Aula PCA
Enggel
2022-09-16
PCA - Principal Components analysis
- Método de obtenção de variáveis importantes;
- Reduz dimensionalidade dos dados, a partir da redução da quantidade de variáveis do banco de dados sem perder de informações;
- É uma análise não-supervisionada que serve como análise exploratória preditiva;
- PCA: transformação/combinação linear das dimensões/variáveis originais não correlacionadas, criando componentes principais (PC), agrupadas segundo a variância;
- Utilizada para capturar padrões fortes;
- PCA somente analisa dados continuos
- Eixos - PC - agrupamento das variáveis (caracteristicas gerais);
- O primeiro componente principal explica a variação máxima do conjunto de dados;
- Melhor ajuste baseada no maior valor - junção das informações importantes num componente por meio do calculo de variância (indica qual componente explica melhor a variação dos dados - PC1)
- O segundo componente tenta explicar a variação restante do conjunto de dados e não está relacionado com o primeiro componente;
- As variáveis devem ser numéricas e os dados devem ser padronizados(em escala); > normalizar os dados para redução de dimensionalidade
\[Z = (valor bruto- média)/desvio padrão\]
- Padronização automatica do R a partir da função
scale; - Youtube : StatQuestPCA
- Dados não lineares podem ser problematicos (?)
- Não é um teste - tem base na distância Euclidiana
Como se calcula?
- Cálculo de transposição de matrizes a partir da tranformação utilizando autovalores e autovetores.
Tutorial em português
names(iris)## [1] "Sepal.Length" "Sepal.Width" "Petal.Length" "Petal.Width" "Species"library(tidyverse)
library(factoextra) # ou (FactoMiner) para análise PCA e plot dos gráficos
library(vegan)## Primeiro selecionamos as colunas que iremos analisar
#Matriz de correlação
pca_t1 = prcomp(iris[,c(1:4)], center = T, scale. = T) #centralizar proximo ao eixo - padronização dos dados
pca_t1## Standard deviations (1, .., p=4):
## [1] 1.7083611 0.9560494 0.3830886 0.1439265
##
## Rotation (n x k) = (4 x 4):
## PC1 PC2 PC3 PC4
## Sepal.Length 0.5210659 -0.37741762 0.7195664 0.2612863
## Sepal.Width -0.2693474 -0.92329566 -0.2443818 -0.1235096
## Petal.Length 0.5804131 -0.02449161 -0.1421264 -0.8014492
## Petal.Width 0.5648565 -0.06694199 -0.6342727 0.5235971summary(pca_t1) # aqui já dá o desvio padrão e a proporção de variância## Importance of components:
## PC1 PC2 PC3 PC4
## Standard deviation 1.7084 0.9560 0.38309 0.14393
## Proportion of Variance 0.7296 0.2285 0.03669 0.00518
## Cumulative Proportion 0.7296 0.9581 0.99482 1.00000variance_pca = (pca_t1$sdev)^2 #variancia
#O quanto que cada valor contribuiu/é importante para a variação.
#Observe que no PC1 cada variavel contribuiu de maneira similar, menos a largura da sépala, mas no PC2 apenas o largura para a variação.
#Standard deviation = Quanto cada eixo explica a correlação
#Proporcion of variance = importancia de cada eixo explicando a variação# Extrair os autovalores - proporção de variância dos valores de componentes principais
eig.val <- get_eigenvalue(pca_t1)
eig.val## eigenvalue variance.percent cumulative.variance.percent
## Dim.1 2.91849782 72.9624454 72.96245
## Dim.2 0.91403047 22.8507618 95.81321
## Dim.3 0.14675688 3.6689219 99.48213
## Dim.4 0.02071484 0.5178709 100.00000Cálculos de matriz somando a correlação dos dados em relação a cada dimensão
Quais eixos são significativos (explicam a variação) e que devem ser utilizados:
- PC1 = eixo x
- PC2 = eixo y
##Cada dimensão/componente/variável tem sua matriz isolada apresentando a importância que cada variavel tem para a explicação dos dados
Variaveis
res.var <- get_pca_var(pca_t1)
res.var$coord # Coordenadas## Dim.1 Dim.2 Dim.3 Dim.4
## Sepal.Length 0.8901688 -0.36082989 0.27565767 0.03760602
## Sepal.Width -0.4601427 -0.88271627 -0.09361987 -0.01777631
## Petal.Length 0.9915552 -0.02341519 -0.05444699 -0.11534978
## Petal.Width 0.9649790 -0.06399985 -0.24298265 0.07535950res.var$contrib # Contr para os eixos PCs - como cada variavel contribui em porcentagem (no nosso caso o comprimento da pétala)## Dim.1 Dim.2 Dim.3 Dim.4
## Sepal.Length 27.150969 14.24440565 51.777574 6.827052
## Sepal.Width 7.254804 85.24748749 5.972245 1.525463
## Petal.Length 33.687936 0.05998389 2.019990 64.232089
## Petal.Width 31.906291 0.44812296 40.230191 27.415396res.var$cos2 # qualidade representacao ## Dim.1 Dim.2 Dim.3 Dim.4
## Sepal.Length 0.7924004 0.130198208 0.075987149 0.0014142127
## Sepal.Width 0.2117313 0.779188012 0.008764681 0.0003159971
## Petal.Length 0.9831817 0.000548271 0.002964475 0.0133055723
## Petal.Width 0.9311844 0.004095980 0.059040571 0.0056790544#Para cada eixo os maiores valores indicam a variável mais representativa
# Results for individuals
res.ind <- get_pca_ind(pca_t1)
res.ind$coord # Coordenadas## Dim.1 Dim.2 Dim.3 Dim.4
