I am facing a statistical problem that I am not sure whether it's solvable. Simply put, I am given multiple weight vectors and here are two examples:
$w_1 = [.2, .3, .4, .1]$ for items A, B, C, D, respectively.
$w_2 = [.1, .1, .05, .05, .03, .03, .02, .5, .12]$ for items A, B, C, D, E, F, G, H, I, respectively.
and I have many weight vectors like this (sum of all elements is 1), but of different sizes.
Now I want to construct an "importance vector" for all 26 items (A ~ Z), each entry represents each item's importance.
Since many weight vectors are of different sizes, their weights are of different scale. I don't think it's a good idea to simply add them up and take average because of the reason stated before. Any ideas? Or any pieces of literature that I can refer to? Or what is this kind of problems called?