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similarity-search methods

Similarity-search methods are computational techniques and algorithms designed to retrieve items from a dataset that are most similar to a given query object, evaluated according to a specified distance or similarity metric. In data management and machine learning, these methods represent objects as multidimensional vectors and identify target data points by locating nearest neighbors in vector or metric spaces. Common approaches include space-partitioning and tree-based indexing structures, clustering algorithms, sequential scans, and approximate search schemes such as vector quantization and hashing, which aim to optimize retrieval speed and scale efficiently even as the dimensionality of the data increases.

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A Quantitative Analysis and Performance Study for Similarity-Search Methods in High-Dimensional Spaces

A Quantitative Analysis and Performance Study for Similarity-Search Methods in High-Dimensional Spaces

Roger Weber, Hans-J. Schek, Stephen Blott

OrganizationsBell LaboratoriesETH ZurichInstitute of Information Systems

Why you should read this

Proves that conventional tree-based indexing structures degenerate into linear scans beyond ten dimensions and introduces the Vector Approximation File to dramatically accelerate similarity search in high-dimensional vector spaces.

For similarity search in high-dimensional vector spaces (or ‘HDVSs’), researchers have proposed a number of new methods (or adaptations of existing methods) based, in the main, on data-space partitioning. However, the performance of these methods generally degrades as dimensionality increases. Although this phenomenon—known as the ‘dimensional curse’ is well known, little or no quantitative analysis of the phenomenon is available. In this paper, we provide a detailed analysis of partitioning and clustering techniques for similarity search in HDVSs. We show formally that these methods exhibit linear complexity at high dimensionality, and that existing methods are outperformed on average by a simple sequential scan if the number of dimensions exceeds around 10. Consequently, we come up with an alternative organization based on approximations to make the unavoidable sequential scan as fast as possible. We describe a simple vector approximation scheme, called VA-file, and report on an experimental evaluation of this and of two tree-based index methods (an R*-tree and an X-tree).

Added

2026-09-18