1.557572e+01 0.423013810 2.1368289 1.557572e+01 0.423013810
## Flavanoids 1.788734e+01 0.001128834 2.2705035 1.788734e+01 0.001128834
## Nonflavanoid 8.912201e+00 0.082825894 2.9025311 8.912201e+00 0.082825894
## Proanthocyanins 9.823804e+00 0.154462537 2.2336591 9.823804e+00 0.154462537
## Colorintensity 7.852920e-01 28.089541241 1.8852996 7.852920e-01 28.089541241
## Hue 8.803953e+00 7.797226784 0.7262776 8.803953e+00 7.797226784
## OD280OD315 1.415019e+01 2.705899746 2.7557523 1.415019e+01 2.705899746
## Proline 8.222684e+00 13.315407665 1.6064528 8.222684e+00 13.315407665
## Dim.6 Dim.7 Dim.8 Dim.9 Dim.10
## Alcohol 4.3007553 2.083097e+00 23.391881971 4.3007553 2.083097e+00
## MalicAcid 0.7923294 6.011695e+00 5.059392535 0.7923294 6.011695e+00
## Ash 39.2156374 4.206853e-04 9.989949520 39.2156374 4.206853e-04
## Alcalinity 37.4642355 5.727426e+00 0.011215874 37.4642355 5.727426e+00
## Magnesium 1.7097376 2.016174e+00 8.978053590 1.7097376 2.016174e+00
## Phenols 2.1368289 1.557572e+01 0.423013810 2.1368289 1.557572e+01
## Flavanoids 2.2705035 1.788734e+01 0.001128834 2.2705035 1.788734e+01
## Nonflavanoid 2.9025311 8.912201e+00 0.082825894 2.9025311 8.912201e+00
## Proanthocyanins 2.2336591 9.823804e+00 0.154462537 2.2336591 9.823804e+00
## Colorintensity 1.8852996 7.852920e-01 28.089541241 1.8852996 7.852920e-01
## Hue 0.7262776 8.803953e+00 7.797226784 0.7262776 8.803953e+00
## OD280OD315 2.7557523 1.415019e+01 2.705899746 2.7557523 1.415019e+01
## Proline 1.6064528 8.222684e+00 13.315407665 1.6064528 8.222684e+00
## Dim.11 Dim.12 Dim.13
## Alcohol 23.391881971 4.3007553 2.083097e+00
## MalicAcid 5.059392535 0.7923294 6.011695e+00
## Ash 9.989949520 39.2156374 4.206853e-04
## Alcalinity 0.011215874 37.4642355 5.727426e+00
## Magnesium 8.978053590 1.7097376 2.016174e+00
## Phenols 0.423013810 2.1368289 1.557572e+01
## Flavanoids 0.001128834 2.2705035 1.788734e+01
## Nonflavanoid 0.082825894 2.9025311 8.912201e+00
## Proanthocyanins 0.154462537 2.2336591 9.823804e+00
## Colorintensity 28.089541241 1.8852996 7.852920e-01
## Hue 7.797226784 0.7262776 8.803953e+00
## OD280OD315 2.705899746 2.7557523 1.415019e+01
## Proline 13.315407665 1.6064528 8.222684e+00res.var$cos2 # Qualidade de representação## Dim.1 Dim.2 Dim.3 Dim.4 Dim.5
## Alcohol 9.802745e-02 5.840891e-01 0.06219202 1.914312e-02 1.995861e-01
## MalicAcid 2.829014e-01 1.263317e-01 0.01145765 5.524591e-02 4.316816e-02
## Ash 1.979682e-05 2.494464e-01 0.56708634 3.865988e-06 8.523706e-02
## Alcalinity 2.695241e-01 2.800574e-04 0.54175981 5.263355e-02 9.569700e-05
## Magnesium 9.487813e-02 2.241796e-01 0.02472404 1.852811e-02 7.660328e-02
## Phenols 7.329700e-01 1.056254e-02 0.03090008 1.431368e-01 3.609273e-03
## Flavanoids 8.417515e-01 2.818668e-05 0.03283311 1.643800e-01 9.631528e-06
## Nonflavanoid 4.193949e-01 2.068141e-03 0.04197269 8.190081e-02 7.066939e-04
## Proanthocyanins 4.622935e-01 3.856889e-03 0.03230032 9.027820e-02 1.317918e-03
## Colorintensity 3.695467e-02 7.013885e-01 0.02726279 7.216629e-03 2.396679e-01
## Hue 4.143009e-01 1.946947e-01 0.01050250 8.090603e-02 6.652814e-02
## OD280OD315 6.658869e-01 6.756561e-02 0.03985016 1.300366e-01 2.308750e-02
## Proline 3.869472e-01 3.324822e-01 0.02323046 7.556432e-02 1.136108e-01
## Dim.6 Dim.7 Dim.8 Dim.9 Dim.10
## Alcohol 0.027596099 1.147846e-02 8.152009e-02 0.012424019 5.226543e-03
## MalicAcid 0.005084037 3.312614e-02 1.763185e-02 0.002288881 1.508349e-02
## Ash 0.251629895 2.318095e-06 3.481471e-02 0.113286111 1.055510e-06
## Alcalinity 0.240391901 3.155974e-02 3.908702e-05 0.108226662 1.437025e-02
## Magnesium 0.010970652 1.110969e-02 3.128828e-02 0.004939089 5.058631e-03
## Phenols 0.013711113 8.582662e-02 1.474192e-03 0.006172870 3.907986e-02
## Flavanoids 0.014568845 9.856432e-02 3.933956e-06 0.006559029 4.487978e-02
## Nonflavanoid 0.018624295 4.910875e-02 2.886461e-04 0.008384830 2.236093e-02
## Proanthocyanins 0.014332430 5.413194e-02 5.382979e-04 0.006452593 2.464817e-02
## Colorintensity 0.012097157 4.327181e-03 9.789131e-02 0.005446252 1.970317e-03
## Hue 0.004660211 4.851227e-02 2.717313e-02 0.002098070 2.208934e-02
## OD280OD315 0.017682479 7.797156e-02 9.429989e-03 0.007960816 3.550318e-02
## Proline 0.010307917 4.530932e-02 4.640384e-02 0.004640720 2.063092e-02
## Dim.11 Dim.12 Dim.13
## Alcohol 5.281621e-02 0.007258395 2.153463e-03
## MalicAcid 1.142353e-02 0.001337216 6.214766e-03
## Ash 2.255617e-02 0.066184323 4.348958e-07
## Alcalinity 2.532417e-05 0.063228478 5.920894e-03
## Magnesium 2.027143e-02 0.002885528 2.084279e-03
## Phenols 9.551171e-04 0.003606331 1.610186e-02
## Flavanoids 2.548778e-06 0.003831934 1.849156e-02
## Nonflavanoid 1.870115e-04 0.004898609 9.213250e-03
## Proanthocyanins 3.487589e-04 0.003769752 1.015565e-02
## Colorintensity 6.342299e-02 0.003181825 8.118187e-04
## Hue 1.760525e-02 0.001225740 9.101345e-03
## OD280OD315 6.109614e-03 0.004650890 1.462818e-02
## Proline 3.006468e-02 0.002711214 8.500441e-03# resultados para indivíduos
res.ind <- get_pca_ind(res.pca)