## 1 -2.25714118 -0.478423832 0.127279624 0.024087508
## 2 -2.07401302 0.671882687 0.233825517 0.102662845
## 3 -2.35633511 0.340766425 -0.044053900 0.028282305
## 4 -2.29170679 0.595399863 -0.090985297 -0.065735340
## 5 -2.38186270 -0.644675659 -0.015685647 -0.035802870
## 6 -2.06870061 -1.484205297 -0.026878250 0.006586116
## 7 -2.43586845 -0.047485118 -0.334350297 -0.036652767
## 8 -2.22539189 -0.222403002 0.088399352 -0.024529919
## 9 -2.32684533 1.111603700 -0.144592465 -0.026769540
## 10 -2.17703491 0.467447569 0.252918268 -0.039766068
## 11 -2.15907699 -1.040205867 0.267784001 0.016675503
## 12 -2.31836413 -0.132633999 -0.093446191 -0.133037725
## 13 -2.21104370 0.726243183 0.230140246 0.002416941
## 14 -2.62430902 0.958296347 -0.180192423 -0.019151375
## 15 -2.19139921 -1.853846555 0.471322025 0.194081578
## 16 -2.25466121 -2.677315230 -0.030424684 0.050365010
## 17 -2.20021676 -1.478655729 0.005326251 0.188186988
## 18 -2.18303613 -0.487206131 0.044067686 0.092779618
## 19 -1.89223284 -1.400327567 0.373093377 0.060891973
## 20 -2.33554476 -1.124083597 -0.132187626 -0.037630354
## 21 -1.90793125 -0.407490576 0.419885937 0.010884821
## 22 -2.19964383 -0.921035871 -0.159331502 0.059398340
## 23 -2.76508142 -0.456813301 -0.331069982 0.019582826
## 24 -1.81259716 -0.085272854 -0.034373442 0.150636353
## 25 -2.21972701 -0.136796175 -0.117599566 -0.269238379
## 26 -1.94532930 0.623529705 0.304620475 0.043416203
## 27 -2.04430277 -0.241354991 -0.086075649 0.067454082
## 28 -2.16133650 -0.525389422 0.206125707 0.010241084
## 29 -2.13241965 -0.312172005 0.270244895 0.083977887
## 30 -2.25769799 0.336604248 -0.068207276 -0.107918349
## 31 -2.13297647 0.502856075 0.074757996 -0.048027970
## 32 -1.82547925 -0.422280389 0.269564311 0.239069476
## 33 -2.60621687 -1.787587272 -0.047070727 -0.228470534
## 34 -2.43800983 -2.143546796 0.082392024 -0.048053409
## 35 -2.10292986 0.458665270 0.169706329 0.028926042
## 36 -2.20043723 0.205419224 0.224688852 0.168343905
## 37 -2.03831765 -0.659349230 0.482919584 0.195702902
## 38 -2.51889339 -0.590315163 -0.019370918 -0.136048774
## 39 -2.42152026 0.901161067 -0.192609402 -0.009705907
## 40 -2.16246625 -0.267981199 0.175296561 0.007023875
## 41 -2.27884081 -0.440240541 -0.034778398 0.106626042
## 42 -1.85191836 2.329610745 0.203552303 0.288896090
## 43 -2.54511203 0.477501017 -0.304745527 -0.066379077
## 44 -1.95788857 -0.470749613 -0.308567588 0.176501717
## 45 -2.12992356 -1.138415464 -0.247604064 -0.150539117
## 46 -2.06283361 0.708678586 0.063716370 0.139801160
## 47 -2.37677076 -1.116688691 -0.057026813 -0.151722682
## 48 -2.38638171 0.384957230 -0.139002234 -0.048671707
## 49 -2.22200263 -0.994627669 0.180886792 -0.014878291
## 50 -2.19647504 -0.009185585 0.152518539 0.049206884
## 51 1.09810244 -0.860091033 0.682300393 0.034717469
## 52 0.72889556 -0.592629362 0.093807452 0.004887251
## 53 1.23683580 -0.614239894 0.552157058 0.009391933
## 54 0.40612251 1.748546197 0.023024633 0.065549239
## 55 1.07188379 0.207725147 0.396925784 0.104387166
## 56 0.38738955 0.591302717 -0.123776885 -0.240027187
## 57 0.74403715 -0.770438272 -0.148472007 -0.077111455
## 58 -0.48569562 1.846243998 -0.248432992 -0.040384912
## 59 0.92480346 -0.032118478 0.594178807 -0.029779844
## 60 0.01138804 1.030565784 -0.537100055 -0.028366154
## 61 -0.10982834 2.645211115 0.046634215 0.013714785
## 62 0.43922201 0.063083852 -0.204389093 0.039992104
## 63 0.56023148 1.758832129 0.763214554 0.045578465
## 64 0.71715934 0.185602819 0.068429700 -0.164256922
## 65 -0.03324333 0.437537419 -0.194282030 0.108684396
## 66 0.87248429 -0.507364239 0.501830204 0.104593326
## 67 0.34908221 0.195656268 -0.489234095 -0.190869932
## 68 0.15827980 0.789451008 0.301028700 -0.204612265
## 69 1.22100316 1.616827281 0.480693656 0.225145511
## 70 0.16436725 1.298259939 0.172260719 -0.051554138
## 71 0.73521959 -0.395247446 -0.614467782 -0.083006045
## 72 0.47469691 0.415926887 0.264067576 0.113189079
## 73 1.23005729 0.930209441 0.367182178 -0.009911322
## 74 0.63074514 0.414997441 0.290921638 -0.273304557
## 75 0.70031506 0.063200094 0.444537765 0.043313222
## 76 0.87135454 -0.249956017 0.471001057 0.101376117
## 77 1.25231375 0.076998069 0.724727099 0.039556002
## 78 1.35386953 -0.330205463 0.259955701 0.066604931
## 79 0.66258066 0.225173502 -0.085577197 -0.036318171
## 80 -0.04012419 1.055183583 0.318506304 0.064571834
## 81 0.13035846 1.557055553 0.149482697 -0.009371129
## 82 0.02337438 1.567225244 0.240745761 -0.032663020
## 83 0.24073180 0.774661195 0.150707074 0.023572390
## 84 1.05755171 0.631726901 -0.104959762 -0.183354200
## 85 0.22323093 0.286812663 -0.663028512 -0.253977520
## 86 0.42770626 -0.842758920 -0.449129446 -0.109308985
## 87 1.04522645 -0.520308714 0.394464890 0.037084781
## 88 1.04104379 1.378371048 