Faster proximity searching with the distal SAT

Chávez, Edgar; Ludueña, Verónica; Reyes, Nora Susana; Roggero, Patricia

doi:10.1016/j.is.2015.10.014

Cited by 23 publications

(46 citation statements)

References 33 publications

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“…Figure 10 shows these results, in each case the bottom line on the graph indicating the best performance of our Hilbert exclusion mechanism in this context 6 . For comparison, the DiSAT [2] results with the two exclusion mechanisms are shown with grey lines; DiSAT/Hyperbolic, the top line on this chart, at the time of its publication was the best known general-purpose indexing mechanism. Figure 11 shows the relative effect of reference point separation when using Hilbert and Hyperbolic exclusion.…”

Section: Resultsmentioning

confidence: 99%

“…The first observation to be made in this context is that any metric space is isometrically 3-embeddable in ℓ 2 2 . This is apparent from the triangle inequality property of a proper metric.…”

Section: Metric Spaces and Finite Isometric Embeddingsmentioning

confidence: 99%

“…This is apparent from the triangle inequality property of a proper metric. In fact the two properties are equivalent: for any semi-metric space (V, d v ) which is isometrically 3-embeddable in ℓ 2 2 , triangle inequality also holds. It is interesting to consider the standard exclusion mechanisms of pivot-based exclusion and hyperplane-based exclusion in the light of an isometric 3-embedding in ℓ 2 2 ; Figure 1 for example shows a basis for hyperplane exclusion using only this property rather than triangle inequality explicitly.…”

Section: Metric Spaces and Finite Isometric Embeddingsmentioning

confidence: 99%

“…For any such strategy, other more complex ways of indexing the data exist; by analogy, for example, various forms of SAT [2], GNAT [1], M-Index [7] etc. will exist.…”

Section: Partitions Of the 2d Planementioning

confidence: 99%

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Similarity Search and Applications

Connor

2016

Lecture Notes in Computer Science

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Abstract. 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 4 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.

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Section: Resultsmentioning

confidence: 99%

Section: Metric Spaces and Finite Isometric Embeddingsmentioning

confidence: 99%

Section: Metric Spaces and Finite Isometric Embeddingsmentioning

confidence: 99%

“…For any such strategy, other more complex ways of indexing the data exist; by analogy, for example, various forms of SAT [2], GNAT [1], M-Index [7] etc. will exist.…”

Section: Partitions Of the 2d Planementioning

confidence: 99%

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Connor

2016

Lecture Notes in Computer Science

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“…The concepts extend to more complex and efficient indexes such as the GNAT [1], MIndex [10] and various forms of SAT trees [7,8,2,3], here we are only concerned with the principles.…”

Section: Partition Treesmentioning

confidence: 99%

Reference Point Hyperplane Trees

Connor¹

2016

Similarity Search and Applications

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Abstract. Our context of interest is tree-structured exact search in metric spaces. We make the simple observation that, the deeper a data item is within the tree, the higher the probability of that item being excluded from a search. Assuming a fixed and independent probability p of any subtree being excluded at query time, the probability of an individual data item being accessed is (1 − p) d for a node at depth d. In a balanced binary tree half of the data will be at the maximum depth of the tree so this effect should be significant and observable. We test this hypothesis with two experiments on partition trees. First, we force a balance by adjusting the partition/exclusion criteria, and compare this with unbalanced trees where the mean data depth is greater. Second, we compare a generic hyperplane tree with a monotone hyperplane tree, where also the mean depth is greater. In both cases the tree with the greater mean data depth performs better in high-dimensional spaces. We then experiment with increasing the mean depth of nodes by using a small, fixed set of reference points to make exclusion decisions over the whole tree, so that almost all of the data resides at the maximum depth. Again this can be seen to reduce the overall cost of indexing. Furthermore, we observe that having already calculated reference point distances for all data, a final filtering can be applied if the distance table is retained. This reduces further the number of distance calculations required, whilst retaining scalability. The final structure can in fact be viewed as a hybrid between a generic hyperplane tree and a LAESA search structure.

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