res.ind$coord # Coordenadas## Dim.1 Dim.2 Dim.3
## R-1 -3.30742097 1.43940225 -0.165272830
## R-2 -2.20324981 -0.33245507 -2.020757060
## R-3 -2.50966069 1.02825072 0.980054055
## R-4 -3.74649719 2.74861839 -0.175696224
## R-5 -1.00607049 0.86738404 2.020987257
## R-6 -3.04167373 2.11643092 -0.627625371
## R-7 -2.44220051 1.17154534 -0.974346376
## R-8 -2.05364379 1.60443714 0.145870400
## R-9 -2.50381135 0.91548847 -1.765987389
## R-10 -2.74588238 0.78721703 -0.981478855
## R-11 -3.46994837 1.29866985 -0.421546086
## R-12 -1.74981688 0.61025577 -1.187528444
## R-13 -2.10751729 0.67380561 -0.862652985
## R-14 -3.44842921 1.12744948 -1.200888789
## R-15 -4.30065228 2.09007971 -1.260357435
## R-16 -2.29870383 1.65787506 0.217289668
## R-17 -2.16584568 2.32075875 0.829390256
## R-18 -1.89362947 1.62677993 0.792677744
## R-19 -3.53202167 2.51125971 -0.484092940
## R-20 -2.07865856 1.05815307 -0.164283255
## R-21 -3.11561376 0.78468361 -0.363860676
## R-22 -1.08351361 0.24106354 0.934325978
## R-23 -2.52809263 -0.09158228 -0.311055210
## R-24 -1.64036108 -0.51482667 0.143480354
## R-25 -1.75662066 -0.31625681 0.887781323
## R-26 -0.98729406 0.93802129 3.810160004
## R-27 -1.77028387 0.68424496 -0.086456523
## R-28 -1.23194878 -0.08955442 -1.382995281
## R-29 -2.18225047 0.68762990 1.390644041
## R-30 -2.24976267 0.19092336 -1.089583673
## R-31 -2.49318704 1.23734344 1.382119063
## R-32 -2.66987964 1.46773335 -0.331327094
## R-33 -1.62399801 0.05255620 -0.166658582
## R-34 -1.89733870 1.62846673 1.168785117
## R-35 -1.40642118 0.69597107 0.478393534
## R-36 -1.89847087 0.17621387 0.449566866
## R-37 -1.38096669 0.65678714 0.457149018
## R-38 -1.11905070 0.11378878 -0.038997270
## R-39 -1.49796891 -0.76726764 -1.422165587
## R-40 -2.52268490 1.79793023 -0.342187120
## R-41 -2.58081526 0.77742329 -0.118144196
## R-42 -0.66660159 0.16948285 -0.781158992
## R-43 -3.06216898 1.15266742 -0.311878313
## R-44 -0.46090897 0.32981177 -0.200909754
## R-45 -2.09544094 -0.07080918 -0.654004547
## R-46 -1.13297020 1.77210849 0.028624988
## R-47 -2.71893118 1.18798353 -0.538254909
## R-48 -2.81340300 0.64444071 -1.152301905
## R-49 -2.00419725 1.24352164 -0.057132823
## R-50 -2.69987528 1.74703922 -0.641304569
## R-51 -3.20587409 0.16652226 -1.968020131
## R-52 -2.85091773 0.74318238 0.004706226
## R-53 -3.49574328 1.60819732 -0.519309620
## R-54 -2.21853316 1.86989325 0.338594715
## R-55 -2.14094846 1.01389147 -0.955068628
## R-56 -2.46238340 1.32526988 0.511993182
## R-57 -2.73380617 1.43250785 -0.610750542
## R-58 -2.16762631 1.20878999 0.261043221
## R-59 -3.13054925 1.72670828 -0.284857863
## B-60 0.92596992 -3.06484062 -4.572166474
## B-61 1.53814123 -1.37755758 -0.872222677
## B-62 1.83108449 -0.82764942 -1.601185434
## B-63 -0.03052074 -1.25923400 -1.779388569
## B-64 -2.04449433 -1.91961759 -0.007348049
## B-65 0.60796583 -1.90269154 0.677446941
## B-66 -0.89769555 -0.76176263 0.571748468
## B-67 -2.24218226 -1.87929123 -2.026124738
## B-68 -0.18286818 -2.42031869 -1.066736425
## B-69 0.81051865 -0.21989369 -0.705016628
## B-70 -1.97006319 -1.39933587 -1.234793017
## B-71 1.56779366 -0.88249373 -0.627228614
## B-72 -1.65301884 -0.95402102 1.947091704
## B-73 0.72333196 -1.06065342 0.080106258
## B-74 -2.55501977 0.25946663 3.364901977
## B-75 -1.82741266 -1.28425547 0.456990911
## B-76 0.86555129 -2.43722606 -1.558935609
## B-77 -0.36897357 -2.14784815 -2.442496359
## B-78 1.45327752 -1.37946048 -0.226667500
## B-79 -1.25937829 -0.76868117 -1.180893359
## B-80 -0.37509228 -1.02415439 1.789418559
## B-81 -0.75992026 -3.36555997 -0.356464512
## B-82 -1.03166776 -1.44662897 -0.361990641
## B-83 0.49348469 -2.37454522 1.331985804
## B-84 2.53183508 -0.08719738 0.472917350
## B-85 -0.83297044 -1.46952520 0.608377416
## B-86 -0.78568828 -2.02092573 -0.254006881
