how to quantify or compare the proportion of 1: 2: 3

Question

Problem description：I'm working on a machine learning project, and one of the features is represented by the proportion of three levels' sample numbers. When I was doing preprocessing normalization, I can't find a suitable method to normalize the proportion. I would like to ask everyone that if there are suitable ways to normalize the proportion.

My ideas:My current ideas are to convert the proportion into a number, or to get a number by comparing the proportion,such as comparing 1:2:3 with 1:1:1, so that it can be normalized, but I have not found a suitable method on the Internet, I hope to receive your suggestions. Thank you!

Answer 1

I think the answer depends on what you want to achieve by normalization. If you have three value $\{ a,b,c \}$ then there are several ways of normalizing them, including the following

• To normalize so that their sum is $0$ but their differences remain the same, subtract $\frac{a+b+c} 3$ from each value.
• To normalize so that their sum is $1$ and they retain the same proportions, divide each value by $a+b+c$.
• To normalize so that the sum of their squares is $1$ (i.e. so that $(a,b,c)$ becomes a unit vector), divide each value by $\sqrt{a^2+b^2+c^2}$