## Figures and Tables from this paper

## 21 Citations

### High-Dimensional Simplexes for Supermetric Search

- MathematicsSISAP
- 2017

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.

### Re-ranking via local embeddings: A use case with permutation-based indexing and the nSimplex projection

- Computer ScienceInf. Syst.
- 2021

### Indexing Metric Spaces for Exact Similarity Search

- BusinessACM Computing Surveys
- 2022

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

- Computer ScienceSISAP
- 2018

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

- Computer ScienceSISAP
- 2019

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

- Computer ScienceSISAP
- 2020

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

- Computer ScienceArXiv
- 2022

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

- Computer Science, MathematicsSISAP
- 2019

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

- Computer ScienceSISAP
- 2019

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.

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