Conflicting Results When Manually Calculating First Principal Component using prcomp












4















I am calculating the PCA for the iris dataset as follows:



data(iris)

ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)


This is the first row of the iris dataset:



head(iris, 1)

#Sepal.Length Sepal.Width Petal.Length Petal.Width Species

#1          5.1         3.5          1.4         0.2  setosa


For the first row, I can see that the value of the first principal component is -2.257141:



head(ir.pca$x, 1)

#           PC1        PC2       PC3        PC4

#[1,] -2.257141 -0.4784238 0.1272796 0.02408751


But when I try extract the loadings:



ir.pca$rotation[, 1]

Sepal.Length  Sepal.Width Petal.Length  Petal.Width 

0.5210659   -0.2693474    0.5804131    0.5648565


and calculate the first principal component myself:



0.5210659 * 5.1  + -0.2693474 * 3.5  + 0.5804131 * 1.4 + 0.5648565 * 0.2


I get a different result of 2.64027.



Why is that?






r pca predict







share|improve this question





























    4















    I am calculating the PCA for the iris dataset as follows:



    data(iris)
    
ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)


    This is the first row of the iris dataset:



    head(iris, 1)
    
#Sepal.Length Sepal.Width Petal.Length Petal.Width Species
    
#1          5.1         3.5          1.4         0.2  setosa


    For the first row, I can see that the value of the first principal component is -2.257141:



    head(ir.pca$x, 1)
    
#           PC1        PC2       PC3        PC4
    
#[1,] -2.257141 -0.4784238 0.1272796 0.02408751


    But when I try extract the loadings:



    ir.pca$rotation[, 1]
    
Sepal.Length  Sepal.Width Petal.Length  Petal.Width 
    
0.5210659   -0.2693474    0.5804131    0.5648565


    and calculate the first principal component myself:



    0.5210659 * 5.1  + -0.2693474 * 3.5  + 0.5804131 * 1.4 + 0.5648565 * 0.2


    I get a different result of 2.64027.



    Why is that?






    r pca predict







    share|improve this question



























      4












      4








      4


      0






      I am calculating the PCA for the iris dataset as follows:



      data(iris)
      
ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)


      This is the first row of the iris dataset:



      head(iris, 1)
      
#Sepal.Length Sepal.Width Petal.Length Petal.Width Species
      
#1          5.1         3.5          1.4         0.2  setosa


      For the first row, I can see that the value of the first principal component is -2.257141:



      head(ir.pca$x, 1)
      
#           PC1        PC2       PC3        PC4
      
#[1,] -2.257141 -0.4784238 0.1272796 0.02408751


      But when I try extract the loadings:



      ir.pca$rotation[, 1]
      
Sepal.Length  Sepal.Width Petal.Length  Petal.Width 
      
0.5210659   -0.2693474    0.5804131    0.5648565


      and calculate the first principal component myself:



      0.5210659 * 5.1  + -0.2693474 * 3.5  + 0.5804131 * 1.4 + 0.5648565 * 0.2


      I get a different result of 2.64027.



      Why is that?






      r pca predict







      share|improve this question
















      I am calculating the PCA for the iris dataset as follows:



      data(iris)
      
ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)


      This is the first row of the iris dataset:



      head(iris, 1)
      
#Sepal.Length Sepal.Width Petal.Length Petal.Width Species
      
#1          5.1         3.5          1.4         0.2  setosa


      For the first row, I can see that the value of the first principal component is -2.257141:



      head(ir.pca$x, 1)
      
#           PC1        PC2       PC3        PC4
      
#[1,] -2.257141 -0.4784238 0.1272796 0.02408751


      But when I try extract the loadings:



      ir.pca$rotation[, 1]
      
Sepal.Length  Sepal.Width Petal.Length  Petal.Width 
      
0.5210659   -0.2693474    0.5804131    0.5648565


      and calculate the first principal component myself:



      0.5210659 * 5.1  + -0.2693474 * 3.5  + 0.5804131 * 1.4 + 0.5648565 * 0.2


      I get a different result of 2.64027.



      Why is that?






      r pca predict




      r pca predict






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited Jan 3 at 14:22









      AkselA

      4,66921326




      4,66921326










      asked Jan 3 at 13:43









      orrymrorrymr

      532824




      532824
























          1 Answer
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          4














          Scaling is the issue.



