Reverse nearest neighbors search in ad-hoc subspaces

Given an object q, modeled by a multidimensional point, a reverse nearest neighbors (RNN) query returns the set of objects in the database that have q as their nearest neighbor. In this paper, we study an interesting generalization of the RNN query, where not all dimensions are considered, but only an ad-hoc subset thereof. The rationale is that (i) the dimensionality might be too high for the result of a regular RNN query to be useful, (ii) missing values may implicitly define a meaningful subspace for RNN retrieval, and (iii) analysts may be interested in the query results only for a set of (ad-hoc) problem dimensions (i.e., object attributes). We consider a suitable storage scheme and develop appropriate algorithms for projected RNN queries, without relying on multidimensional indexes. Our methods are experimentally evaluated with real and synthetic data.