I need to compare two datasets to see if they are "similar" in terms of numerical similarity between given columns. The problem is, however, that I do not know the characteristics of the 2nd dataset. It is possible the second dataset 1)matches fully to the 1st dataset, 2)matches partially to the 1st dataset 3) does not match at all. By matching, I mean whether the entities intersect or not. For instance, if I need to compare two datasets which contain country names and their respective GDP values, I have no idea, which countries exists in the second dataset, what the intersecting entities are, and whether the GDP values are in the same order of magnitude (in millions, billions, etc. ) beforehand. This makes it impossible to apply Cosine similarity, since the two vectors need to have the same length. Moreover, Cosine similarity does not consider entity-to-entity similarity. Using Euclidian distance is also not an option, because outliers will affect the overall similarity score.
I need a more complex similarity measure which can take into account all these unknown characteristics inherent to the 2nd dataset. The similarity measure I am looking for, should be robust to outliers and should somehow capture general, overall similarity between two datasets.