fiabilidad PCA

Iniciamos el proceso de PCA convirtiendo nuestras filas en rowindex by names, esto nos permitira analizar mas adelante la tendencia de la PCA

names(USArrests )

[1] "Murder"   "Assault"  "UrbanPop" "Rape"    

Aplicaremos la funcion mean,var

apply(USArrests , 2, var)

    Murder    Assault   UrbanPop       Rape 
  18.97047 6945.16571  209.51878   87.72916 

construimos el PCA basado en USArrests

 pr.out$scale

   Murder   Assault  UrbanPop      Rape 
 4.355510 83.337661 14.474763  9.366385 

la matriz rotation describe los eigen vectores

pr.out$rotation

                PC1        PC2        PC3         PC4
Murder   -0.5358995  0.4181809 -0.3412327  0.64922780
Assault  -0.5831836  0.1879856 -0.2681484 -0.74340748
UrbanPop -0.2781909 -0.8728062 -0.3780158  0.13387773
Rape     -0.5434321 -0.1673186  0.8177779  0.08902432

biplot (pr.out , scale =0)

pr.out$rotation=-pr.out$rotation
 pr.out$x=-pr.out$x
 biplot (pr.out , scale =0)

lo que podemos observar en la sdev es como cada eigen vector dispersa la data

pr.out$sdev

[1] 1.5748783 0.9948694 0.5971291 0.4164494

pr.var=pr.out$sdev ^2
pr.var

[1] 2.4802416 0.9897652 0.3565632 0.1734301

pve=pr.var/sum(pr.var)
 pve 

[1] 0.62006039 0.24744129 0.08914080 0.04335752

plot(pve,xlab="Principal Component",ylab="Proportion of Variance Explained", ylim=c(0,1) )

plot(cumsum(pve), xlab="Principal Component", ylab="Cumulative Proportion of Variance Explained", ylim=c(0,1))

la funcion de suma acumulada muestra PVE de los elmentos del vector

plot(pve , xlab=" Principal Component ", ylab="Proportion of Variance Explained ", ylim=c(0,1))

plot(cumsum(pve), xlab="Principal Component ", ylab="Cumulative Proportion of Variance Explained ", ylim=c(0,1))

a=c(1,2,8,-3)
cumsum(a)

[1]  1  3 11  8

summary(pr.out)

Importance of components:
                          PC1    PC2     PC3     PC4
Standard deviation     1.5749 0.9949 0.59713 0.41645
Proportion of Variance 0.6201 0.2474 0.08914 0.04336
Cumulative Proportion  0.6201 0.8675 0.95664 1.00000