Transform the Scaled Matrix to its Original Form in R Programming – Using Matrix Computations

In R programming, a matrix can be scaled and centred using scale() function. But, there is no in-built function to transform the scaled matrix back to the original matrix. In this article, we’ll learn to transform the scaled matrix back to the original matrix using some simple computations.

Using Matrix Attributes

Attributes of the scaled matrix can be used to unscale the matrix back to its original matrix.

filter_none

edit
close

play_arrow

link
brightness_4
code

# Create matrix
mt <- matrix(c(1:20), ncol = 5)
  
# Print original matrix
cat("Original matrix:\n")
print(mt)
  
# Scale the matrix
scaled.mt <- scale(mt)
  
# Print Scaled matrix
cat("Scaled matrix:\n")
print(scaled.mt)
  
# Unscale the matrix
unscaled.mt <- t(apply(scaled.mt, 1, 
                function(r) r * attr(scaled.mt, 'scaled:scale') + 
                                attr(scaled.mt, 'scaled:center')))
  
# Print Unscaled matrix
cat("Unscaled matrix:\n")
print(unscaled.mt)

chevron_right


Output:

Original matrix:
     [, 1] [, 2] [, 3] [, 4] [, 5]
[1, ]    1    5    9   13   17
[2, ]    2    6   10   14   18
[3, ]    3    7   11   15   19
[4, ]    4    8   12   16   20
Scaled matrix:
           [, 1]       [, 2]       [, 3]       [, 4]       [, 5]
[1, ] -1.1618950 -1.1618950 -1.1618950 -1.1618950 -1.1618950
[2, ] -0.3872983 -0.3872983 -0.3872983 -0.3872983 -0.3872983
[3, ]  0.3872983  0.3872983  0.3872983  0.3872983  0.3872983
[4, ]  1.1618950  1.1618950  1.1618950  1.1618950  1.1618950
attr(, "scaled:center")
[1]  2.5  6.5 10.5 14.5 18.5
attr(, "scaled:scale")
[1] 1.290994 1.290994 1.290994 1.290994 1.290994
Unscaled matrix:
     [, 1] [, 2] [, 3] [, 4] [, 5]
[1, ]    1    5    9   13   17
[2, ]    2    6   10   14   18
[3, ]    3    7   11   15   19
[4, ]    4    8   12   16   20

Using Mean and Standard Deviation

In this example, we’ll unscale the scaled matrix using mean and standard deviation of the original matrix.

filter_none

edit
close

play_arrow

link
brightness_4
code

# Create matrix
a <- rnorm(5, 5, 2)
b <- rnorm(5, 7, 5) 
  
mt <- cbind(a, b)
  
# get center and scaling values 
m <- apply(df, 2, mean)
s <- apply(df, 2, sd)
  
# Print original matrix
cat("Original matrix:\n")
print(mt)
  
# Scale the matrix
scaled.mt <- scale(mt, center = m, scale = s)
  
# Print Scaled matrix
cat("Scaled matrix:\n")
print(scaled.mt)
  
# Unscale the matrix
unscaled.mt <- t((t(scaled.mt) * s) + m)
  
# Print Unscaled matrix
cat("Unscaled matrix:\n")
print(unscaled.mt)

chevron_right


Output:

Original matrix:
            a          b
[1, ] 5.552301  1.9865159
[2, ] 3.936486 17.5327829
[3, ] 5.379720 15.0981877
[4, ] 3.546333  0.5230305
[5, ] 5.043194  2.0930855

Scaled matrix:
               a         b
[1, ]  0.01543556 -2.062174
[2, ] -0.69057233  5.252016
[3, ] -0.05997146  4.106591
[4, ] -0.86104456 -2.750713
[5, ] -0.20701146 -2.012036
attr(, "scaled:center")
       a        b 
5.516974 6.369655 
attr(, "scaled:scale")
       a        b 
2.288663 2.125494 

Unscaled matrix:
            a          b
[1, ] 5.552301  1.9865159
[2, ] 3.936486 17.5327829
[3, ] 5.379720 15.0981877
[4, ] 3.546333  0.5230305
[5, ] 5.043194  2.0930855
attr(, "scaled:center")
       a        b 
5.516974 6.369655 
attr(, "scaled:scale")
       a        b 
2.288663 2.125494 



My Personal Notes arrow_drop_up

Check out this Author's contributed articles.

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.


Article Tags :

Be the First to upvote.


Please write to us at contribute@geeksforgeeks.org to report any issue with the above content.