Analyse en composante principale

Une analyse en composantes principales (ACP) est effectu?e en utilisant la fonction int?gr?e de R prcomp() et le jeu de donn?es iris:

data(iris)
head(iris)

  Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1          5.1         3.5          1.4         0.2  setosa
2          4.9         3.0          1.4         0.2  setosa
3          4.7         3.2          1.3         0.2  setosa
4          4.6         3.1          1.5         0.2  setosa
5          5.0         3.6          1.4         0.2  setosa
6          5.4         3.9          1.7         0.4  setosa

# La variable Species (index = 5) est supprim?e
# avant la PCA
res.pca <- prcomp(iris[, -5],  scale = TRUE)

Extraire les r?sultats pour les variables

var <- get_pca_var(res.pca)
var

Principal Component Analysis Results for variables
 ===================================================
  Name       Description                                    
1 "$coord"   "Coordinates for the variables"                
2 "$cor"     "Correlations between variables and dimensions"
3 "$cos2"    "Cos2 for the variables"                       
4 "$contrib" "contributions of the variables"               

# Coordonn?es des variables
head(var$coord)

                  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  0.07535950

# Cos2 des variables
head(var$cos2)

                 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

# Contribution des variables
head(var$contrib)

                 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 27.415396

Extract the results for individuals

ind <- get_pca_ind(res.pca)
ind

Principal Component Analysis Results for individuals
 ===================================================
  Name       Description                       
1 "$coord"   "Coordinates for the individuals" 
2 "$cos2"    "Cos2 for the individuals"        
3 "$contrib" "contributions of the individuals"

# Coordonn?es des individus
head(ind$coord)

      Dim.1      Dim.2       Dim.3        Dim.4
1 -2.257141 -0.4784238  0.12727962  0.024087508
2 -2.074013  0.6718827  0.23382552  0.102662845
3 -2.356335  0.3407664 -0.04405390  0.028282305
4 -2.291707  0.5953999 -0.09098530 -0.065735340
5 -2.381863 -0.6446757 -0.01568565 -0.035802870
6 -2.068701 -1.4842053 -0.02687825  0.006586116

# Cos2 des individus
head(ind$cos2)

      Dim.1      Dim.2        Dim.3        Dim.4
1 0.9539975 0.04286032 0.0030335249 1.086460e-04
2 0.8927725 0.09369248 0.0113475382 2.187482e-03
3 0.9790410 0.02047578 0.0003422122 1.410446e-04
4 0.9346682 0.06308947 0.0014732682 7.690193e-04
5 0.9315095 0.06823959 0.0000403979 2.104697e-04
6 0.6600989 0.33978301 0.0001114335 6.690714e-06

# Contribution des individus
head(ind$contrib)

      Dim.1      Dim.2       Dim.3       Dim.4
1 1.1637691 0.16694510 0.073591567 0.018672867
2 0.9825900 0.32925696 0.248367113 0.339198420
3 1.2683043 0.08469576 0.008816151 0.025742863
4 1.1996857 0.25856249 0.037605617 0.139067312
5 1.2959338 0.30313118 0.001117674 0.041253702
6 0.9775628 1.60670454 0.003281801 0.001396002

get_pca

# Vous pouvez aussi utiliser la fonction get_pca()
get_pca(res.pca, "ind") # Resultats pour les individus

Principal Component Analysis Results for individuals
 ===================================================
  Name       Description                       
1 "$coord"   "Coordinates for the individuals" 
2 "$cos2"    "Cos2 for the individuals"        
3 "$contrib" "contributions of the individuals"

get_pca(res.pca, "var") # Resultats pour les variables

Principal Component Analysis Results for variables
 ===================================================
  Name       Description                                    
1 "$coord"   "Coordinates for the variables"                
2 "$cor"     "Correlations between variables and dimensions"
3 "$cos2"    "Cos2 for the variables"                       
4 "$contrib" "contributions of the variables"