0.685997804 0.136378719
## 89 0.06935597 0.218770433 -0.290605718 -0.146653279
## 90 0.28253073 1.324886147 -0.089111491 0.008876070
## 91 0.27814596 1.116288852 -0.094172116 -0.269753497
## 92 0.62248441 -0.024839814 0.020412763 -0.147193289
## 93 0.33540673 0.985103828 0.198724011 0.006508757
## 94 -0.36097409 2.012495825 -0.105467721 0.019505467
## 95 0.28762268 0.852873116 -0.130452657 -0.107043742
## 96 0.09105561 0.180587142 -0.128547696 -0.229191812
## 97 0.22695654 0.383634868 -0.155691572 -0.132163118
## 98 0.57446378 0.154356489 0.270743347 -0.019794366
## 99 -0.44617230 1.538637456 -0.189765199 0.199278855
## 100 0.25587339 0.596852285 -0.091572385 -0.058426315
## 101 1.83841002 -0.867515056 -1.002044077 -0.049085303
## 102 1.15401555 0.696536401 -0.528389994 -0.040385459
## 103 2.19790361 -0.560133976 0.202236658 0.058986583
## 104 1.43534213 0.046830701 -0.163083761 -0.234982858
## 105 1.86157577 -0.294059697 -0.394307408 -0.016243853
## 106 2.74268509 -0.797736709 0.580364827 -0.101045973
## 107 0.36579225 1.556289178 -0.983598122 -0.132679346
## 108 2.29475181 -0.418663020 0.649530452 -0.237246445
## 109 1.99998633 0.709063226 0.392675073 -0.086221779
## 110 2.25223216 -1.914596301 -0.396224508 0.104488870
## 111 1.35962064 -0.690443405 -0.283661780 0.107500284
## 112 1.59732747 0.420292431 -0.023108991 0.058136869
## 113 1.87761053 -0.417849815 -0.026250468 0.145926073
## 114 1.25590769 1.158379741 -0.578311891 0.098826244
## 115 1.46274487 0.440794883 -1.000517746 0.274738504
## 116 1.58476820 -0.673986887 -0.636297054 0.191222383
## 117 1.46651849 -0.254768327 -0.037306280 -0.154811637
## 118 2.41822770 -2.548124795 0.127454475 -0.272892966
## 119 3.29964148 -0.017721580 0.700957033 0.045037725
## 120 1.25954707 1.701046715 0.266643612 -0.064963167
## 121 2.03091256 -0.907427443 -0.234015510 0.167390481
## 122 0.97471535 0.569855257 -0.825362161 0.027662914
## 123 2.88797650 -0.412259950 0.854558973 -0.126911337
## 124 1.32878064 0.480202496 0.005410239 0.139491837
## 125 1.69505530 -1.010536476 -0.297454114 -0.061437911
## 126 1.94780139 -1.004412720 0.418582432 -0.217609339
## 127 1.17118007 0.315338060 -0.129503907 0.125001677
## 128 1.01754169 -0.064131184 -0.336588365 -0.008625505
## 129 1.78237879 0.186735633 -0.269754304 0.030983849
## 130 1.85742501 -0.560413289 0.713244682 -0.207519953
## 131 2.42782030 -0.258418706 0.725386035 -0.017863520
## 132 2.29723178 -2.617554417 0.491826144 -0.210968943
## 133 1.85648383 0.177953334 -0.352966242 0.099675959
## 134 1.11042770 0.291944582 0.182875741 -0.185721512
## 135 1.19845835 0.808606364 0.164173760 -0.487849130
## 136 2.78942561 -0.853942542 0.541093785 0.294893130
## 137 1.57099294 -1.065013214 -0.942695700 0.035486875
## 138 1.34179696 -0.421020154 -0.180271551 -0.214702016
## 139 0.92173701 -0.017165594 -0.415434449 0.005220919
## 140 1.84586124 -0.673870645 0.012629804 0.194543500
## 141 2.00808316 -0.611835930 -0.426902678 0.246711805
## 142 1.89543421 -0.687273065 -0.129640697 0.468128374
## 143 1.15401555 0.696536401 -0.528389994 -0.040385459
## 144 2.03374499 -0.864624030 -0.337014969 0.045036251
## 145 1.99147547 -1.045665670 -0.630301866 0.213330527
## 146 1.86425786 -0.385674038 -0.255418178 0.387957152
## 147 1.55935649 0.893692855 0.026283300 0.219456899
## 148 1.51609145 -0.268170747 -0.179576781 0.118773236
## 149 1.36820418 -1.007877934 -0.930278721 0.026041407
## 150 0.95744849 0.024250427 -0.526485033 -0.162533529res.ind$contrib # Contr para os eixos PCs## Dim.1 Dim.2 Dim.3 Dim.4
## 1 1.163769e+00 0.1669451003 0.0735915668 0.0186728665
## 2 9.825900e-01 0.3292569626 0.2483671131 0.3391984199
## 3 1.268304e+00 0.0846957585 0.0088161508 0.0257428626
## 4 1.199686e+00 0.2585624933 0.0376056170 0.1390673121
## 5 1.295934e+00 0.3031311820 0.0011176741 0.0412537017
## 6 9.775628e-01 1.6067045417 0.0032818011 0.0013960019
## 7 1.355367e+00 0.0016446107 0.5078245697 0.0432355278
## 8 1.131260e+00 0.0360769120 0.0354983728 0.0193650869
## 9 1.236757e+00 0.9012557191 0.0949733177 0.0230626422
## 10 1.082630e+00 0.1593726804 0.2905833193 0.0508923526
## 11 1.064843e+00 0.7891992507 0.3257463332 0.0089492183
## 12 1.227758e+00 0.0128309199 0.0396673776 0.5696090090
## 13 1.116719e+00 0.3846911581 0.2405998928 0.0001880007
## 14 1.573183e+00 0.6698039928 0.1474970499 0.0118039439
## 15 1.096964e+00 2.5066611786 1.0091268322 1.2122602427
## 16 1.161213e+00 5.2281384944 0.0042049654 0.0816366321
## 17 1.105809e+00 1.5947117975 0.0001288705 1.1397416412
## 18 1.088607e+00 0.1731304890 0.0088216692 0.2770335663
## 19 8.178968e-01 1.4302348082 0.6323322952 0.1193293649
## 20 1.246022e+00 0.9216059879 0.0793764898 0.0455726047
## 21 8.315240e-01 0.1211108929 0.8008901320 0.0038130266
## 22 1.105234e+00 0.6187299744 0.1153223765 0.1135470477
## 23 1.746486e+00 