## B-87 0.80456258 -2.22754675 0.770681796
## B-88 0.55647288 -2.36631035 2.301120220
## B-89 1.11197430 -1.79717757 0.956554981
## B-90 0.55415961 -2.65006452 0.846738350
## B-91 1.34548982 -2.11204365 -0.047518277
## B-92 1.56008180 -1.84700434 0.778869932
## B-93 1.92711944 -1.55510868 -0.089023551
## B-94 -0.74456561 -2.30642556 0.114357181
## B-95 -0.95476209 -2.21727377 0.142044084
## B-96 -2.53670943 0.16879786 0.786478429
## B-97 0.54242248 -0.36788878 1.305214079
## B-98 -1.02814946 -2.55835254 -1.083334218
## B-99 -2.24557492 -1.42871116 -0.229560681
## B-100 -1.40624916 -2.16009839 0.746789806
## B-101 -0.79547585 -2.37026258 -1.563701517
## B-102 0.54798592 -2.28667820 -1.494718900
## B-103 0.16072037 -1.16120769 1.000889713
## B-104 0.65793897 -2.67242260 -0.762769188
## B-105 -0.39125074 -2.09282809 -0.470522719
## B-106 1.76751314 -1.71245783 0.944369222
## B-107 0.36523707 -2.16325103 -0.479970296
## B-108 1.61611371 -1.35177021 0.286351238
## B-109 -0.08230361 -2.29974728 -0.462270978
## B-110 -1.57383547 -1.45792167 1.774639908
## B-111 -1.41657326 -1.41421730 0.138884054
## B-112 0.27791878 -1.92513751 0.078449257
## B-113 1.29947929 -0.76102555 1.993971755
## B-114 0.45578615 -2.26303187 1.058353479
## B-115 0.49279573 -1.93359062 1.320213907
## B-116 -0.48071836 -3.86089273 1.340489862
## B-117 0.25217752 -2.81355567 -0.301788475
## B-118 0.10692601 -1.92349609 0.688206893
## B-119 2.42616867 -1.25360477 -1.897674293
## B-120 0.54953935 -2.21591073 -0.355226778
## B-121 -0.73754141 -1.40499335 1.122179957
## B-122 -1.33256273 0.25262431 5.330351896
## B-123 1.17377592 -0.66209914 3.001754299
## B-124 0.46103449 -0.61654897 0.482082470
## B-125 -0.97572169 -1.44150419 1.477070337
## B-126 0.09653741 -2.10406268 0.433602974
## B-127 -0.03837888 -1.26319878 0.685643794
## B-128 1.59266578 -1.20474513 3.351720753
## B-129 0.47821593 -1.93338681 1.292860514
## B-130 1.78779033 -1.14705241 0.780598199
## T-131 1.32336859 0.16990994 -1.176694043
## T-132 2.37779336 0.37352893 -0.721786522
## T-133 2.92867865 0.26311960 -0.167168254
## T-134 2.14077227 0.36721907 -0.452026190
## T-135 2.36320318 -0.45834188 -1.098301611
## T-136 3.05522315 0.35241870 -1.096032328
## T-137 3.90473898 0.15414769 0.221203810
## T-138 3.92539034 0.65783157 1.707399051
## T-139 3.08557209 0.34786148 -1.023942993
## T-140 2.36779237 0.29115903 1.238420896
## T-141 2.77099630 0.28599811 0.607955155
## T-142 2.28012931 0.37146000 -0.968909854
## T-143 2.97723506 0.48784177 0.944289205
## T-144 2.36851341 0.48097694 -0.252172645
## T-145 2.20364930 1.15678934 -1.241622757
## T-146 2.61823528 0.56157662 -0.853553310
## T-147 4.26859758 0.64784348 -1.454095134
## T-148 3.57256360 1.26912271 -0.110472408
## T-149 2.79916760 1.56611596 -0.471198739
## T-150 2.89150275 2.03531563 -0.494564703
## T-151 2.31420887 2.34973775 0.436450569
## T-152 2.54265841 2.03952982 -0.311389606
## T-153 1.80744271 1.52334876 1.358756891
## T-154 2.75238051 2.13291565 -0.961915241
## T-155 2.72945105 0.40873328 -1.187056141
## T-156 3.59472857 1.79731421 -0.093772341
## T-157 2.88169708 1.91980308 -0.780121925
## T-158 3.38261413 1.30818615 1.597519558
## T-159 1.04523342 3.50520194 1.156775441
## T-160 1.60538369 2.39986842 0.547016629
## T-161 3.13428951 0.73608464 -0.090742750
## T-162 2.23385546 1.17215877 -0.101091765
## T-163 2.83966343 0.55447984 0.801953005
## T-164 2.59019044 0.69600220 -0.882450235
## T-165 2.94100316 1.55093397 -0.980634475
## T-166 3.52010248 0.88004430 -0.464718213
## T-167 2.39934228 2.58506402 0.427021634
## T-168 2.92084537 1.27086200 -1.209945161
## T-169 2.17527658 2.07169331 0.761634073
## T-170 2.37423037 2.58138565 1.414055150
## T-171 3.20258311 -0.25054235 -0.844746224
## T-172 3.66757294 0.84536318 -1.335652516
## T-173 2.45862032 2.18762727 -0.916196480
## T-174 3.36104305 2.21005484 -0.341605883
## T-175 2.59463669 1.75228636 0.206997440
## T-176 2.67030685 2.75313287 -0.938295059
## T-177 2.38030254 2.29088437 -0.549147119
## T-178 3.19973210 2.76113075 1.011061581res.ind$contrib # contribuições para os PCs## Dim.1 Dim.2 Dim.3
## R-1 1.3059328513 0.466155036 1.061190e-02
## R-2 0.5795212676 0.024867490 1.586420e+00
## R-3 0.7519204777 0.237883364 3.731558e-01
## R-4 1.6756862924 1.699788630 1.199264e-02
## R-5 0.1208366607 0.169273460 1.586782e+00
## R-6 1.1045036289 1.007799684 1.530351e-01
## R-7 0.7120402294 0.308804932 