How do i denormalize the data after i have used the "normalize" function?

Hi,

I have normalized my data using the formula given and now i need to renormalize it to the original version, not (0,1) or (-1,1). What function do i use? Pls help! i couldnt find a "denormalize" function anywhere!

%Data needs to be normalized
inputs = normalize(inputs);
targets = normalize(targets);
inputs2020 = normalize(inputs2020);
targets2020 = normalize(targets2020);

[Star Strider]

If you used the default 'zscore', you would have to have saved the mean and standard deviation (std) of your data first in order to ‘denormalise’ it. If you did not do that, likely all hope is lost.

It is always appropriate to save all the original data so reversing a potentially irreversible process is not necessary.

[CLHE]

i have the original files with me and can find the mean and standard deviation of the data. What should i do next?

[Star Strider]

Then do not bother with the denormalisation and just use the original data.

[CLHE]

Sorry, am a beginner here. I am currently trying to code the ANN for my data and my lecturer mentioned to use the normalization function in the coding for the report, and then denormalize it again after the training for neural network is done. I have 1 input and 1 output, but the values are very different from each other. If i dont normalize it, will this impact the results?

[dpb]

If z=(x-mu)/s, then x=z*s+mu

It can make quite a bit of difference in the result if do not standardize inputs if they (the inputs) are of markedly differing amplitudes. As the "More About" section of thd documenation for normalize says, using it scales the data to a zero mean and variance of 1 for all variables, retaining shape. This can aid quite a lot in numerical calculations where otherwise differences can become insiginficant of one variable to another or apparent importance owing to magnitude alone.

It would seem to have been a convenience for the user if normalize had also the ability to return the needed parameters when called as optional additional outputs or if rescale had the option to convert back from z-scores besides just the linear scaling it does.

I'd never used either; it's so trivial an operation always just code it inline so had to go look up what each actually did as implemented...

[Star Strider]

@CLHE —

The neural network information is new. To denormalise the results of the neural network, multiply them by the standard deviation and then add the mean.

[dpb]

Isn't the output rescaled back to the same units as the original? I've not used the ML NN models/don't have the TB so not sure how they actually work in that regards...

Answer 1

[John D'Errico]

You can't. Well, you can, but only if you do what you need in advance.

X = 1:5
X =
     1     2     3     4     5
     
normalize(X)
ans =
      -1.2649     -0.63246            0      0.63246       1.2649
      
normalize(2*X)
ans =
      -1.2649     -0.63246            0      0.63246       1.2649

Can you see that normaize produces exactly the same result for both X and 2*X? If so, then you must surely understand that merely from the normalized data, you can never recover the original data.

You absolutely need to save the transformation parameters for how the data was normalized. Otherwise, denormalization is impossible.

However, if we store the normalization parameters, then recovery is possible.

mu = mean(X);
S = std(X);
Xnorm = (X - mu)/S
Xnorm =
      -1.2649     -0.63246            0      0.63246       1.2649

Xnorm*S + mu
ans =
     1     2     3     4     5

As you see, Xnorm is the same thing as what normalize produced, but now we can recover X from Xnorm.

[CLHE]

ok, i think ive got it,thanks!