0.1522038183 0.4979089066 0.0123417844
## 24 7.505022e-01 0.0053035866 0.0053673055 0.7302756440
## 25 1.125508e+00 0.0136488474 0.0628234415 2.3329270877
## 26 8.644415e-01 0.2835713581 0.4215299790 0.0606639806
## 27 9.546404e-01 0.0424874469 0.0336566510 0.1464346017
## 28 1.067073e+00 0.2013310301 0.1930076853 0.0033753524
## 29 1.038711e+00 0.0710781268 0.3317609610 0.2269640755
## 30 1.164343e+00 0.0826394184 0.0211335127 0.3748157374
## 31 1.039253e+00 0.1844316577 0.0253878299 0.0742361937
## 32 7.612077e-01 0.1300618396 0.3300920545 1.8393970811
## 33 1.551567e+00 2.3306795967 0.0100649611 1.6799162326
## 34 1.357751e+00 3.3513053886 0.0308376041 0.0743148571
## 35 1.010180e+00 0.1534404206 0.1308297057 0.0269280716
## 36 1.106031e+00 0.0307772800 0.2293365804 0.9120570964
## 37 9.490588e-01 0.3170874647 1.0593998813 1.2325988708
## 38 1.449336e+00 0.2541651167 0.0017045537 0.5956847703
## 39 1.339447e+00 0.5923152410 0.1685253554 0.0030317927
## 40 1.068189e+00 0.0523789418 0.1395908895 0.0015877452
## 41 1.186253e+00 0.1413605198 0.0054945159 0.3658927545
## 42 7.834171e-01 3.9583554310 0.1882185078 2.6860281585
## 43 1.479664e+00 0.1663016924 0.4218761391 0.1418043811
## 44 8.756394e-01 0.1616322466 0.4325246809 1.0025939972
## 45 1.036281e+00 0.9452564290 0.2785003996 0.7293331623
## 46 9.720257e-01 0.3663082389 0.0184421832 0.6289973043
## 47 1.290399e+00 0.9095201026 0.0147729928 0.7408465370
## 48 1.300856e+00 0.1080868918 0.0877715656 0.0762395610
## 49 1.127817e+00 0.7215545001 0.1486359959 0.0071241548
## 50 1.102052e+00 0.0000615406 0.1056709368 0.0779253864
## 51 2.754451e-01 0.5395564725 2.1147621386 0.0387903180
## 52 1.213612e-01 0.2561618179 0.0399746769 0.0007686992
## 53 3.494407e-01 0.2751845871 1.3849546075 0.0028388158
## 54 3.767589e-02 2.2299867801 0.0024082176 0.1382810102
## 55 2.624489e-01 0.0314721359 0.7156965220 0.3506884360
## 56 3.428034e-02 0.2550162267 0.0695968181 1.8541638250
## 57 1.264558e-01 0.4329360634 0.1001381226 0.1913661085
## 58 5.388622e-02 2.4861438831 0.2803682455 0.0524886636
## 59 1.953657e-01 0.0007524159 1.6037792817 0.0285411898
## 60 2.962424e-05 0.7746392619 1.3104506708 0.0258957301
## 61 2.755359e-03 5.1035073490 0.0098791511 0.0060534820
## 62 4.406741e-02 0.0029025818 0.1897691953 0.0514725574
## 63 7.169426e-02 2.2563000215 2.6460836577 0.0668569603
## 64 1.174845e-01 0.0251256441 0.0212715702 0.8683095863
## 65 2.524402e-04 0.1396299131 0.1714650265 0.3801558050
## 66 1.738860e-01 0.1877533841 1.1439943439 0.3520749913
## 67 2.783587e-02 0.0279212975 1.0872857962 1.1724714283
## 68 5.722691e-03 0.4545675544 0.4116480768 1.3473814312
## 69 3.405516e-01 1.9066690798 1.0496561728 1.6313750533
## 70 6.171347e-03 1.2293382046 0.1347977971 0.0855370533
## 71 1.234763e-01 0.1139426227 1.7151753137 0.2217413425
## 72 5.147332e-02 0.1261775408 0.3167673709 0.4123217874
## 73 3.456209e-01 0.6311165257 0.6124539923 0.0031614795
## 74 9.087767e-02 0.1256142483 0.3844698885 2.4039253534
## 75 1.120305e-01 0.0029132886 0.8976925200 0.0603765390
## 76 1.734360e-01 0.0455696043 1.0077528786 0.3307489955
## 77 3.582413e-01 0.0043242195 2.3859387184 0.0503560918
## 78 4.187000e-01 0.0795273615 0.3069792186 0.1427709995
## 79 1.002829e-01 0.0369813391 0.0332679776 0.0424497530
## 80 3.677578e-04 0.8120899169 0.4608359480 0.1341879371
## 81 3.881752e-03 1.7683013649 0.1015060986 0.0028262530
## 82 1.248043e-04 1.7914756244 0.2632858870 0.0343352262
## 83 1.323781e-02 0.4376950853 0.1031757327 0.0178827571
## 84 2.554775e-01 0.2910762749 0.0500444540 1.0819543973
## 85 1.138304e-02 0.0599990964 1.9969844984 2.0759542931
## 86 4.178694e-02 0.5180298465 0.9163330325 0.3845377313
## 87 2.495572e-01 0.1974559686 0.7068495614 0.0442607405
## 88 2.475639e-01 1.3857355269 2.1377441870 0.5985775797
## 89 1.098796e-03 0.0349080284 0.3836353292 0.6921668346
## 90 1.823395e-02 1.2802806599 0.0360726216 0.0025355292
## 91 1.767237e-02 0.9088688983 0.0402860733 2.3418625363
## 92 8.851285e-02 0.0004500334 0.0018928398 0.6972736501
## 93 2.569762e-02 0.7078024803 0.1793952642 0.0013634002
## 94 2.976469e-02 2.9540513664 0.0505300128 0.0122444682
## 95 1.889712e-02 0.5305385134 0.0773065230 0.3687650886
## 96 1.893925e-03 0.0237860166 0.0750652404 1.6905399174
## 97 1.176616e-02 0.1073455914 0.1101134811 0.5621442642
## 98 7.538322e-02 0.0173779222 0.3329859203 0.0126098647
## 99 4.547310e-02 1.7267150230 0.1635849802 1.2780553698
## 100 1.495545e-02 0.2598255104 0.0380924876 0.1098611712
## 101 7.720299e-01 0.5489112205 4.5612506062 0.0775407832
## 102 3.042094e-01 0.3538634450 1.2682925835 0.0524900853
## 103 1.103486e+00 0.2288399792 0.1857932980 0.1119782595
## 104 4.706090e-01 0.0015995926 0.1208180219 1.7770497946
## 105 7.916091e-01 0.0630694549 0.7062852826 0.0084919091
## 106 