3.688220e-01
## R-8 0.5034914806 0.579177176 8.266553e-03
## R-9 0.7484195107 0.188569646 1.211617e+00
## R-10 0.9001310769 0.139429601 3.742415e-01
## R-11 1.4374340275 0.379457846 6.903673e-02
## R-12 0.3655334259 0.083789541 5.478708e-01
## R-13 0.5302542837 0.102149272 2.891095e-01
## R-14 1.4196605880 0.285996160 5.602678e-01
## R-15 2.2080583968 0.982860140 6.171313e-01
## R-16 0.6308236029 0.618400201 1.834291e-02
## R-17 0.5600114595 1.211786245 2.672440e-01
## R-18 0.4280868667 0.595420296 2.441088e-01
## R-19 1.4893220312 1.418891806 9.104322e-02
## R-20 0.5158319163 0.251920214 1.048520e-02
## R-21 1.1588550606 0.138533620 5.143519e-02
## R-22 0.1401556576 0.013074620 3.391462e-01
## R-23 0.7630058381 0.001887074 3.758937e-02
## R-24 0.3212334834 0.059633197 7.997882e-03
## R-25 0.3683815451 0.022503279 3.061978e-01
## R-26 0.1163683686 0.197966369 5.639966e+00
## R-27 0.3741344667 0.105339012 2.903927e-03
## R-28 0.1811870697 0.001804430 7.430730e-01
## R-29 0.5685269873 0.106383807 7.513150e-01
## R-30 0.6042481193 0.008201328 4.612233e-01
## R-31 0.7420815214 0.344466143 7.421317e-01
## R-32 0.8509915752 0.484685856 4.264852e-02
## R-33 0.3148566581 0.000621461 1.079060e-02
## R-34 0.4297655737 0.596655711 5.307126e-01
## R-35 0.2361417032 0.108980401 8.891206e-02
## R-36 0.4302786245 0.006986284 7.851971e-02
## R-37 0.2276713067 0.097054416 8.119059e-02
## R-38 0.1495000793 0.002913164 5.908245e-04
## R-39 0.2678844434 0.132452385 7.857609e-01
## R-40 0.7597451041 0.727296828 4.549015e-02
## R-41 0.7951622043 0.135981903 5.422691e-03
## R-42 0.0530486805 0.006462753 2.370658e-01
## R-43 1.1194383982 0.298933137 3.778857e-02
## R-44 0.0253613409 0.024473627 1.568166e-02
## R-45 0.5241948444 0.001128094 1.661696e-01
## R-46 0.1532423742 0.706556075 3.183323e-04
## R-47 0.8825479821 0.317531537 1.125553e-01
## R-48 0.9449433814 0.093439812 5.158491e-01
## R-49 0.4795377692 0.347914649 1.268123e-03
## R-50 0.8702204792 0.686706776 1.597787e-01
## R-51 1.2269724664 0.006238937 1.504697e+00
## R-52 0.9703116912 0.124267290 8.604700e-06
## R-53 1.4588846617 0.581895092 1.047714e-01
## R-54 0.5875891193 0.786682798 4.454002e-02
## R-55 0.5472103730 0.231285797 3.543719e-01
## R-56 0.7238577731 0.395161551 1.018400e-01
## R-57 0.8922310541 0.461700182 1.449165e-01
## R-58 0.5609326516 0.328751492 2.647372e-02
## R-59 1.1699922230 0.670816855 3.152438e-02
## B-60 0.1023612666 2.113400532 8.121461e+00
## B-61 0.2824452786 0.426958386 2.955594e-01
## B-62 0.4002751826 0.154119949 9.960321e-01
## B-63 0.0001112070 0.356762258 1.230075e+00
## B-64 0.4990151343 0.829078145 2.097656e-05
## B-65 0.0441265765 0.814521961 1.782956e-01
## B-66 0.0962055300 0.130558561 1.269989e-01
## B-67 0.6001830417 0.794610314 1.594860e+00
## B-68 0.0039922540 1.317987014 4.420835e-01
## B-69 0.0784274186 0.010879065 1.931029e-01
## B-70 0.4633425729 0.440564962 5.923500e-01
## B-71 0.2934402630 0.175222260 1.528417e-01
## B-72 0.3262101739 0.204777346 1.472865e+00
## B-73 0.0624621887 0.253112166 2.493004e-03
## B-74 0.7793462032 0.015147084 4.398807e+00
## B-75 0.3986714652 0.371081130 8.113443e-02
## B-76 0.0894391179 1.336465189 9.441618e-01
## B-77 0.0162529583 1.037942209 2.317704e+00
## B-78 0.2521384089 0.428138761 1.996037e-02
## B-79 0.1893452011 0.132940869 5.417656e-01
## B-80 0.0167964751 0.235991784 1.243982e+00
## B-81 0.0689410576 2.548476837 4.936540e-02
## B-82 0.1270637326 0.470847578 5.090785e-02
## B-83 0.0290729613 1.268606443 6.892699e-01
## B-84 0.7652665328 0.001710696 8.688816e-02
## B-85 0.0828325573 0.485870015 1.437925e-01
## B-86 0.0736957507 0.918896785 2.506577e-02
## B-87 0.0772790110 1.116399615 2.307492e-01
## B-88 0.0369683361 1.259822704 2.057163e+00
## B-89 0.1476153060 0.726688024 3.554757e-01
## B-90 0.0366616187 1.580079431 2.785406e-01
## B-91 0.2161238648 1.003625765 8.772259e-04
## B-92 0.2905605416 0.767541484 2.356785e-01
## B-93 0.4433627052 0.544111012 3.078931e-03
## B-94 0.0661832123 1.196864286 5.080623e-03
## B-95 0.1088258910 1.106126159 7.838562e-03
## B-96 0.7682159884 0.006410618 2.403055e-01
## B-97 0.0351250745 0.030450828 6.618409e-01
## B-98 0.1261985606 1.472606810 4.559477e-01
## B-99 0.6020006978 0.459256061 2.047317e-02
## B-100 0.2360839395 1.049815766 2.166640e-01
## B-101 0.0755432898 1.264034545 9.499436e-01
## B-102 0.0358493017 1.176457184 8.679788e-01
## B-103 0.0030837824 0.303379222 