Efficient Approximate Search for Sets of Vectors

Michael Leybovich; Oded Shmueli

RECORD

Efficient Approximate Search for Sets of Vectors

Michael Leybovich, Oded Shmueli

Data Structures and Algorithms · Submitted 14 Jul 2021

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The proposed approximate approach achieves significant performance gains over an optimized, exact search on vector sets.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗

Cite ▾

Claim paper

The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,613 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.15 · human participants 0.03 · controlled comparison 0.44 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.88 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We consider a similarity measure between two sets $A$ and $B$ of vectors, that balances the average and maximum cosine distance between pairs of vectors, one from set $A$ and one from set $B$. As a motivation for this measure, we present lineage tracking in a database. To practically realize this measure, we need an approximate search algorithm that given a set of vectors $A$ and sets of vectors $B_1,...,B_n$, the algorithm quickly locates the set $B_i$ that maximizes the similarity measure. For the case where all sets are singleton sets, essentially each is a single vector, there are known efficient approximate search algorithms, e.g., approximated versions of tree search algorithms, locality-sensitive hashing (LSH), vector quantization (VQ) and proximity graph algorithms. In this work, we present approximate search algorithms for the general case. The underlying idea in these algorithms is encoding a set of vectors via a "long" single vector. The proposed approximate approach achieves significant performance gains over an optimized, exact search on vector sets.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider a similarity measure between two sets $A$ and $B$ of vectors, that balances the average and maximum cosine distance between pairs of vectors, one from set $A$ and one from set $B$.	contribution 0.68	0.55	0.04	asserted 0.99
s1	As a motivation for this measure, we present lineage tracking in a database.	background 0.98	0.48	0.02	asserted 0.98
s2	To practically realize this measure, we need an approximate search algorithm that given a set of vectors $A$ and sets of vectors $B_1,...,B_n$, the algorithm quickly locates the set $B_i$ that maximizes the similarity measure.	background 0.65	0.20	0.06	asserted 0.99
s3	For the case where all sets are singleton sets, essentially each is a single vector, there are known efficient approximate search algorithms, e.g., approximated versions of tree search algorithms, locality-sensitive hashing (LSH), vector quantization (VQ) and proximity graph algorithms.	background 0.98	0.03	0.03	asserted 1.00
s4	In this work, we present approximate search algorithms for the general case.	contribution 0.99	0.92	0.13	asserted 1.00
s5	The underlying idea in these algorithms is encoding a set of vectors via a "long" single vector.	method 0.98	0.80	0.07	asserted 1.00
s6	The proposed approximate approach achieves significant performance gains over an optimized, exact search on vector sets.	result 1.00	0.91	0.69	asserted 1.00

What kind of paper the classifier reports this is: method or tool 1.00 · evidence from simulation or computation 0.69.

What was examined, and what was not

sources read

arXiv listing abstract v2

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original abstract

We consider a similarity measure between two sets $A$ and $B$ of vectors, that balances the average and maximum cosine distance between pairs of vectors, one from set $A$ and one from set $B$. As a motivation for this measure, we present lineage tracking in a database. To practically realize this measure, we need an approximate search algorithm that given a set of vectors $A$ and sets of vectors $B_1,...,B_n$, the algorithm quickly locates the set $B_i$ that maximizes the similarity measure. For the case where all sets are singleton sets, essentially each is a single vector, there are known efficient approximate search algorithms, e.g., approximated versions of tree search algorithms, locality-sensitive hashing (LSH), vector quantization (VQ) and proximity graph algorithms. In this work, we present approximate search algorithms for the general case. The underlying idea in these algorithms is encoding a set of vectors via a "long" single vector. The proposed approximate approach achieves significant performance gains over an optimized, exact search on vector sets.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

2 arXiv papers cite this in 4 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 3 sentences without a confident label

Uses its method or tool 1 paper

Next, given an initial state of the DB, a set $V_t$ containing a single vector is obtained for each tuple $t$, using the word vectors model $M$ over the underlying text of $t$. $V_t$ is inserted into an efficient vector set search structure [ref] .

ML Based Lineage in Databases · System Life Cycle · 1.00

What it cites · 2 sentences without a confident label

Uses the method or tool of 1 paper

Note that known approximate vector search techniques, such as LSH [ref] (or any other technique, as mentioned in section [ref]), can be utilized here for efficiency. * For each candidate set of vectors $V$ of cardinality $|V| ∈[1, M]$, and its respective construction of $M$ long candidate vectors $L⃗_V^n ∈ℝ^n ×|V| ×D$, for each $n ∈[1, M]$, insert $L⃗_V^n$ into the vector search structure $S_n, |V|$. * Now, suppose you are given a target set of vectors $A$ of cardinality $|A| ∈[1, M]$.

Practical and Optimal LSH for Angular Distance · Search Method · 0.88

Cites as background 2 papers

The most popular solutions are based on approximated versions of tree algorithms [ref] , LSH [ref] , VQ [ref] and proximity graph algorithms [ref] .

Practical and Optimal LSH for Angular Distance · Introduction · 0.92
In NLP, word vectors are vectors, whose elements are real numbers, which represent the “semantic ties” of a word in a text [ref] .

Efficient Estimation of Word Representations in Vector Space · Outline · 1.00

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.