k-Distance Approximation for Memory-Efficient RkNN Retrieval

Abstract

For a given query object, Reverse k-Nearest Neighbor queries retrieve those objects that have the query object among their k-nearest neighbors. However, computing the k-nearest neighbor sets for all points in a database is expensive in terms of computational costs. Therefore, specific index structures have been invented to apply pruning heuristics which aim at reducing the search space. At time, the state-of-the-art index structure for enabling fast RkNN query processing in general metric spaces is the MRkNNCoP-Tree which uses linear functions to approximate lower and upper bounds on the k-distances to prune the search space. Storing those linear functions results in additional storage costs in $\mathcal {O}(n)$ which might be infeasible in situation where storage space is limited, e.g., on mobile devices. In this work, we present a novel index based on the MRkNNCoP-Tree as well as recent developments in the field of neural indexing. By learning a single neural network model that approximates the k-nearest neighbor distance bounds for all points in a database, the storage complexity of the proposed index structure is reduced to $\mathcal {O}(1)$ while the index is still able to guarantee exact query results. As shown in our experimental evaluations on synthetic and real-world data sets, our approach can significantly reduce the required storage space in trade-off to some growth in terms of refinement sets when relying on exact query processing. We provide our code at www.github.com/mberr/k-distance-prediction.