1.718309e+00 0.4641594756 1.5300740568 0.3285982553
## 107 3.056458e-02 1.7665610943 4.3948662809 0.5665443042
## 108 1.202876e+00 0.1278430931 1.9165021791 1.8114512828
## 109 9.136996e-01 0.3667059788 0.7004496935 0.2392550940
## 110 1.158712e+00 2.6736373374 0.7131698168 0.3513721211
## 111 4.222648e-01 0.3476996374 0.3655206628 0.3719173659
## 112 5.828238e-01 0.1288401449 0.0024258963 0.1087753546
## 113 8.053050e-01 0.1273469344 0.0031302886 0.6853193985
## 114 3.603005e-01 0.9787008691 1.5192684821 0.3143198543
## 115 4.887497e-01 0.1417167409 4.5473656407 2.4292168817
## 116 5.736947e-01 0.3313225236 1.8392048707 1.1768054851
## 117 4.912748e-01 0.0473411645 0.0063222867 0.7713197291
## 118 1.335807e+00 4.7357574871 0.0737938996 2.3966902897
## 119 2.487041e+00 0.0002290620 2.2319942857 0.0652799975
## 120 3.623916e-01 2.1104766332 0.3229777854 0.1358193387
## 121 9.421755e-01 0.6005814104 0.2487708947 0.9017553873
## 122 2.170226e-01 0.2368520698 3.0945634613 0.0246276560
## 123 1.905183e+00 0.1239625096 3.3173734224 0.5183559297
## 124 4.033258e-01 0.1681887304 0.0001329668 0.6262169547
## 125 6.563222e-01 0.7448212441 0.4019298327 0.1214786946
## 126 8.666400e-01 0.7358215024 0.7959252404 1.5239906160
## 127 3.133262e-01 0.0725271899 0.0761861495 0.5028736831
## 128 2.365123e-01 0.0029997605 0.5146458595 0.0023943978
## 129 7.256871e-01 0.0254332853 0.3305575265 0.0308956950
## 130 7.880830e-01 0.2290682601 2.3109330770 1.3859480497
## 131 1.346426e+00 0.0487075139 2.3902793768 0.0102697845
## 132 1.205477e+00 4.9973469817 1.0988375855 1.4323999192
## 133 7.872845e-01 0.0230972527 0.5659481268 0.3197481753
## 134 2.816631e-01 0.0621654248 0.1519226338 1.1100732945
## 135 3.280917e-01 0.4768945695 0.1224384360 7.6594626423
## 136 1.777374e+00 0.5318698436 1.3300114350 2.7987012581
## 137 5.637646e-01 0.8272905416 4.0369496821 0.0405287062
## 138 4.112662e-01 0.1292866965 0.1476266199 1.4835407418
## 139 1.940722e-01 0.0002149145 0.7839986174 0.0008772455
## 140 7.783008e-01 0.3312082477 0.0007246086 1.2180375705
## 141 9.211127e-01 0.2730348104 0.8278812428 1.9588766725
## 142 8.206667e-01 0.3445138729 0.0763471797 7.0527284429
## 143 3.042094e-01 0.3538634450 1.2682925835 0.0524900853
## 144 9.448054e-01 0.5452587825 0.5159512463 0.0652757227
## 145 9.059397e-01 0.7975056464 1.8047101851 1.4646479398
## 146 7.938918e-01 0.1084897918 0.2963561117 4.8438954251
## 147 5.554439e-01 0.5825385063 0.0031381238 1.5499786180
## 148 5.250494e-01 0.0524530651 0.1464909008 0.4540089451
## 149 4.276133e-01 0.7409074137 3.9313024575 0.0218250944
## 150 2.094017e-01 0.0004289304 1.2591641287 0.8501844611res.ind$cos2 # qualidade representacao## Dim.1 Dim.2 Dim.3 Dim.4
## 1 9.539975e-01 4.286032e-02 3.033525e-03 1.086460e-04
## 2 8.927725e-01 9.369248e-02 1.134754e-02 2.187482e-03
## 3 9.790410e-01 2.047578e-02 3.422122e-04 1.410446e-04
## 4 9.346682e-01 6.308947e-02 1.473268e-03 7.690193e-04
## 5 9.315095e-01 6.823959e-02 4.039790e-05 2.104697e-04
## 6 6.600989e-01 3.397830e-01 1.114335e-04 6.690714e-06
## 7 9.809239e-01 3.727715e-04 1.848124e-02 2.220962e-04
## 8 9.884478e-01 9.872384e-03 1.559692e-03 1.200972e-04
## 9 8.115435e-01 1.852153e-01 3.133777e-03 1.074134e-04
## 10 9.434549e-01 4.349669e-02 1.273359e-02 3.147862e-04
## 11 8.015666e-01 1.860553e-01 1.233027e-02 4.781468e-05
## 12 9.918759e-01 3.246413e-03 1.611452e-03 3.266207e-03
## 13 8.938769e-01 9.643777e-02 9.684299e-03 1.068108e-06
## 14 8.786492e-01 1.171616e-01 4.142463e-03 4.679349e-05
## 15 5.650488e-01 4.043808e-01 2.613836e-02 4.432120e-03
## 16 4.148109e-01 5.849066e-01 7.553351e-05 2.069881e-04
## 17 6.854138e-01 3.095680e-01 4.016660e-06 5.014193e-03
## 18 9.505502e-01 4.734550e-02 3.873412e-04 1.716953e-03
## 19 6.298932e-01 3.449666e-01 2.448797e-02 6.522857e-04
## 20 8.096466e-01 1.875497e-01 2.593586e-03 2.101821e-04
## 21 9.140097e-01 4.169275e-02 4.426781e-02 2.974870e-05
## 22 8.465230e-01 1.484182e-01 4.441578e-03 6.172806e-04
## 23 9.599880e-01 2.620158e-02 1.376225e-02 4.815049e-05
## 24 9.906097e-01 2.192409e-03 3.562427e-04 6.841630e-03
## 25 9.791281e-01 3.718675e-03 2.748222e-03 1.440503e-02
## 26 8.867166e-01 9.109885e-02 2.174287e-02 4.416744e-04
## 27 9.834773e-01 1.370839e-02 1.743550e-03 1.070756e-03
## 28 9.361470e-01 5.531742e-02 8.514587e-03 2.101799e-05
## 29 9.624243e-01 2.062572e-02 1.545739e-02 1.492626e-03
## 30 9.752045e-01 2.167720e-02 8.900726e-04 2.228202e-03
## 31 9.457919e-01 5.256672e-02 1.161820e-03 4.795258e-04
## 32 9.153582e-01 4.898229e-02 1.996007e-02 1.569949e-02
## 33 6.763790e-01 3.182025e-01 2.206332e-04 5.197918e-03
## 34 5.635205e-01 4.356170e-01 6.435898e-04 2.189209e-04
## 35 9.485212e-01 4.512209e-02 6.177227e-03 1.794632e-04
## 36 9.756149e-01 8.502422e-03 1.017240e-02 5.710252e-03
## 37 8.547102e-01 8.943472e-02 