3.891908e-01
## B-104 0.0516788835 1.606853549 2.260354e-01
## B-105 0.0182747831 0.985446692 8.601046e-02
## B-106 0.3729642409 0.659790101 3.464765e-01
## B-107 0.0159254454 1.052882387 8.949913e-02
## B-108 0.3118069014 0.411122991 3.185578e-02
## B-109 0.0008086856 1.189943251 8.302012e-02
## B-110 0.2957062830 0.478227345 1.223519e+00
## B-111 0.2395631287 0.449985288 7.493675e-03
## B-112 0.0092209927 0.833853074 2.390935e-03
## B-113 0.2015954009 0.130306026 1.544643e+00
## B-114 0.0248007114 1.152251713 4.351626e-01
## B-115 0.0289918391 0.841191908 6.771404e-01
## B-116 0.0275881968 3.353833477 6.980992e-01
## B-117 0.0075919723 1.781053846 3.538306e-02
## B-118 0.0013649245 0.832431757 1.840044e-01
## B-119 0.7027225266 0.353579679 1.399051e+00
## B-120 0.0360528410 1.104766625 4.902318e-02
## B-121 0.0649403636 0.444134552 4.892323e-01
## B-122 0.2119909016 0.014358739 1.103829e+01
## B-123 0.1644796914 0.098630689 3.500583e+00
## B-124 0.0253751558 0.085526594 9.028857e-02
## B-125 0.1136563773 0.467517467 8.476029e-01
## B-126 0.0011125849 0.996055120 7.304233e-02
## B-127 0.0001758436 0.359012373 1.826363e-01
## B-128 0.3028246287 0.326555035 4.364412e+00
## B-129 0.0273017173 0.841014582 6.493718e-01
## B-130 0.3815707386 0.296027832 2.367256e-01
## T-131 0.2090756910 0.006495365 5.379194e-01
## T-132 0.6749787745 0.031391676 2.023987e-01
## T-133 1.0239655302 0.015576591 1.085670e-02
## T-134 0.5471203096 0.030340063 7.938113e-02
## T-135 0.6667208206 0.047265593 4.686335e-01
## T-136 1.1143657790 0.027943701 4.666989e-01
## T-137 1.8202285045 0.005346137 1.900970e-02
## T-138 1.8395330383 0.097363336 1.132557e+00
## T-139 1.1366147543 0.027225679 4.073255e-01
## T-140 0.6693127959 0.019073331 5.958359e-01
## T-141 0.9166716205 0.018403157 1.435930e-01
## T-142 0.6206701372 0.031044891 3.647177e-01
## T-143 1.0582009450 0.053545624 3.464178e-01
## T-144 0.6697204940 0.052049257 2.470507e-02
## T-145 0.5797314382 0.301074920 5.989208e-01
## T-146 0.8183879659 0.070955174 2.830423e-01
## T-147 2.1752657485 0.094429176 8.214398e-01
## T-148 1.5237082961 0.362387537 4.741303e-03
## T-149 0.9354050300 0.551840862 8.625779e-02
## T-150 0.9981346081 0.932029284 9.502466e-02
## T-151 0.6393622676 1.242238003 7.400486e-02
## T-152 0.7718233875 0.935892881 3.767023e-02
## T-153 0.3900057171 0.522113246 7.172550e-01
## T-154 0.9043964339 1.023560187 3.594709e-01
## T-155 0.8893905560 0.037587724 5.474351e-01
## T-156 1.5426737909 0.726798529 3.416171e-03
## T-157 0.9913763309 0.829238374 2.364368e-01
## T-158 1.3659877711 0.385039353 9.914766e-01
## T-159 0.1304272892 2.764344149 5.198622e-01
## T-160 0.3076802263 1.295808681 1.162495e-01
## T-161 1.1727896197 0.121905004 3.198998e-03
## T-162 0.5957335125 0.309128400 3.970285e-03
## T-163 0.9626659932 0.069173150 2.498549e-01
## T-164 0.8009497807 0.108990149 3.025315e-01
## T-165 1.0326017948 0.541193583 3.735979e-01
## T-166 1.4792872318 0.174250924 8.390145e-02
## T-167 0.6872682955 1.503517993 7.084184e-02
## T-168 1.0184952952 0.363381498 5.687501e-01
## T-169 0.5648990761 0.965643792 2.253631e-01
## T-170 0.6729574506 1.499242234 7.768243e-01
## T-171 1.2244546728 0.014123045 2.772315e-01
## T-172 1.6058294319 0.160787646 6.930699e-01
## T-173 0.7216470316 1.076744546 3.261124e-01
## T-174 1.3486213908 1.098935301 4.533575e-02
## T-175 0.8037019191 0.690837948 1.664639e-02
## T-176 0.8512639319 1.705376869 3.420337e-01
## T-177 0.6764040757 1.180789172 1.171568e-01
## T-178 1.2222755713 1.715299528 3.971415e-01res.ind$cos2 # Qualidade de representação## Dim.1 Dim.2 Dim.3
## R-1 0.8389969832 0.158908015 2.095002e-03
## R-2 0.5364888774 0.012215160 4.512960e-01
## R-3 0.7573645483 0.127137305 1.154981e-01
## R-4 0.6491643921 0.349407935 1.427673e-03
## R-5 0.1730537291 0.128631398 6.983149e-01
## R-6 0.6549944832 0.317117774 2.788774e-02
## R-7 0.7197912444 0.165638819 1.145699e-01
## R-8 0.6190347941 0.377842010 3.123196e-03
## R-9 0.6130580307 0.081960414 3.049816e-01
## R-10 0.8264790130 0.067929267 1.055917e-01
## R-11 0.8659278580 0.121292291 1.277985e-02
## R-12 0.6320285386 0.076873256 2.910982e-01
## R-13 0.7875489637 0.080501602 1.319494e-01
## R-14 0.8142220263 0.087035092 9.874288e-02
## R-15 0.7563879638 0.178649435 6.496260e-02
## R-16 0.6539811385 0.340175304 5.843558e-03
## R-17 0.4357658706 0.500331894 6.390224e-02
## R-18 0.5226716612 0.385741668 9.158667e-02
