We have a dataset of I items who have been measured over two different sets of features A, with cardinality N, and B with cardinality M, and N > M. We would like to know in which feature space the items are more similar.
Therefore, for each feature space, we first scaled our measurements to have mean 0 and standard deviation 1 (z-scores) and then evaluated the Euclidean distance among all pairs of items. We finally compared the distribution of the distances in the two feature spaces using a Wilcoxon's test.
However, we are now wondering whether the fact that the cardinality of the two feature spaces is different introduces a bias in the distance evaluation, with a higher cardinality leading to a higher distance.
Could this be possible? If yes, how can we make the two feature spaces comparable? Is there a better distance than the Euclidian distance? Dividing the distance by the cardinality would suffice?
Many thanks in advance, any input will be highly appreciated :)