4.797608e-02 7.878975e-03
## 38 9.452702e-01 5.191636e-02 5.590322e-05 2.757564e-03
## 39 8.734875e-01 1.209721e-01 5.526313e-03 1.403307e-05
## 40 9.785321e-01 1.502744e-02 6.430181e-03 1.032357e-05
## 41 9.617761e-01 3.589435e-02 2.240088e-04 2.105584e-03
## 42 3.818483e-01 6.042461e-01 4.613167e-03 9.292455e-03
## 43 9.521845e-01 3.351629e-02 1.365155e-02 6.476937e-04
## 44 9.167790e-01 5.299912e-02 2.277138e-02 7.450520e-03
## 45 7.667622e-01 2.190454e-01 1.036211e-02 3.830287e-03
## 46 8.900194e-01 1.050436e-01 8.491279e-04 4.087828e-03
## 47 8.160634e-01 1.801414e-01 4.697940e-04 3.325449e-03
## 48 9.710330e-01 2.526848e-02 3.294562e-03 4.039311e-04
## 49 8.284719e-01 1.660006e-01 5.490379e-03 3.714452e-05
## 50 9.946874e-01 1.739593e-05 4.796002e-03 4.992129e-04
## 51 4.998618e-01 3.066571e-01 1.929814e-01 4.996436e-04
## 52 5.960682e-01 3.940322e-01 9.872793e-03 2.679752e-05
## 53 6.915685e-01 1.705639e-01 1.378277e-01 3.987688e-05
## 54 5.110830e-02 9.473960e-01 1.642717e-04 1.331413e-03
## 55 8.444751e-01 3.171536e-02 1.158004e-01 8.009136e-03
## 56 2.620665e-01 6.105701e-01 2.675438e-02 1.006090e-01
## 57 4.710788e-01 5.051030e-01 1.875830e-02 5.059902e-03
## 58 6.362155e-02 9.192932e-01 1.664541e-02 4.398597e-04
## 59 7.066943e-01 8.523983e-04 2.917205e-01 7.327866e-04
## 60 9.595978e-05 7.858559e-01 2.134528e-01 5.953775e-04
## 61 1.720338e-03 9.979427e-01 3.101660e-04 2.682643e-05
## 62 8.029139e-01 1.656293e-02 1.738666e-01 6.656551e-03
## 63 7.862358e-02 7.749373e-01 1.459187e-01 5.203999e-04
## 64 8.860991e-01 5.934992e-02 8.067524e-03 4.648345e-02
## 65 4.564686e-03 7.907372e-01 1.559075e-01 4.879060e-02
## 66 5.940507e-01 2.008852e-01 1.965268e-01 8.537215e-03
## 67 2.795423e-01 8.781721e-02 5.490673e-01 8.357322e-02
## 68 3.208691e-02 7.982287e-01 1.160627e-01 5.362166e-02
## 69 3.398538e-01 5.959170e-01 5.267388e-02 1.155540e-02
## 70 1.548382e-02 9.659862e-01 1.700670e-02 1.523262e-03
## 71 4.999383e-01 1.444842e-01 3.492051e-01 6.372381e-03
## 72 4.685974e-01 3.597502e-01 1.450098e-01 2.664257e-02
## 73 6.020253e-01 3.442909e-01 5.364475e-02 3.908654e-05
## 74 5.454390e-01 2.361181e-01 1.160354e-01 1.024076e-01
## 75 7.067637e-01 5.756026e-03 2.847768e-01 2.703512e-03
## 76 7.204579e-01 5.928516e-02 2.105051e-01 9.751919e-03
## 77 7.464447e-01 2.821831e-03 2.499887e-01 7.447254e-04
## 78 9.101054e-01 5.413854e-02 3.355342e-02 2.202677e-03
## 79 8.809180e-01 1.017402e-01 1.469515e-02 2.646707e-03
## 80 1.318942e-03 9.121560e-01 8.310921e-02 3.415854e-03
## 81 6.897068e-03 9.839981e-01 9.069177e-03 3.564264e-05
## 82 2.171750e-04 9.763206e-01 2.303811e-02 4.240747e-04
## 83 8.505812e-02 8.807901e-01 3.333620e-02 8.155603e-04
## 84 7.159556e-01 2.554710e-01 7.052264e-03 2.152111e-02
## 85 7.832704e-02 1.293003e-01 6.909830e-01 1.013896e-01
## 86 1.652746e-01 6.416844e-01 1.822459e-01 1.079510e-02
## 87 7.186556e-01 1.780829e-01 1.023568e-01 9.046727e-04
## 88 3.120681e-01 5.470709e-01 1.355055e-01 5.355556e-03
## 89 3.032379e-02 3.017123e-01 5.323828e-01 1.355811e-01
## 90 4.330787e-02 9.523411e-01 4.308269e-03 4.274416e-05
## 91 5.506021e-02 8.868405e-01 6.311564e-03 5.178769e-02
## 92 9.446604e-01 1.504234e-03 1.015833e-03 5.281956e-02
## 93 1.002241e-01 8.645554e-01 3.518273e-02 3.774200e-05
## 94 3.108397e-02 9.661717e-01 2.653527e-03 9.076054e-05
## 95 9.864922e-02 8.673937e-01 2.029333e-02 1.366375e-02
## 96 7.540386e-02 2.965881e-01 1.502826e-01 4.777254e-01
## 97 2.142720e-01 6.122323e-01 1.008348e-01 7.266088e-02
## 98 7.718989e-01 5.572946e-02 1.714552e-01 9.164701e-04
## 99 7.534247e-02 8.959985e-01 1.362912e-02 1.502994e-02
## 100 1.510282e-01 8.217536e-01 1.934358e-02 7.874535e-03
## 101 6.576882e-01 1.464500e-01 1.953930e-01 4.688547e-04
## 102 6.348502e-01 2.312787e-01 1.330936e-01 7.774957e-04
## 103 9.309818e-01 6.046551e-02 7.882131e-03 6.705488e-04
## 104 9.608218e-01 1.022806e-03 1.240376e-02 2.575161e-02
## 105 9.346725e-01 2.332217e-02 4.193416e-02 7.116659e-05
## 106 8.843819e-01 7.481817e-02 3.959954e-02 1.200400e-03
## 107 3.778803e-02 6.840153e-01 2.732251e-01 4.971551e-03
## 108 8.896069e-01 2.961119e-02 7.127311e-02 9.508809e-03
## 109 8.575580e-01 1.077902e-01 3.305796e-02 1.593835e-03
## 110 5.695564e-01 4.115901e-01 1.762760e-02 1.225887e-03
## 111 7.647242e-01 1.972084e-01 3.328672e-02 4.780668e-03
## 112 9.339097e-01 6.465768e-02 1.954695e-04 1.237144e-03
## 113 9.471838e-01 4.690981e-02 1.851388e-04 5.721225e-03
## 114 4.833376e-01 4.111848e-01 1.024848e-01 2.992814e-03
## 115 6.273744e-01 5.697216e-02 2.935210e-01 2.213241e-02
## 116 7.371151e-01 1.333235e-01 1.188293e-01 1.073202e-02
## 117 9.597199e-01 2.896412e-02 6.210597e-04 1.069490e-02
## 118 4.704046e-01 5.222982e-01 1.306734e-03 5.990483e-03
## 119 9.566234e-01 2.759385e-05 4.317082e-02 1.782216e-04
## 120 3.482637e-01 