## R-19 0.6560375976 0.331638748 1.232365e-02
## R-20 0.7902739345 0.204789806 4.936259e-03
## R-21 0.9284447018 0.058892227 1.266307e-02
## R-22 0.5576997683 0.027605447 4.146948e-01
## R-23 0.9838152303 0.001291072 1.489370e-02
## R-24 0.9040345986 0.089048828 6.916574e-03
## R-25 0.7764975861 0.025168881 1.983335e-01
## R-26 0.0595377706 0.053743372 8.867189e-01
## R-27 0.8682209288 0.129708263 2.070809e-03
## R-28 0.4413973263 0.002332483 5.562702e-01
## R-29 0.6642844303 0.065956012 2.697596e-01
## R-30 0.8053095562 0.005799728 1.888907e-01
## R-31 0.6436593616 0.158535631 1.978050e-01
## R-32 0.7589488643 0.229363059 1.168808e-02
## R-33 0.9885538592 0.001035326 1.041081e-02
## R-34 0.4725599725 0.348116799 1.793232e-01
## R-35 0.7349802704 0.179981250 8.503848e-02
## R-36 0.9392389300 0.008091861 5.266921e-02
## R-37 0.7486265825 0.169335539 8.203788e-02
## R-38 0.9885780534 0.010221398 1.200549e-03
## R-39 0.4621698032 0.121252228 4.165780e-01
## R-40 0.6551586877 0.332786851 1.205446e-02
## R-41 0.9150502733 0.083032136 1.917591e-03
## R-42 0.4101921648 0.026515889 5.632919e-01
## R-43 0.8680053598 0.122990662 9.003979e-03
## R-44 0.5875282935 0.300836672 1.116350e-01
## R-45 0.9102879359 0.001039458 8.867261e-02
## R-46 0.2900964490 0.709718370 1.851808e-04
## R-47 0.8129430205 0.155197427 3.185955e-02
## R-48 0.8195234879 0.042999504 1.374770e-01
## R-49 0.7216144133 0.277799184 5.864023e-04
## R-50 0.6779038404 0.283848104 3.824806e-02
## R-51 0.7248761525 0.001955760 2.731681e-01
## R-52 0.9363666501 0.063630798 2.551657e-06
## R-53 0.8105636238 0.171548418 1.788796e-02
## R-54 0.5768039739 0.409760436 1.343559e-02
## R-55 0.7026067198 0.157573366 1.398199e-01
## R-56 0.7502443804 0.217320182 3.243544e-02
## R-57 0.7550109983 0.207305994 3.768301e-02
## R-58 0.7544418278 0.234616549 1.094162e-02
## R-59 0.7619012274 0.231790448 6.308324e-03
## B-60 0.0275207826 0.301496873 6.709823e-01
## B-61 0.4708857008 0.377696188 1.514181e-01
## B-62 0.5078822540 0.103762183 3.883556e-01
## B-63 0.0001959919 0.333626865 6.661771e-01
## B-64 0.5314669411 0.468526194 6.865127e-06
## B-65 0.0830837802 0.813756897 1.031593e-01
## B-66 0.4704263866 0.338744975 1.908286e-01
## B-67 0.3969727490 0.278873369 3.241539e-01
## B-68 0.0047573333 0.833359550 1.618831e-01
## B-69 0.5463839682 0.040215870 4.134002e-01
## B-70 0.5270433258 0.265907103 2.070496e-01
## B-71 0.6770935961 0.214533023 1.083734e-01
## B-72 0.3675742794 0.122434946 5.099908e-01
## B-73 0.3162126078 0.679909134 3.878259e-03
## B-74 0.3643331187 0.003757276 6.319096e-01
## B-75 0.6424972224 0.317322483 4.018030e-02
## B-76 0.0821510558 0.651357119 2.664918e-01
## B-77 0.0127054774 0.430534156 5.567604e-01
## B-78 0.5193942905 0.467970613 1.263510e-02
## B-79 0.4440912996 0.165444504 3.904642e-01
## B-80 0.0320370828 0.238840278 7.291226e-01
## B-81 0.0479970825 0.941441763 1.056115e-02
## B-82 0.3236929564 0.636455218 3.985183e-02
## B-83 0.0318079247 0.736459466 2.317326e-01
## B-84 0.9651801272 0.001144839 3.367503e-02
## B-85 0.2152464159 0.669932162 1.148214e-01
## B-86 0.1295237999 0.856938653 1.353755e-02
## B-87 0.1043521411 0.799899375 9.574848e-02
## B-88 0.0276379335 0.499759392 4.726027e-01
## B-89 0.2297734007 0.600194808 1.700318e-01
## B-90 0.0381628764 0.872738741 8.909838e-02
## B-91 0.2885776895 0.711062376 3.599344e-04
## B-92 0.3772296835 0.528745825 9.402449e-02
## B-93 0.6048440444 0.393865224 1.290732e-03
## B-94 0.0941689875 0.903609602 2.221411e-03
## B-95 0.1558759984 0.840673873 3.450128e-03
## B-96 0.9086350033 0.004023295 8.734170e-02
## B-97 0.1379286080 0.063447143 7.986242e-01
## B-98 0.1204542763 0.745813940 1.337318e-01
## B-99 0.7065917906 0.286023924 7.384286e-03
## B-100 0.2746099400 0.647945937 7.744412e-02
## B-101 0.0727662554 0.646054188 2.811796e-01
## B-102 0.0386801814 0.673534425 2.877854e-01
## B-103 0.0108715817 0.567506332 4.216221e-01
## B-104 0.0530719558 0.875596743 7.133130e-02
## B-105 0.0321969538 0.921237399 4.656565e-02
## B-106 0.4496115971 0.422038408 1.283500e-01
## B-107 0.0264499077 0.927872501 4.567759e-02
## B-108 0.5776960581 0.404167433 1.813651e-02
## B-109 0.0012295351 0.959982555 3.878791e-02
## B-110 0.3195316122 0.274197540 4.062708e-01
## B-111 0.4984327367 0.496776185 4.791078e-03
## B-112 0.0203820763 0.977993908 1.624016e-03
## B-113 0.2704547625 0.092758643 6.367866e-01
## B-114 0.0322120724 0.794104690 