Istituto di Scienza e Tecnologie dell'Informazione     
Connor R., Vadicamo L., Cardillo F. A., Rabitti F. Supermetric search with the four-point property. In: SISAP 2016 - Similarity Search and Applications. 9th International Conference (Tokyo, Japan, 24- 26 October 2016). Proceedings, pp. 51 - 64. Amsaleg L., Houle M., Schubert E (eds.). (Lecture Notes in Computer Science, vol. 9939). Springer, 2016.
Metric indexing research 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 such 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 4-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 guarantees. We coin the term supermetric space as, in terms of metric search, they are significantly more tractable. We show some stronger geometric guarantees deriving from the four-point property which can be used in indexing to great effect, and show results for two of the SISAP benchmark searches that are substantially better than any previously published.
URL: http://link.springer.com/chapter/10.1007/978-3-319-46759-7_4
DOI: 10.1007/978-3-319-46759-7_4
Subject Similarity search
Metric Space
Supermetric Space
Metric Indexing
Four-point property
Hilbert Embedding
H.3.3 INFORMATION STORAGE AND RETRIEVAL. Information Search and Retrieval

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