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

In R programming, a matrix can be scaled and centered 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.

R

# 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)

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.

R

# 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)

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