1.736832e-01
## B-115 0.0424218746 0.653108066 3.044701e-01
## B-116 0.0136461188 0.880244253 1.061096e-01
## B-117 0.0078794881 0.980835797 1.128471e-02
## B-118 0.0027320066 0.884092331 1.131757e-01
## B-119 0.5322634331 0.142103876 3.256327e-01
## B-120 0.0565696169 0.919793129 2.363725e-02
## B-121 0.1440110342 0.522602502 3.333865e-01
## B-122 0.0586973444 0.002109567 9.391931e-01
## B-123 0.1272553731 0.040490374 8.322543e-01
## B-124 0.2576119827 0.460717160 2.816709e-01
## B-125 0.1826720826 0.398705368 4.186225e-01
## B-126 0.0020152774 0.957328400 4.065632e-02
## B-127 0.0007125107 0.771880513 2.274070e-01
## B-128 0.1666390600 0.095349379 7.380116e-01
## B-129 0.0405611648 0.662979117 2.964597e-01
## B-130 0.6241034656 0.256915287 1.189812e-01
## T-131 0.5533727285 0.009122075 4.375052e-01
## T-132 0.8953978931 0.022096135 8.250597e-02
## T-133 0.9887971653 0.007981236 3.221598e-03
## T-134 0.9310906598 0.027396904 4.151244e-02
## T-135 0.7976961934 0.030006441 1.722974e-01
## T-136 0.8756565256 0.011651070 1.126924e-01
## T-137 0.9952549505 0.001551045 3.194005e-03
## T-138 0.8215057000 0.023071419 1.554229e-01
## T-139 0.8906040616 0.011319467 9.807647e-02
## T-140 0.7759886282 0.011733529 2.122778e-01
## T-141 0.9444755091 0.010061092 4.546340e-02
## T-142 0.8284241127 0.021986590 1.495893e-01
## T-143 0.8869604892 0.023814199 8.922531e-02
## T-144 0.9500524019 0.039178191 1.076941e-02
## T-145 0.6277351101 0.172981643 1.992832e-01
## T-146 0.8678425987 0.039924701 9.223270e-02
## T-147 0.8779045293 0.020221671 1.018738e-01
## T-148 0.8871912447 0.111960425 8.483302e-04
## T-149 0.7455066237 0.233368122 2.112525e-02
## T-150 0.6558565204 0.324956445 1.918703e-02
## T-151 0.4839078519 0.498880293 1.721186e-02
## T-152 0.6029899477 0.387966433 9.043619e-03
## T-153 0.4394670660 0.312173435 2.483595e-01
## T-154 0.5804963519 0.348602028 7.090162e-02
## T-155 0.8253763272 0.018508934 1.561147e-01
## T-156 0.7995736334 0.199882270 5.440963e-04
## T-157 0.6591448159 0.292548285 4.830690e-02
## T-158 0.7285396666 0.108965090 1.624952e-01
## T-159 0.0742343373 0.834842113 9.092355e-02
## T-160 0.2984368728 0.666913717 3.464941e-02
## T-161 0.9469766639 0.052229584 7.937522e-04
## T-162 0.7828500731 0.215546681 1.603245e-03
## T-163 0.8945475276 0.034106819 7.134565e-02
## T-164 0.8415577036 0.060763353 9.767894e-02
## T-165 0.7197995244 0.200173779 8.002670e-02
## T-166 0.9259846534 0.057876497 1.613885e-02
## T-167 0.4561051224 0.529447791 1.444709e-02
## T-168 0.7348016619 0.139107256 1.260911e-01
## T-169 0.4927023145 0.446896097 6.040159e-02
## T-170 0.3941916636 0.465980248 1.398281e-01
## T-171 0.9296316276 0.005689477 6.467889e-02
## T-172 0.8433445841 0.044805796 1.118496e-01
## T-173 0.5179814436 0.410088814 7.192974e-02
## T-174 0.6931436254 0.299696165 7.160210e-03
## T-175 0.6837786792 0.311869286 4.352035e-03
## T-176 0.4573591448 0.486171362 5.646949e-02
## T-177 0.5051770267 0.467935085 2.688789e-02
## T-178 0.5421564677 0.403711713 5.413182e-02# Dados para as vinhos suplementares
ind.sup <- dadoswine[24:27, 1:13]
ind.sup[, 1:6]## Alcohol MalicAcid Ash Alcalinity Magnesium Phenols
## R-24 12.85 1.60 2.52 17.8 95 2.48
## R-25 13.50 1.81 2.61 20.0 96 2.53
## R-26 13.05 2.05 3.22 25.0 124 2.63
## R-27 13.39 1.77 2.62 16.1 93 2.85ind.sup.coord <- predict(res.pca, newdata = ind.sup)
ind.sup.coord[, 1:ncol(ind.sup.coord)]## PC1 PC2 PC3
## R-24 -1.6403611 -0.5148267 0.14348035
## R-25 -1.7566207 -0.3162568 0.88778132
## R-26 -0.9872941 0.9380213 3.81016000
## R-27 -1.7702839 0.6842450 -0.08645652# Amostra atual
p <- fviz_pca_ind(res.pca, repel = TRUE)
# Amostra suplementar
fviz_add(p, ind.sup.coord, color ="blue")
# Centralizando e dimensionando os vinhos suplementares
ind.scaled <- scale(ind.sup,
center = res.pca$center,
scale = res.pca$scale)
# Coordenadas dos vinhos
coord_func <- function(ind, loadings){
r <- loadings*ind
apply(r, 2, sum)
}
pca.loadings <- res.pca$rotation
ind.sup.coord <- t(apply(ind.scaled, 1, coord_func, pca.loadings ))
ind.sup.coord[, 1:ncol(ind.sup.coord)]## PC1 PC2 PC3
## R-24 -1.6403611 -0.5148267 0.14348035
## R-25 -1.7566207 -0.3162568 0.88778132
## R-26 -0.9872941 0.9380213 3.81016000
## R-27 -1.7702839 0.6842450 -0.08645652groups <- as.factor(base$Classe[1:linhas])
fviz_pca_ind(res.pca,
col.ind = groups, # color by groups
palette = c("#00AFBB", "#E7B800", "#FC4E07"),
addEllipses = TRUE, # Concentration ellipses
