A comprehensive survey and experimental comparison of graph-based approximate nearest neighbor search

Approximate nearest neighbor search (ANNS) constitutes an important operation in a multitude of applications, including recommendation systems, information retrieval, and pattern recognition. In the past decade, graph-based ANNS algorithms have been the leading paradigm in this domain, with dozens of graph-based ANNS algorithms proposed. Such algorithms aim to provide effective, efficient solutions for retrieving the nearest neighbors for a given query. Nevertheless, these efforts focus on developing and optimizing algorithms with different approaches, so there is a real need for a comprehensive survey about the approaches' relative performance, strengths, and pitfalls. Thus here we provide a thorough comparative analysis and experimental evaluation of 13 representative graph-based ANNS algorithms via a new taxonomy and fine-grained pipeline. We compared each algorithm in a uniform test environment on eight real-world datasets and 12 synthetic datasets with varying sizes and characteristics. Our study yields novel discoveries, offerings several useful principles to improve algorithms, thus designing an optimized method that outperforms the state-of-the-art algorithms. This effort also helped us pinpoint algorithms' working portions, along with rule-of-thumb recommendations about promising research directions and suitable algorithms for practitioners in different fields.

Metric Spaces with Expensive Distances

In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We introduce a different model, where we assume that the computation of a single distance is an expensive operation and consequently, the goal is to minimize the number of such distance queries. This model is motivated by metric spaces that appear in the context of topological data analysis. We consider two standard operations on metric spaces, namely the construction of a [Formula: see text]-spanner and the computation of an approximate nearest neighbor for a given query point. In both cases, we partially explore the metric space through distance queries and infer lower and upper bounds for yet unexplored distances through triangle inequality. For spanners, we evaluate several exploration strategies through extensive experimental evaluation. For approximate nearest neighbors, we prove that our strategy returns an approximate nearest neighbor after a logarithmic number of distance queries.