Efficient Similarity Search and Classification via Rank Aggregation

Abstract

We propose a novel approach to performing efficient similarity search and classification in high dimensional data. In this framework, the database elements are vectors in a Euclidean space. Given a query vector in the same space, the goal is to find elements of the database that are similar to the query. In our approach, a small number of independent "voters" rank the database elements based on similarity to the query. These rankings are then combined by a highly efficient aggregation algorithm. Our methodology leads both to techniques for computing approximate nearest neighbors and to a conceptually rich alternative to nearest neighbors. One instantiation of our methodology is as follows. Each voter projects all the vectors (database elements and the query) on a random line (different for each voter), and ranks the database elements based on the proximity of the projections to the projection of the query. The aggregation rule picks the database element that has the best median rank. This combination has several appealing features. On the theoretical side, we prove that with high probability, it produces a result that is a (1+ε)-factor approximation to the Euclidean nearest neighbor. On the practical side, it turns out to be extremely efficient, often exploring no more than 5% of the data to obtain very high-quality results. This method is also database-friendly, in that it accesses data primarily in a pre-defined order without random accesses, and, unlike other methods for approximate nearest neighbors, requires almost no extra storage. Also, we extend our approach to deal with the k nearest neighbors. We conduct two sets of experiments to evaluate the efficacy of our methods. Our experiments include two scenarios where nearest neighbors are typically employed - similarity search and classification problems. In both cases, we study the performance of our methods with respect to several evaluation criteria, and conclude that they are uniformly excellent, both in terms of quality of results and in terms of efficiency.