6.352021e-01 1.560780e-02 9.264325e-04
## 121 8.198686e-01 1.636762e-01 1.088557e-02 5.569591e-03
## 122 4.855240e-01 1.659527e-01 3.481322e-01 3.910668e-04
## 123 9.010088e-01 1.836048e-02 7.889070e-02 1.739973e-03
## 124 8.759355e-01 1.143969e-01 1.452106e-05 9.653019e-03
## 125 7.207085e-01 2.561509e-01 2.219381e-02 9.468142e-04
## 126 7.549599e-01 2.007516e-01 3.486555e-02 9.423009e-03
## 127 9.123146e-01 6.613785e-02 1.115483e-02 1.039271e-02
## 128 8.980987e-01 3.567452e-03 9.826930e-02 6.453402e-05
## 129 9.669461e-01 1.061345e-02 2.214823e-02 2.921952e-04
## 130 7.993811e-01 7.276930e-02 1.178714e-01 9.978173e-03
## 131 9.085510e-01 1.029352e-02 8.110630e-02 4.918700e-05
## 132 4.250633e-01 5.518683e-01 1.948351e-02 3.584933e-03
## 133 9.539992e-01 8.765525e-03 3.448514e-02 2.750088e-03
## 134 8.895068e-01 6.148505e-02 2.412575e-02 2.488245e-02
## 135 6.098699e-01 2.776295e-01 1.144455e-02 1.010561e-01
## 136 8.752553e-01 8.202807e-02 3.293444e-02 9.782154e-03
## 137 5.494001e-01 2.524935e-01 1.978260e-01 2.803340e-04
## 138 8.755744e-01 8.620357e-02 1.580425e-02 2.241773e-02
## 139 8.308982e-01 2.881718e-04 1.687869e-01 2.665801e-05
## 140 8.737961e-01 1.164569e-01 4.090771e-05 9.706116e-03
## 141 8.672096e-01 8.050645e-02 3.919390e-02 1.309003e-02
## 142 8.353172e-01 1.098228e-01 3.907659e-03 5.095232e-02
## 143 6.348502e-01 2.312787e-01 1.330936e-01 7.774957e-04
## 144 8.273394e-01 1.495359e-01 2.271900e-02 4.057095e-04
## 145 7.208004e-01 1.987242e-01 7.220417e-02 8.271249e-03
## 146 9.050786e-01 3.873603e-02 1.698940e-02 3.919601e-02
## 147 7.415355e-01 2.435666e-01 2.106691e-04 1.468722e-02
## 148 9.510633e-01 2.975647e-02 1.334317e-02 5.837082e-03
## 149 4.986771e-01 2.706036e-01 2.305387e-01 1.806536e-04
## 150 7.508462e-01 4.816803e-04 2.270347e-01 2.163745e-02#podemos ver melhor as explicações por plot de correlação
library(corrplot) #pacote para comparar modelos
corrplot(res.var$cos2, is.corr=FALSE) #checa a qualidade de representação
##ou mesmo de barra, # inves do cosseno pode usar a contribuição, ou outro aspecto, depende do interesse
fviz_contrib(pca_t1, choice = c("var"), axes= 1) #podemos ver melhor as explicações por plot de correlação
#contribuições abaixo e acima da linha, mais (acima) ou menos significante#Gráfico montrando a proporção da variância de cada variável - vamos ver a distribui��o das dimens�es em termos de explica��o da variancia
fviz_eig(pca_t1, addlabels = T)
#Quando os valores estão mais regulares quer dizer que os valores não "funcionaram" para o plot da pca (?)
#Extrair os resultados das variaveis do PCA - agora vamos iniciar primeiro plotando as medidas dos individuos
fviz_pca_ind(pca_t1)
fviz_pca_ind(pca_t1)+
labs(title = "PCA", x = "PC1 (73%)", y = "PC2 (23%)") + #dar nomes
xlim(-4,4) + ylim(-4,4) #mudar escala manual
#adicionando contribui��o dos individuos
fviz_pca_ind(pca_t1, geom = "point", col.ind = "cos2")+ #"cos2", contrib
labs(title = "PCA", x = "PC1(73%)", y = "PC2(23%)")+ #dar nomes aos bois
xlim(-4,4) + ylim(-4,4) +
scale_color_gradient2(low="gold", mid="red", #escalas importancia manual
high="blue", midpoint=0.6)
#Quando os valores estão mais regulares quer dizer que os valores não "funcionaram" para o plot da pca (?)#Extrair os resultados das variaveis do PCA - agora vamos iniciar primeiro plotando as medidas dos individuos
fviz_pca_ind(pca_t1)
fviz_pca_ind(pca_t1)+
labs(title = "PCA", x = "PC1 (73%)", y = "PC2 (23%)")+ #dar nomes aos bois
xlim(-4,4) + ylim(-4,4) #mudar escala manual
#adicionando contribui��o dos individuos
fviz_pca_ind(pca_t1, geom = "point", col.ind = "cos2")+ #"cos2", contrib
labs(title = "PCA", x = "PC1(73%)", y = "PC2(23%)")+ #dar nomes aos bois
xlim(-4,4) + ylim(-4,4) + #mudar escala grafico manual
scale_color_gradient2(low="gold", mid="red", #escalas importancia manual
high="blue", midpoint=0.6)
#Os valores que mais contribuem são os extremos
#adicionando as elipses
fviz_pca_ind(pca_t1, geom = "point", habillage = iris$Species,
addEllipses=TRUE, ellipse.level=0.95)+
labs(title = "PCA", x = "PC1(73%)", y = "PC2(23%)")+ #dar nomes aos bois
xlim(-4,4) + ylim(-4,4) + theme_minimal() #mudar escala grafico manual
#selecionando alguns de acordo com criterios ou individual
fviz_pca_ind(pca_t1, geom = "point", habillage = iris$Species,
addEllipses=TRUE, ellipse.level=0.95,
select.ind = list(cos2 = 0.95))+ #criterios de sele��o
labs(title = "PCA", x = "PC1(73%)", y = "PC2(23%)")+ #dar nomes aos bois
xlim(-4,4) + ylim(-4,4) + theme_minimal() #mudar escala grafico manual
#Selecionar quais são os individuos que se deja plotar
fviz_pca_ind(pca_t1, geom = "point", habillage = iris$Species, #ind(linhas)
addEllipses=TRUE, ellipse.level=0.95,
select.ind = list(name = c("1", "15", "74")))+ #selecionar individual
labs(title = "PCA", x = "PC1(73%)", y = "PC2(23%)")+ #dar nomes aos bois
