1. ## Normalization

I have a variety of variables that might be part of an equation. A look at the graph of these variables shows that they all have roughly similar distributions, but some have a range of a few thousand to a few hundred thousand (6K - 200K), while others range from perhaps -5 to 5, while others are 33.X, where X ranges from 0.6 to 0.9.

In theory, for my purposes, these different ranges shouldn't matter all that much, but what I'm doing is highly speculative, so theory can be quite wrong. So, what I'm looking to do is shift them all such that they all have roughly the same range. A simple approach to that was to take the mean of the variable with the highest range (the one that varies from 6K to 200K), and multiply all the others by roughly that mean. It wasn't exactly that mean, as any that ranged from 10 to 30, might be multiplied by a tenth of that mean, while ones that were varying from 0 to 1 would be multiplied by the mean, but the idea was to exaggerate the variability in the variables with a smaller range.

What I'm looking for is alternate transformations that would retain the variability within each variable, but scale it up to the magnitude of the largest of the variables. Any suggestions?

2. ## Re: Normalization

Assuming you want a transformation of, for example, your -5 to 5 range into an "equivalent" 6000 to 200000 range, then the "worked out math" would be something like this:

-5*a+b=6000
5*a+b=200000
2*b=206000
b=103000
5*a+103000=200000
a=19400

So the transform from x where -5<=x<=5 would be:
x' = 19400*x + 103000 (The ' just notates that it is a transformed value, not a derivative notation)

The process to calculate the slope and intercept of the transform is just a generalized solution of two simultaneous equations with two unknowns, which I'm sure you can handle in code.

3. ## Re: Normalization

I had forgotten about this thread. I got distracted by a different aspect of the problem and moved away from the normalization. I did see this, and sat and pondered whether or not I really wanted to do that. I'm still not sure.

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