Suppose that I'm calculating distances of a company branches in every state from main branch of that state. After that I'm combining this feature with other features to creating a composite indicator with different weights (using factor analysis). Distances are based on kilometers. There isn't any problem to calculate branches distances but as you know for main company in every state the distance is
0 so the contribution of this feature to indicator is zero.
Let's see data after normalization (use mean or trimmed mean as denominator of this feature for normalization):
c_1 0.518240612 c_2 0.497028927 c_3 0.437494131 c_4 0.557290719 c_5 0.995532618 c_6 0 c_7 0.24987914 c_8 1.090686096 c_9 1.399784307
0 (main company in above state) has very very low value like
0.000001 and we're comparing this value to c_5 branch normalized distance value (
0.995532618) so c_5 is
0.995532618/0.000001=995532.618 times bigger than main capital c_6 in this feature. I think this a problem in our calculation. Is this idea true? What is your idea about changing 0 (main companies in every state) to average of all distances (in all states) and after that normalize data and create composite indicator?
PS. The objective of factor analysis here is to calculate weights of every feature to design composite indicator. We are combining some features to calculate performance of every branch. We are giving higher scores to companies that have higher values of distance because of welfare issues.