Supermetric Search

@article{Connor2019SupermetricS,
  title={Supermetric Search},
  author={Richard C. H. Connor and Lucia Vadicamo and Franco Alberto Cardillo and Fausto Rabitti},
  journal={ArXiv},
  year={2019},
  volume={abs/1707.08361}
}

High-Dimensional Simplexes for Supermetric Search

TLDR
The n-point property is a generalisation of triangle inequality where, for any \((n+1)\) objects in the space, there exists an n-dimensional simplex whose edge lengths correspond to the distances among the objects.

Indexing Metric Spaces for Exact Similarity Search

TLDR
Different strengths and weaknesses of different indexing techniques are revealed in order to offer guidance on selecting an appropriate indexing technique for a given setting, and directing the future research for metric indexes.

Re-ranking Permutation-Based Candidate Sets with the n-Simplex Projection

TLDR
This work proposes a refining approach based on a metric embedding, called n-Simplex projection, that can be used on metric spaces meeting the n-point property, and proposes to reuse the distances computed for building the data permutations to derive these bounds and shows how to use them to improve the permutation-based results.

Metric Embedding into the Hamming Space with the n-Simplex Projection

TLDR
This work proposes a novel transformation technique that uses the n-Simplex projection to transform metric objects into a low-dimensional Euclidean space, and then transform this space to the Hamming space.

Accelerating Metric Filtering by Improving Bounds on Estimated Distances

TLDR
This paper enhances the existing definition of bounds on the unknown distance with information about possible angles within triangles, and shows that two lower bounds and one upper bound on each distance exist in case of limited angles.

A Ptolemaic Partitioning Mechanism

TLDR
A novel partitioning mechanism for the Ptolemaic lower bound is presented and is always better than either pivot or hyperplane partitioning and can be combined with Hilbert exclusion to give a new maximum for exclusion power with respect to the number of distances measured per query.

SPLX-Perm: A Novel Permutation-Based Representation for Approximate Metric Search

TLDR
A novel approach to transform metric objects into permutations using the object-pivot distances in combination with a metric transformation, called n-Simplex projection, is presented, which is suitable only for the large class of metric space satisfying the n-point property.

Query Filtering with Low-Dimensional Local Embeddings

TLDR
The concept of local pivoting is to partition a metric space so that each element in the space is associated with precisely one of a fixed set of reference objects or pivots, maximising the probability of excluding that particular object from a search.

References

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Supermetric Search with the Four-Point Property

TLDR
This paper examines a class of semimetric space which is finitely 4-embeddable in three-dimensional Euclidean space and coin the term supermetric space as, in terms of metric search, they are significantly more tractable.

Hilbert Exclusion

TLDR
It is shown that many common metric spaces, notably including those using Euclidean and Jensen-Shannon distances, also have a stronger property, sometimes called the four-point property, and one in particular, which is named the Hilbert Exclusion property, allows any indexing mechanism which uses hyperplane partitioning to perform better.

Searching in metric spaces by spatial approximation

  • G. Navarro
  • Computer Science
    6th International Symposium on String Processing and Information Retrieval. 5th International Workshop on Groupware (Cat. No.PR00268)
  • 1999
TLDR
This work proposes a new data structure, called sa-tree (“spatial approximation tree”), which is based on approaching the searched objects spatially, that is, getting closer and closer to them, rather than the classic divide-and-conquer approach of other data structures.

Searching in metric spaces

TLDR
A unified view of all the known proposals to organize metric spaces, so as to be able to understand them under a common framework, and presents a quantitative definition of the elusive concept of "intrinsic dimensionality".

Index-driven similarity search in metric spaces (Survey Article)

Similarity search is a very important operation in multimedia databases and other database applications involving complex objects, and involves finding objects in a data set S similar to a query

Similarity Search - The Metric Space Approach

TLDR
Similarity Search focuses on the state of the art in developing index structures for searching the metric space, and provides an extensive survey of specific techniques for a large range of applications.

Metric Databases

TLDR
The metric space model, described herein, is an extension of the exact searching paradigm aiming to cope with the new requirements of large unstructured repositories containing textual and multimedia data.

A Data Structure and an Algorithm for the Nearest Point Problem

TLDR
A tree structure for storing points from a normed space whose norm is effectively computable and an algorithm for finding the nearest point from the tree to a given query point is given.