xlim(-4,4) + ylim(-4,4) + theme_minimal() #mudar escala grafico manual
#Extrair os resultados das variaveis do PCA - agora vamos de graficos para as vari�veis
fviz_pca_var(pca_t1, col.var = "cornflowerblue") #setas que mostram onde cada variavel está mais distribuida (circulo 3) - gráfico de PCA
fviz_pca_var(pca_t1, col.var="cos2")+
scale_color_gradient2(low="gold", mid="red",
high="blue", midpoint=0.955) 
fviz_pca_var(pca_t1, select.var = list(contrib = 4))
fviz_pca_var(pca_t1, select.var = list(names = c("Sepal.Width"))) #plotar só a variável que você quer
#sepal width que está separado apresenta uma explicação melhor
#repel = não sobrepor informaões
#agora vamos fazer um grafico juntando ambos acima
pca_t = fviz_pca_biplot(pca_t1,
# Individuals
geom.ind = "point",
pointshape = 21,
fill.ind = iris$Species,
col.ind = "black",
pointsize = 3,
addEllipses = T,
ellipse.level=0.95,
# Variables
col.var = "contrib",
legend.title = list(fill = "Espécies de Plantas",
color = "Contr(metrics)"),
ggtheme = theme_classic(base_size=15),
label = "all",
palette = "Set1",
title = "",
repel = T)+
scale_color_gradient2(low = "gold",mid = "red",
high="blue", midpoint = 25)+
labs(x = "PC1(73%)", y = "PC2(23%)")
pca_t
#Quais dimensões serão utilizadas para fazer uma análise de variância?
#usar as dimensoes da pca como vari�vel explicativa
# usar significancia do autovalor das dimensoes#install.packages("BiodiversityR")
library(BiodiversityR)
#eixo 2 não é diferente do nulo - aconselhavel não usar
#devtools::install_github("arleyc/PCAtest", force= TRUE)
library(PCAtest)
result = PCAtest(iris[,1:4], nperm = 999, nboot = 999, alpha = 0.05,
varcorr=T, counter=F, indload = T, plot=T)##
## Sampling bootstrap replicates... Please wait
##
## Calculating confidence intervals of empirical statistics... Please wait
##
## Sampling random permutations... Please wait
##
## Comparing empirical statistics with their null distributions... Please wait
##
## ========================================================
## Test of PCA significance: 4 variables, 150 observations
## 999 bootstrap replicates, 999 random permutations
## ========================================================
##
## Empirical Psi = 5.3750, Max null Psi = 0.2747, Min null Psi = 0.0033, p-value = 0
## Empirical Phi = 0.6693, Max null Phi = 0.1513, Min null Phi = 0.0166, p-value = 0
##
## Empirical eigenvalue #1 = 2.9185, Max null eigenvalue = 1.41874, p-value = 0
## Empirical eigenvalue #2 = 0.91403, Max null eigenvalue = 1.22853, p-value = 1
## Empirical eigenvalue #3 = 0.14676, Max null eigenvalue = 1.03718, p-value = 1
## Empirical eigenvalue #4 = 0.02071, Max null eigenvalue = 0.9593, p-value = 1
##
## PC 1 is significant and accounts for 73% (95%-CI:70.1-76.4) of the total variation
##
## Variables 1, 3, and 4 have significant loadings on PC 1
##
## Variables 1, 3, and 4 have significant correlations with PC 1
#vamos usar a dimensão 1 (PC1) em uma anova
pca_t1## Standard deviations (1, .., p=4):
## [1] 1.7083611 0.9560494 0.3830886 0.1439265
##
## Rotation (n x k) = (4 x 4):
## PC1 PC2 PC3 PC4
## Sepal.Length 0.5210659 -0.37741762 0.7195664 0.2612863
## Sepal.Width -0.2693474 -0.92329566 -0.2443818 -0.1235096
## Petal.Length 0.5804131 -0.02449161 -0.1421264 -0.8014492
## Petal.Width 0.5648565 -0.06694199 -0.6342727 0.5235971m1 = aov(pca_t1$x[,1]~iris$Species)
summary(m1)## Df Sum Sq Mean Sq F value Pr(>F)
## iris$Species 2 406.4 203.21 1051 <2e-16 ***
## Residuals 147 28.4 0.19
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1#outro pacote para plotar
library(ggfortify)
library(ggthemes)library(EnvStats)
t = autoplot(pca_t1, data=iris, colour = "Species", label = F, scale = T,
label.size = 2, loadings = T, loadings.label = T, #size = "IVG",
frame.type = "norm",# shape = "trat",
loadings.colour = 'black',
loadings.label.colour = "black", loadings.label.size = 4)
t=t+theme_classic()+labs(tags = "A")+
scale_color_brewer(palette = "Dark2", aesthetics = "colour")
t
library(RColorBrewer)
mycolor = brewer.pal(3, "Dark2")
a = autoplot(pca_t1, data=iris, colour = "Species", label = F, scale = T,
label.size = 2, loadings = T, loadings.label = T, #size = "plantula",
frame.type = "norm", loadings.colour = 'black',#shape = "trat",
loadings.label.colour = "black", loadings.label.size = 4)
a=a+theme_classic()+
scale_color_brewer(palette = "Set1", aesthetics = "colour")
a
- A PCA é direcionado para conjunto de dados de mais de 3 dimensões;
- O conjunto de dados deve ser númerico ou transformado para tal.
- Número de eixo é igual ao numero de variaveis, porém são utilizados os dois primeiros eixos que representam melhor as explicações das variáveis
Enggel Carmo
Engenheira Agrônoma e Mestre em Entomologia (UFRPE)
Estudante de Doutorado em Entomologia (UFLA)
Sou um leão do Norte.