I am trying to find a similarity measure for a very specific problem.
I have a list of cities that have some characteritisques. For example bilingual school, firemen stations, etc. These cities are represented as binary vectors where each element corresponds to a characteristic.
On the other side I have possible citizens. The citizens give a punctuation between 0 and 1 to the importance they give to each of the characteristics in the cities.
So I could have : Citizen 1 = {0.83, 0.3, 0, 1}
City 1 = {1, 0, 0, 1} City 2 = {1, 0, 1, 1}
I would like to find the best city for each citizen. The important thing would be to find cities with a 1 in the characteristics that the citizen cares about and we don't mind if the city has a zero when the citizen did not care or not care much ( less weight or not weight at all if the citizen does not care)
I have tried some distance (eg hamming, cosine) but they give weight when the citizen and the city have both zero in the same characteristic.
what would be a good similarity to use in this case?
Thanks