ellipse.type = "confidence",
legend.title = "Groups",
repel = TRUE
)
library(ggpubr)
library(ggplot2)
library(ggfortify)
ggplot2::autoplot(res.pca, data=base, colour="Classe", frame=TRUE, frame.type="t") 
library(ggplot2)
ggplot(res.pca,aes(PC1, PC2))+
geom_point() +
stat_density_2d(aes(alpha=..level.., fill=base$Classe), bins=4, geom="polygon")
library(magrittr)
library(dplyr)
# 1. coordenadas dos vinhos
res.ind <- get_pca_ind(res.pca)
# 2. Coordenadasdos grupos
coord.groups <- res.ind$coord %>%
as_data_frame() %>%
select(Dim.1, Dim.2) %>%
mutate(competition = groups) %>%
group_by(competition) %>%
summarise(
Dim.1 = mean(Dim.1),
Dim.2 = mean(Dim.2)
)
coord.groups## # A tibble: 3 × 3
## competition Dim.1 Dim.2
## <fct> <dbl> <dbl>
## 1 B 0.0389 -1.64
## 2 R -2.28 0.965
## 3 T 2.74 1.24quanti.sup <- decathlon2[1:linhas, 11:12, drop = FALSE]
head(quanti.sup)## Rank Points
## SEBRLE 1 8217
## CLAY 2 8122
## BERNARD 4 8067
## YURKOV 5 8036
## ZSIVOCZKY 7 8004
## McMULLEN 8 7995# Prever coordenadas e calcular cos2
quanti.coord <- cor(quanti.sup, res.pca$x)
quanti.cos2 <- quanti.coord^2
# Gráfico de variáveis incluindo variáveis suplementares
p <- fviz_pca_var(res.pca)
fviz_add(p, quanti.coord, color ="blue", geom="arrow")
#::::::::::::::::::::::::::::::::::::::::
var_coord_func <- function(loadings, comp.sdev){
loadings*comp.sdev
}
#::::::::::::::::::::::::::::::::::::::::
loadings <- res.pca$rotation
sdev <- res.pca$sdev
var.coord <- t(apply(loadings, 1, var_coord_func, sdev))
head(var.coord[, 1:ncol(ind.sup.coord)])## [,1] [,2] [,3]
## Alcohol -0.313093350 0.76425725 -0.2493833
## MalicAcid 0.531884726 0.35543171 0.1070404
## Ash 0.004449362 0.49944611 0.7530514
## Alcalinity 0.519157081 -0.01673492 0.7360433
## Magnesium -0.308022936 0.47347612 0.1572388
## Phenols -0.856136658 0.10277424 0.1757842#::::::::::::::::::::::::::::::::::::::::
var.cos2 <- var.coord^2
head(var.cos2[, 1:ncol(ind.sup.coord)])## [,1] [,2] [,3]
## Alcohol 9.802745e-02 0.5840891486 0.06219202
## MalicAcid 2.829014e-01 0.1263317027 0.01145765
## Ash 1.979682e-05 0.2494464155 0.56708634
## Alcalinity 2.695241e-01 0.0002800574 0.54175981
## Magnesium 9.487813e-02 0.2241796399 0.02472404
## Phenols 7.329700e-01 0.0105625437 0.03090008#::::::::::::::::::::::::::::::::::::::::
comp.cos2 <- apply(var.cos2, 2, sum)
contrib <- function(var.cos2, comp.cos2){var.cos2*100/comp.cos2}
var.contrib <- t(apply(var.cos2,1, contrib, comp.cos2))
head(var.contrib[, 1:ncol(ind.sup.coord)])## [,1] [,2] [,3]
## Alcohol 2.083097e+00 23.39188197 4.3007553
## MalicAcid 6.011695e+00 5.05939254 0.7923294
## Ash 4.206853e-04 9.98994952 39.2156374
## Alcalinity 5.727426e+00 0.01121587 37.4642355
## Magnesium 2.016174e+00 8.97805359 1.7097376
## Phenols 1.557572e+01 0.42301381 2.1368289#::::::::::::::::::::::::::::::::::
ind.coord <- res.pca$x
head(ind.coord[, 1:ncol(ind.sup.coord)])## PC1 PC2 PC3
## R-1 -3.307421 1.4394023 -0.1652728
## R-2 -2.203250 -0.3324551 -2.0207571
## R-3 -2.509661 1.0282507 0.9800541
## R-4 -3.746497 2.7486184 -0.1756962
## R-5 -1.006070 0.8673840 2.0209873
## R-6 -3.041674 2.1164309 -0.6276254# Cos2 de indivíduos
#:::::::::::::::::::::::::::::::::
# 1. quadrado da distância entre um indivíduo e o centro de gravidade do PCA
center <- res.pca$center
scale<- res.pca$scale
getdistance <- function(ind_row, center, scale){
return(sum(((ind_row-center)/scale)^2))
}
d2 <- apply(dadoswine,1,getdistance, center, scale)
# 2. Calcule o cos2. A soma de cada linha é 1
cos2 <- function(ind.coord, d2){return(ind.coord^2/d2)}
ind.cos2 <- apply(ind.coord, 2, cos2, d2)
head(ind.cos2[, 1:ncol(ind.sup.coord)])## PC1 PC2 PC3
## R-1 0.6874080 0.130196702 0.001716479
## R-2 0.4261832 0.009703642 0.358506506
## R-3 0.5740096 0.096357876 0.087536511
## R-4 0.5988669 0.322335688 0.001317056
## R-5 0.1430059 0.106296731 0.577064302
## R-6 0.5977278 0.289391906 0.025449495# Contribuições de vinhos
#:::::::::::::::::::::::::::::::
contrib <- function(ind.coord, comp.sdev, n.ind){
100*(1/n.ind)*ind.coord^2/comp.sdev^2
}
ind.contrib <- t(apply(ind.coord, 1, contrib,
res.pca$sdev, nrow(ind.coord)))
head(ind.contrib[, 1:ncol(ind.sup.coord)])## [,1] [,2] [,3]
## R-1 1.3059329 0.46615504 0.01061190
## R-2 0.5795213 0.02486749 1.58642045
## R-3 0.7519205 0.23788336 0.37315576
## R-4 1.6756863 1.69978863 0.01199264
## R-5 0.1208367 0.16927346 1.58678191
## R-6 1.1045036 1.00779968 0.15303511