Supermetric Search
Richard Connor, Lucia Vadicamo, Franco Alberto Cardillo, Fausto, Rabitti

TL;DR
This paper explores supermetric spaces, a class of semimetric spaces with strong geometric properties, demonstrating their advantages in metric search efficiency and presenting improved indexing methods for exact search.
Contribution
It introduces the concept of supermetric spaces, investigates their use in various hyperplane partition indexing structures, and achieves new performance benchmarks in exact metric search.
Findings
Supermetric spaces include Euclidean, Cosine, Jensen-Shannon, and Triangular distances.
Using supermetric properties improves indexing performance for exact search.
Achieved a new best performance on a standard benchmark for metric search.
Abstract
Metric search is concerned with the efficient evaluation of queries in metric spaces. In general,a large space of objects is arranged in such a way that, when a further object is presented as a query, those objects most similar to the query can be efficiently found. Most mechanisms rely upon the triangle inequality property of the metric governing the space. The triangle inequality property is equivalent to a finite embedding property, which states that any three points of the space can be isometrically embedded in two-dimensional Euclidean space. In this paper, we examine a class of semimetric space which is finitely four-embeddable in three-dimensional Euclidean space. In mathematics this property has been extensively studied and is generally known as the four-point property. All spaces with the four-point property are metric spaces, but they also have some stronger geometric…
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Taxonomy
TopicsData Management and Algorithms
