How to revert back scalling of data in R? - r

Question

I had a data set with data like this:
value
[1,] 41601325
[2,] 54917632
[3,] 64616616
[4,] 90791277
[5,] 35335221
[6,] .
. .
. .
which I had to scale down to range [0,1] using
apply(data1, MARGIN = 2, FUN = function(X) (X - min(X))/diff(range(X)))
as I needed to fit the data in GP_fit() of GPfit package. The scaled down values became say:
value
[1,] .4535
[2,] .56355
[3,] .64616
[4,] .70791
[5,] .35563
[6,] .
. .
. .
After I applied GP_fit() on the scaled data and used predict() and as output I got the new values which again are in range[0,1] like:
value
[1,] .0135
[2,] .234355
[3,] .6716
[4,] .325079
[5,] .95563
[6,] .
. .
. .
but I want to take these back to the original range. How can I do that?
Basically I want to revert back/ return to original format for showing the output of predict()
NOTE: The original range is not fixed and can vary but normally the maximum value possible is about 20 million .
UPDATE: I tired to implement the code written by #JustinFletcher. My data was :
value
[1,] 54.2
[2,] 53.8
[3,] 53.9
[4,] 53.8
[5,] 54.9
[6,] 55.0
[7,] 38.5
[8,] 38.0
[9,] 38.1
[10,] 38.0
[11,] 38.8
[12,] 38.9
[13,] 24.3
[14,] 24.1
[15,] 24.3
[16,] 24.1
[17,] 24.4
[18,] 24.4
[19,] 57.3
[20,] 57.2
[21,] 57.6
[22,] 57.7
[23,] 58.1
[24,] 57.9
I wrote this to rescale it in range [0,1]:
data_new <- apply(data_test, MARGIN = 2, FUN = function(X) (X - min(X))/diff(range(X)))
and I got
value
[1,] 0.885294118
[2,] 0.873529412
[3,] 0.876470588
[4,] 0.873529412
[5,] 0.905882353
[6,] 0.908823529
[7,] 0.423529412
[8,] 0.408823529
[9,] 0.411764706
[10,] 0.408823529
[11,] 0.432352941
[12,] 0.435294118
[13,] 0.005882353
[14,] 0.000000000
[15,] 0.005882353
[16,] 0.000000000
[17,] 0.008823529
[18,] 0.008823529
[19,] 0.976470588
[20,] 0.973529412
[21,] 0.985294118
[22,] 0.988235294
[23,] 1.000000000
[24,] 0.994117647
then to revert it back to original scale I wrote this:
data_revert <- apply(data_new, MARGIN = 2, FUN = function(X, Y) (X + min(Y))*diff(range(Y)), Y=data_test)
and I got
value
[1,] 849.5
[2,] 849.1
[3,] 849.2
[4,] 849.1
[5,] 850.2
[6,] 850.3
[7,] 833.8
[8,] 833.3
[9,] 833.4
[10,] 833.3
[11,] 834.1
[12,] 834.2
[13,] 819.6
[14,] 819.4
[15,] 819.6
[16,] 819.4
[17,] 819.7
[18,] 819.7
[19,] 852.6
[20,] 852.5
[21,] 852.9
[22,] 853.0
[23,] 853.4
[24,] 853.2
This output is not correct.

Answer 1

This is simple algebra. To scale data, you calculate
n = (e - e_min)/(e_max - e_min)
Now you need back e, based on arbitrary e_min and e_max. It is trivial to show that
n(e_max - e_min) + e_min = e
Example:
e <- 1:10
n <- (e - min(e))/(max(e) - min(e))
new.e <- (n*(10-1)) + 1
> all(e == new.e)
[1] TRUE

Answer 2

You just need to apply the inverse of the function FUN to the output data. This requires the original data be passed to the function.
apply(dataOutput, MARGIN = 2, FUN = function(X, Y) (X + min(Y))*diff(range(Y)), Y=data1)
For a great description of the 'apply' function, see here.
P.S.: Romans response is exactly the same idea, I just implemented it with your variables, using apply, because I thought it was interesting.