Selecting Sketches for Similarity Search

Mic, Vladimir; Novák, David; Vadicamo, Lucia; Zezula, Pavel

doi:10.1007/978-3-319-98398-1_9

Cited by 5 publications

(7 citation statements)

References 16 publications

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“…As would be expected, increasing the number of reference objects has a significant effect of the number of distance calculations performed. However the number of reference objects used in these experiments is really quite small, much smaller than has been reported for other regional approaches eg [13,1] given the accuracy shown by the relatively small number of residual distance calculations required. In particular we have the quite stunning result Fig.…”

Section: Experiments and Resultsmentioning

confidence: 88%

Querying Metric Spaces with Bit Operations

Connor

Dearle

2018

Similarity Search and Applications

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Metric search techniques can be usefully characterised by the time at which distance calculations are performed during a query. Most exact search mechanisms use a "just-in-time" approach where distances are calculated as part of a navigational strategy. An alternative is to use a "one-time" approach, where distances to a fixed set of reference objects are calculated at the start of each query. These distances are typically used to re-cast data and queries into a different space where querying is more efficient, allowing an approximate solution to be obtained. In this paper we use a "one-time" approach for an exact search mechanism. A fixed set of reference objects is used to define a large set of regions within the original space, and each query is assessed with respect to the definition of these regions. Data is then accessed if, and only if, it is useful for the calculation of the query solution. As dimensionality increases, the number of defined regions must increase, but the memory required for the exclusion calculation does not. We show that the technique gives excellent performance over the SISAP benchmark data sets, and most interestingly we show how increases in dimensionality may be countered by relatively modest increases in the number of reference objects used. 1 Context To set a formal context, we are interested in searching a (large) finite set of objects S which is a subset of an infinite set U , where (U, d) is a metric space: that is, an ordered pair (U, d), where U is a domain of objects and d is a total distance function d : U ×U → R, satisfying postulates of non-negativity, identity, symmetry, and triangle inequality [20]. The general requirement is to efficiently find members of S which are similar to an arbitrary member of U given as a query, where the distance function d gives the only way by which any two objects may be compared. There are many important practical examples captured by this mathematical framework, see for example [16, 20]. The simplest type of similarity query is the range search query: for some threshold t, based on a query q ∈ U , the solution set is R = {s ∈ S| d(q, s) ≤ t}. The essence of metric search is to spend time pre-processing the finite set S so that solutions to queries can be efficiently calculated using only distances among objects. In all cases therefore, distances between the data and selected This is a post-peer-review, pre-copyedit version of a paper published in Marchand-Maillet S., Silva Y., Chávez E.

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Section: Experiments and Resultsmentioning

confidence: 88%

Querying Metric Spaces with Bit Operations

Connor

Dearle

2018

Similarity Search and Applications

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“…The same heuristic as in case of the technique GHP 50 is than employed to select λ pivots that produces low correlated bits. PCA 50 is a simple sketching technique surprisingly well approximating the Euclidean spaces [4,12,13,15,17]. It uses the Principal Component Analysis (PCA) to shrink the original vectors, which are then rotated using a random matrix and binarized by the thresholding.…”

Section: Bit String Sketches For Speeding-up Similarity Searchmentioning

confidence: 99%

“…Sketching techniques applicable to generic metric spaces, e.g., GHP 50 and BP 50, are usually of a worse quality than vector-based sketching techniques when dealing with the vectors spaces [4,17]. Moreover, they require an expensive learning of the transformation.…”

Section: Bit String Sketches For Speeding-up Similarity Searchmentioning

confidence: 99%

“…Another class of metric space transformations is formed by sketching techniques that transform data objects into short bit-strings called sketches [4,17,19]. The similarity of sketches is expressed by the Hamming distance, and sketches are exploited to prune the search space during query executions [18,19].…”

Section: Introductionmentioning

confidence: 99%

“…While some sketching techniques are applicable in generic metric spaces, others are designed for specific spaces [4]. The metric-based sketching techniques are broadly applicable, but their performance is often worse than that of the vectorbased sketching approaches when dealing with the vector spaces [4,17].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Vadicamo

Mic

Falchi

et al. 2019

Similarity Search and Applications

Self Cite

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Transformations of data objects into the Hamming space are often exploited to speed-up the similarity search in metric spaces. Techniques applicable in generic metric spaces require expensive learning, e.g., selection of pivoting objects. However, when searching in common Euclidean space, the best performance is usually achieved by transformations specifically designed for this space. We propose a novel transformation technique that provides a good trade-off between the applicability and the quality of the space approximation. It uses the n-Simplex projection to transform metric objects into a low-dimensional Euclidean space, and then transform this space to the Hamming space. We compare our approach theoretically and experimentally with several techniques of the metric embedding into the Hamming space. We focus on the applicability, learning cost, and the quality of search space approximation.

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An Alternating Optimization Scheme for Binary Sketches for Cosine Similarity Search

Thordsen,

Schubert

2023

Lecture Notes in Computer Science

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Selecting Sketches for Similarity Search

Cited by 5 publications

References 16 publications

Querying Metric Spaces with Bit Operations

Querying Metric Spaces with Bit Operations

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

An Alternating Optimization Scheme for Binary Sketches for Cosine Similarity Search

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