Efficient Approximate Search for Sets of Vectors

We consider a similarity measure between two sets $A$ and $B$ of vectors, that balances the average and maximum cosine distance between pairs of vectors, one from set $A$ and one from set $B$. As a motivation for this measure, we present lineage tracking in a database. To practically realize this measure, we need an approximate search algorithm that given a set of vectors $A$ and sets of vectors $B_1,...,B_n$, the algorithm quickly locates the set $B_i$ that maximizes the similarity measure. For the case where all sets are singleton sets, essentially each is a single vector, there are known efficient approximate search algorithms, e.g., approximat