# MinMax normalization when all elements are same

I'm using min-max normalization to normalize time series which I compare in the following.

My question is, by definition min-max normalization is defined as:

x[i]=(x[i]-min(x))/(max(x)-min(x))


My question is, what should the new value be if all values in the array are same? That is, max=min.

One possibility is to set all elements to 0, the other is to set them all to 1. I could also set all values to half of the range, that is 0.5. But what is the proper approach?

If a variable is actually constant, then it provides no information whatsoever in your model. Saying it in plain English: when you are building a statistical model, or making predictions, you use your data to learn what knowing that $X = x$ tells us about the value of $Y$.
In this case, $X$ is always the same, so values of $Y$ are totally unrelated to it. All humans are mortal, I'm a human, so what can you say about the color of my eyes given this information?
• +1. Another way to see this is that if constant variables were really useful, then we could add predictors to a model indefinitely with constant values such as 42 or $\pi$. But that wouldn't help one bit. – Nick Cox Apr 6 '16 at 11:00