          Either drop scaling in the prcomp() call



          data(iris)
          
ir.pca <- prcomp(iris[, 1:4], center = FALSE, scale. = FALSE)
          

          
head(ir.pca$x, 1)
          
           # PC1      PC2         PC3         PC4
          
# [1,] -5.912747 2.302033 0.007401536 0.003087706
          

          
ir.pca$rotation[, 1] %*% t(iris[1, 1:4])
          
             # 1
          
# [1,] -5.912747


          Or scale iris before you manually apply the loadings



          ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)
          

          
head(ir.pca$x, 1)
          
           # PC1        PC2       PC3        PC4
          
# [1,] -2.257141 -0.4784238 0.1272796 0.02408751
          

          
ir.pca$rotation[, 1] %*% scale(iris[, 1:4])[1,]
          
          # [,1]
          
# [1,] -2.257141





          share|improve this answer
























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            active

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            4














            Scaling is the issue.



            Either drop scaling in the prcomp() call



            data(iris)
            
ir.pca <- prcomp(iris[, 1:4], center = FALSE, scale. = FALSE)
            

            
head(ir.pca$x, 1)
            
           # PC1      PC2         PC3         PC4
            
# [1,] -5.912747 2.302033 0.007401536 0.003087706
            

            
ir.pca$rotation[, 1] %*% t(iris[1, 1:4])
            
             # 1
            
# [1,] -5.912747


            Or scale iris before you manually apply the loadings



            ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)
            

            
head(ir.pca$x, 1)
            
           # PC1        PC2       PC3        PC4
            
# [1,] -2.257141 -0.4784238 0.1272796 0.02408751
            

            
ir.pca$rotation[, 1] %*% scale(iris[, 1:4])[1,]
            
          # [,1]
            
# [1,] -2.257141





            share|improve this answer




























              4














              Scaling is the issue.



              Either drop scaling in the prcomp() call



              data(iris)
              
ir.pca <- prcomp(iris[, 1:4], center = FALSE, scale. = FALSE)
              

              
head(ir.pca$x, 1)
              
           # PC1      PC2         PC3         PC4
              
# [1,] -5.912747 2.302033 0.007401536 0.003087706
              

              
ir.pca$rotation[, 1] %*% t(iris[1, 1:4])
              
             # 1
              
# [1,] -5.912747


              Or scale iris before you manually apply the loadings



              ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)
              

              
head(ir.pca$x, 1)
              
           # PC1        PC2       PC3        PC4
              
# [1,] -2.257141 -0.4784238 0.1272796 0.02408751
              

              
ir.pca$rotation[, 1] %*% scale(iris[, 1:4])[1,]
              
          # [,1]
              
# [1,] -2.257141





              share|improve this answer


























                4












                4








                4







                Scaling is the issue.



                Either drop scaling in the prcomp() call



                data(iris)
                
ir.pca <- prcomp(iris[, 1:4], center = FALSE, scale. = FALSE)
                

                
head(ir.pca$x, 1)
                
           # PC1      PC2         PC3         PC4
                
# [1,] -5.912747 2.302033 0.007401536 0.003087706
                

                
ir.pca$rotation[, 1] %*% t(iris[1, 1:4])
                
             # 1
                
# [1,] -5.912747


                Or scale iris before you manually apply the loadings



                ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)
                

                
head(ir.pca$x, 1)
                
           # PC1        PC2       PC3        PC4
                
# [1,] -2.257141 -0.4784238 0.1272796 0.02408751
                

                
ir.pca$rotation[, 1] %*% scale(iris[, 1:4])[1,]
                
          # [,1]
                
# [1,] -2.257141





                share|improve this answer













                Scaling is the issue.



                Either drop scaling in the prcomp() call



                data(iris)
                
ir.pca <- prcomp(iris[, 1:4], center = FALSE, scale. = FALSE)
                

                
head(ir.pca$x, 1)
                
           # PC1      PC2         PC3         PC4
                
# [1,] -5.912747 2.302033 0.007401536 0.003087706
                

                
ir.pca$rotation[, 1] %*% t(iris[1, 1:4])
                
             # 1
                
# [1,] -5.912747


                Or scale iris before you manually apply the loadings



                ir.pca <- prcomp(iris[, 1:4], center = TRUE, scale. = TRUE)
                

                
head(ir.pca$x, 1)
                
           # PC1        PC2       PC3        PC4
                
# [1,] -2.257141 -0.4784238 0.1272796 0.02408751
                

                
ir.pca$rotation[, 1] %*% scale(iris[, 1:4])[1,]
                
          # [,1]
                
# [1,] -2.257141






                share|improve this answer












                share|improve this answer



                share|improve this answer










                answered Jan 3 at 14:17









                AkselAAkselA

                4,66921326




                4,66921326
































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