# Normalisation of an 'image' when pixel intensities are unbounded

I have a dataset from particle physics of 3D 'images' containing three spacial coordinates and one energy coordinate. I want to train a generative model for generation of a similar dataset. I am using GANs at the moment for this. An important pre-processing step for this is normalisation of the data between -1 and 1. If this was an image, I could have divided all the entries by 255 to achieve this since that's the maximum value that a pixel intensity can reach. However, in this case, there is no upper bound for the energy. I am not sure what to do in this case. Any suggestion is welcome.

• Just use the largest and smallest values observed in the data. – Sycorax Jun 24 '18 at 22:03
• To be clear, you mean divide everything by the largest intensity value in the entire image. Right? I did think of that but if you do so, then you model will never generate any intensity larger than that right? Also, the largest quantity is several order or magnitudes larger than the average value. Is it really wise to divide everything by such a large number? – ANANDA PADHMANABHAN S Jun 24 '18 at 22:08
• Note that dividing everything by the largest intensity would only enforce an upper bound at 1, but do nothing to enforce a particular lower bound. It seems that your stuck between trying to fit a square peg in to a round hole (rescaling everything to $[-1,1]$ so that you can use a GAN) or else you would need to use a model that is more flexible in the kind of data it can accommodate. But maybe re-scaling in this way isn't necessary -- someone could have written a paper on the topic. Or maybe you could try fitting the model and decide whether or not it's good enough. – Sycorax Jun 24 '18 at 22:11
• Conventional re-scaling to a bounded interval uses only max and the min. There's no reason you're restricted to these options. You could re-scale by transforming the ecdf. The ecdf for an absolutely continuous distribution is, by construction, uniform between 0 and 1. – Sycorax Jun 24 '18 at 23:37