Towards Efficient Index Construction and Approximate Nearest Neighbor Search in High-Dimensional Spaces

The approximate nearest neighbor (ANN) search in high-dimensional spaces is a fundamental but computationally very expensive problem. Many methods have been designed for solving the ANN problem, such as LSH-based methods and graph-based methods. The LSH-based methods can be costly to reach high query quality due to the hash-boundary issues, while the graph-based methods can achieve better query performance by greedy expansion in an approximate proximity graph (APG). However, the construction cost of these APGs can be one or two orders of magnitude higher than that for building hash-based indexes. In addition, they fail short in incrementally maintaining APGs as the underlying dataset evolves. In this paper, we propose a novel approach named LSH-APG to build APGs and facilitate fast ANN search using a lightweight LSH framework. LSH-APG builds an APG via consecutively inserting points based on their nearest neighbor relationship with an efficient and accurate LSH-based search strategy. A high-quality entry point selection technique and an LSH-based pruning condition are developed to accelerate index construction and query processing by reducing the number of points to be accessed during the search. LSH-APG supports fast maintenance of APGs in lieu of building them from scratch as dataset evolves. Its maintenance cost and query cost for a point is proven to be less affected by dataset cardinality. Extensive experiments on real-world and synthetic datasets demonstrate that LSH-APG incurs significantly less construction cost but achieves better query performance than existing graph-based methods.