Learning to Top-K Search using Pairwise Comparisons

Given a collection of N items with some unknown underlying ranking, we examine how to use pairwise comparisons to determine the top ranked items in the set. Resolving the top items from pairwise comparisons has application in diverse fields ranging from recommender systems to image-based search to protein structure analysis. In this paper we introduce techniques to resolve the top ranked items using significantly fewer than all the possible pairwise comparisons using both random and adaptive sampling methodologies. Using randomly-chosen comparisons, a graph-based technique is shown to efficiently resolve the top O(\logN) items when there are no comparison errors. In terms of adaptively-chosen comparisons, we show how the top O(\logN) items can be found, even in the presence of corrupted observations, using a voting methodology that only requires O(N\log^2N) pairwise comparisons.