R principal comp

usaremos mtcars para calcular los mpegs con principal component analisis veremos los eigen valos a los que corresponde el analisis

glimpse(mtcars)

Observations: 32
Variables: 11
$ mpg  <dbl> 21.0, 21.0, 22.8, 21.4, 18.7, 18.1, 14.3, 24.4, 22.8, 19.2, 17.8, 16.4, 17.3, 15.2, 10.4, 10.4, 14.7, 32.4, 30.4, 33.9, 21.5, 15.5, 15.2...
$ cyl  <dbl> 6, 6, 4, 6, 8, 6, 8, 4, 4, 6, 6, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 8, 8, 8, 8, 4, 4, 4, 8, 6, 8, 4
$ disp <dbl> 160.0, 160.0, 108.0, 258.0, 360.0, 225.0, 360.0, 146.7, 140.8, 167.6, 167.6, 275.8, 275.8, 275.8, 472.0, 460.0, 440.0, 78.7, 75.7, 71.1,...
$ hp   <dbl> 110, 110, 93, 110, 175, 105, 245, 62, 95, 123, 123, 180, 180, 180, 205, 215, 230, 66, 52, 65, 97, 150, 150, 245, 175, 66, 91, 113, 264, ...
$ drat <dbl> 3.90, 3.90, 3.85, 3.08, 3.15, 2.76, 3.21, 3.69, 3.92, 3.92, 3.92, 3.07, 3.07, 3.07, 2.93, 3.00, 3.23, 4.08, 4.93, 4.22, 3.70, 2.76, 3.15...
$ wt   <dbl> 2.620, 2.875, 2.320, 3.215, 3.440, 3.460, 3.570, 3.190, 3.150, 3.440, 3.440, 4.070, 3.730, 3.780, 5.250, 5.424, 5.345, 2.200, 1.615, 1.8...
$ qsec <dbl> 16.46, 17.02, 18.61, 19.44, 17.02, 20.22, 15.84, 20.00, 22.90, 18.30, 18.90, 17.40, 17.60, 18.00, 17.98, 17.82, 17.42, 19.47, 18.52, 19....
$ vs   <dbl> 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1
$ am   <dbl> 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1
$ gear <dbl> 4, 4, 4, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 4
$ carb <dbl> 4, 4, 1, 1, 2, 1, 4, 2, 2, 4, 4, 3, 3, 3, 4, 4, 4, 1, 2, 1, 1, 2, 2, 4, 2, 1, 2, 2, 4, 6, 8, 2

nos quedamos unicamente con los valores menos con la variable que deseamos predecir

glimpse(mtproy)

Observations: 32
Variables: 10
$ cyl  <dbl> 6, 6, 4, 6, 8, 6, 8, 4, 4, 6, 6, 8, 8, 8, 8, 8, 8, 4, 4, 4, 4, 8, 8, 8, 8, 4, 4, 4, 8, 6, 8, 4
$ disp <dbl> 160.0, 160.0, 108.0, 258.0, 360.0, 225.0, 360.0, 146.7, 140.8, 167.6, 167.6, 275.8, 275.8, 275.8, 472.0, 460.0, 440.0, 78.7, 75.7, 71.1,...
$ hp   <dbl> 110, 110, 93, 110, 175, 105, 245, 62, 95, 123, 123, 180, 180, 180, 205, 215, 230, 66, 52, 65, 97, 150, 150, 245, 175, 66, 91, 113, 264, ...
$ drat <dbl> 3.90, 3.90, 3.85, 3.08, 3.15, 2.76, 3.21, 3.69, 3.92, 3.92, 3.92, 3.07, 3.07, 3.07, 2.93, 3.00, 3.23, 4.08, 4.93, 4.22, 3.70, 2.76, 3.15...
$ wt   <dbl> 2.620, 2.875, 2.320, 3.215, 3.440, 3.460, 3.570, 3.190, 3.150, 3.440, 3.440, 4.070, 3.730, 3.780, 5.250, 5.424, 5.345, 2.200, 1.615, 1.8...
$ qsec <dbl> 16.46, 17.02, 18.61, 19.44, 17.02, 20.22, 15.84, 20.00, 22.90, 18.30, 18.90, 17.40, 17.60, 18.00, 17.98, 17.82, 17.42, 19.47, 18.52, 19....
$ vs   <dbl> 0, 0, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1
$ am   <dbl> 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1
$ gear <dbl> 4, 4, 4, 3, 3, 3, 3, 4, 4, 4, 4, 3, 3, 3, 3, 3, 3, 4, 4, 4, 3, 3, 3, 3, 3, 4, 5, 5, 5, 5, 5, 4
$ carb <dbl> 4, 4, 1, 1, 2, 1, 4, 2, 2, 4, 4, 3, 3, 3, 4, 4, 4, 1, 2, 1, 1, 2, 2, 4, 2, 1, 2, 2, 4, 6, 8, 2

armamos nuestro pca

summary(res.pca)

