Sarah_devid asked . 2022-06-17

Standardisation (zero-mean, unit-variance)

Hi there, I am working with the neural network toolbox in matlab. My problem is not with the toolbox but with the data preparation before it is used and my resulting output. I standardise the input and targte output on which I train the network but this means that my estimated output, when I simulate the network on a new set of values has also a zero-mean, unit-vairance. I do not want this because while the estimated output correctly follows the trend and amplitude changes of my target output I want the physical values not these standardised values. Is there a way to 'de-standardise' my output i.e. add on the mean and multiply by the standard deviation. The mean of my time series is not constant so I am sure this is not as straightforward as I have said.

neural network , zero-mean , standardisation , data preparation , AI, Data Science, and Statistics ,

Expert Answer

John Michell answered . 2024-12-21 00:36:13

> I standardise the input and targte output on which I train the network but this means that my estimated >output, when I simulate the network on a new >set of values has also a zero-mean, unit-vairance.

In the best of all worlds!

Then you can use the mean and variance of the original output data to convert the new output to the correct location and scale.

A basic assumption of NN regression and classification models is that both design (train + val) and nondesign (test) data can be assumed to come from the same probability distribution.

If you expect that assumption might invalid for the new input data, you can always compare the summary statistics (e.g., mean, variance, correlations ...) of the new input data with that of the original input (design + test) data.

You can also compare the outputs when the new input data is normalized with it's own mean and variance vs using the mean and variance of the original data.

Are you using newfit(~newff) or fitnet(~feedforwardnet)?

Are your original standari"z"ations done with mapstd before creating the net or are you using net.input{i}.processFcn, (i = 1,2)?

>I do not want this because while the estimated output correctly follows the trend and amplitude >changes of my target output I want the physical values not these standardised values. Is there a way to >'de-standardise' my output i.e. add on the mean and multiply by the standard deviation. The mean of >my time series is not constant so I am sure this is not as straightforward as I have said.

This readily done using the 'reverse' option of mapstd. I don't remember if it is done automatically or you have to do it explicitly. See the documentation and examples of mapstd (or mapminmax,... the same principles apply).

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