Importance of components:
                         PC1   PC2     PC3     PC4     PC5     PC6     PC7     PC8     PC9    PC10
Standard deviation     2.400 1.628 0.77280 0.51914 0.47143 0.45839 0.36458 0.28405 0.23163 0.15426
Proportion of Variance 0.576 0.265 0.05972 0.02695 0.02223 0.02101 0.01329 0.00807 0.00537 0.00238
Cumulative Proportion  0.576 0.841 0.90071 0.92766 0.94988 0.97089 0.98419 0.99226 0.99762 1.00000

vemos la matriz de pca por cada dimension y lo que notamos como valores son los factores de la combinacion lineal de cada componente principal

res.pca

Standard deviations (1, .., p=10):
 [1] 2.4000453 1.6277725 0.7727968 0.5191403 0.4714341 0.4583857 0.3645821 0.2840450 0.2316298 0.1542606

Rotation (n x k) = (10 x 10):
            PC1         PC2         PC3           PC4         PC5         PC6         PC7         PC8          PC9          PC10
cyl   0.4029711 -0.03901479  0.13874360 -8.040022e-05  0.06148048 -0.18206407 -0.04257067  0.07041306 -0.863268748  0.1670687388
disp  0.3959243  0.05393117  0.01633491 -2.646304e-01  0.33851109  0.35738419  0.19767431 -0.14361684 -0.020039738 -0.6838300858
hp    0.3543255 -0.24496137 -0.18225874  6.000387e-02  0.52828704 -0.03269674 -0.08503414  0.58708325  0.291428365  0.2462606844
drat -0.3155948 -0.27847781 -0.13057734 -8.528509e-01  0.10299748 -0.23386885  0.03226657  0.04010725 -0.086765162  0.0544414772
wt    0.3668004  0.14675805 -0.38579961 -2.527210e-01 -0.14410292  0.43201764 -0.03368560 -0.36605124  0.075971836  0.5318885631
qsec -0.2198982  0.46066271 -0.40307004 -7.174202e-02 -0.21341845  0.29265169 -0.03797611  0.59621869 -0.244573292 -0.1545795278
vs   -0.3333571  0.22751987 -0.41252247  2.119502e-01  0.62369179 -0.11710663 -0.23387904 -0.36246041 -0.182200371 -0.0055443849
am   -0.2474991 -0.43201042  0.23493804  3.190779e-02  0.04930286  0.60874338 -0.54631997  0.02588771 -0.154149509 -0.0003995261
gear -0.2214375 -0.46516217 -0.27929375  2.623809e-01  0.02039816  0.24560902  0.69429321 -0.01069942 -0.198369367  0.0741152014
carb  0.2267080 -0.41169300 -0.56172255  1.233534e-01 -0.36576403 -0.25782743 -0.33623769 -0.08067483  0.003086198 -0.3585136181

visualizamos el aporte de la variavilidad por cada pc como podemos ver en el punto del pc4 llegamos al de mas aporte

graficaremos el conjunto de vectores de las principal componentes en una elipse

projectamos nuestros vectores en un circulo para las variables

fviz_pca_ind(res.pca, geom.ind = "point", pointshape = 21, 
             pointsize = 1, 
             fill.ind = as.factor(decathlon2$Competition[1:23]), 
             col.ind = "black", 
             palette = "jco", 
             addEllipses = TRUE,
             label = "var",
             col.var = "black",
             repel = TRUE,
             legend.title = "Diagnosis") +
     ggtitle("2D PCA-plot from 30 feature dataset") +
     theme(plot.title = element_text(hjust = 0.5))

Error in fviz(X, element = "ind", axes = axes, geom = geom.ind, habillage = habillage,  : 
  The length of fill variableshould be the same as the number of rows in the data.