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] | p | Where $v^+_i$ and $v^-_i$ are the positive and negative examples of each pair, and $s(v)$ is the similarity function. | [
"documentation",
"documentation/concepts",
"documentation/concepts/explore"
] | 7,003 |
[
"Explore - Qdrant",
"Context search"
] | /documentation/concepts/explore/ | html > body > div:nth-of-type(1) > section > div > div > div:nth-of-type(2) > article > p:nth-of-type(42) | [
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] | p | If you need to find some similar objects in vector space, provided e.g. by embeddings or matching NN, you can choose among a variety of libraries: Annoy, FAISS or NMSLib. | [
"articles",
"articles/filtrable-hnsw"
] | 7,016 |
[
"Filtrable HNSW - Qdrant",
"Filtrable HNSW"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(1) | [
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] | p | I did not find any simple solutions for this. | [
"articles",
"articles/filtrable-hnsw"
] | 7,020 |
[
"Filtrable HNSW - Qdrant",
"Filtrable HNSW"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(2) | [
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] | p | There are several discussions like this, but they only suggest to iterate over top search results and apply conditions consequently after the search. | [
"articles",
"articles/filtrable-hnsw"
] | 7,021 |
[
"Filtrable HNSW - Qdrant",
"Filtrable HNSW"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(3) | [
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] | p | Tree index implies that we will meet same problem that appears in relational databases: | [
"articles",
"articles/filtrable-hnsw"
] | 7,024 |
[
"Filtrable HNSW - Qdrant",
"Filtrable HNSW"
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"Filtrable HNSW - Qdrant",
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] | p | There is another algorithm which shows top results on the benchmark. | [
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[
"Filtrable HNSW - Qdrant",
"Filtrable HNSW"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(5) | [
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"Filtrable HNSW - Qdrant",
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] | p | The original paper is well written and very easy to read, so I will only give the main idea here. | [
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] | p | It turns out that even with this naive modification algorithm can cover some use cases. | [
"articles",
"articles/filtrable-hnsw"
] | 7,035 |
[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(9) | [
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] | 7,036 |
[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(9) | [
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[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(9) | [
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"articles",
"articles/filtrable-hnsw"
] | 7,038 |
[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(9) | [
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] | p | Therefore, the theoretical conclusions obtained in the Percolation theory become applicable: | [
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"articles/filtrable-hnsw"
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[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > blockquote > p | [
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] | p | Percolation is related to the robustness of the graph (called also network). | [
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[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > blockquote > p | [
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"articles",
"articles/filtrable-hnsw"
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[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > blockquote > p | [
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] | p | Next we remove randomly a fraction $1-p$ of nodes and leave only a fraction $p$. | [
"articles",
"articles/filtrable-hnsw"
] | 7,042 |
[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > blockquote > p | [
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] | p | There exists a critical percolation threshold $ pc = \frac{1}{\langle k\rangle} $ below which the network becomes fragmented while above $pc$ a giant connected component exists. | [
"articles",
"articles/filtrable-hnsw"
] | 7,043 |
[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(10) | [
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] | p | This statement also confirmed by experiments: | [
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"articles/filtrable-hnsw"
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"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > figure:nth-of-type(1) > figcaption > p | [
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] | p | Dependency of connectivity to the number of edges | [
"articles",
"articles/filtrable-hnsw"
] | 7,045 |
[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > figure:nth-of-type(2) > figcaption > p | [
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] | p | The graphs also show that this threshold can be shifted by increasing the $m$ parameter of the algorithm, which is responsible for the degree of nodes. | [
"articles",
"articles/filtrable-hnsw"
] | 7,049 |
[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(12) | [
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] | p | Let’s consider some other filtering conditions we might want to apply in the search: | [
"articles",
"articles/filtrable-hnsw"
] | 7,050 |
[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > ul:nth-of-type(2) > li:nth-of-type(1) | [
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[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > ul:nth-of-type(2) > li:nth-of-type(1) > ul > li:nth-of-type(3) | [
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[
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[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
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"Filtrable HNSW - Qdrant",
"How can we modify it?"
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"Filtrable HNSW - Qdrant",
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[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(16) | [
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[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(16) | [
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[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(16) | [
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] | p | Now we can estimate expected graph connectivity by number of excluded categories, not nodes. | [
"articles",
"articles/filtrable-hnsw"
] | 7,064 |
[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(16) | [
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] | p | Depending on labeled subsets size ration we can go for one of the following scenarios: | [
"articles",
"articles/filtrable-hnsw"
] | 7,069 |
[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > ul:nth-of-type(3) > li:nth-of-type(1) | [
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] | li | if at least one subset is small: perform search over the label containing smallest subset and then filter points consequently. | [
"articles",
"articles/filtrable-hnsw"
] | 7,070 |
[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > ul:nth-of-type(3) > li:nth-of-type(2) | [
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] | li | if large subsets give large intersection: perform regular search with constraints expecting that intersection size fits connectivity threshold. | [
"articles",
"articles/filtrable-hnsw"
] | 7,071 |
[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > ul:nth-of-type(3) > li:nth-of-type(3) | [
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] | li | if large subsets give small intersection: perform linear search over intersection expecting that it is small enough to fit a time frame. | [
"articles",
"articles/filtrable-hnsw"
] | 7,072 |
[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(18) | [
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[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
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[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(18) | [
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"Filtrable HNSW - Qdrant",
"How can we modify it?"
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[
"Filtrable HNSW - Qdrant",
"How can we modify it?"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(21) | [
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] | h2 | Conclusion | [
"articles",
"articles/filtrable-hnsw"
] | 7,080 |
[
"Filtrable HNSW - Qdrant",
"Conclusion"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(22) | [
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] | p | It is possible to enchant HNSW algorithm so that it will support filtering points in a first search phase. | [
"articles",
"articles/filtrable-hnsw"
] | 7,081 |
[
"Filtrable HNSW - Qdrant",
"Conclusion"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(22) | [
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] | p | Filtering can be carried out on the basis of belonging to categories, | [
"articles",
"articles/filtrable-hnsw"
] | 7,082 |
[
"Filtrable HNSW - Qdrant",
"Conclusion"
] | /articles/filtrable-hnsw/ | html > body > div:nth-of-type(1) > div:nth-of-type(1) > div > section > article > p:nth-of-type(22) | [
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[
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"Conclusion"
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[
"Filtrable HNSW - Qdrant",
"Conclusion"
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"articles/filtrable-hnsw"
] | 7,085 |
[
"AWS Marketplace - Qdrant"
] | /documentation/cloud/aws-marketplace/ | html > body > div:nth-of-type(1) > section > div > div > div:nth-of-type(2) > article > h1 | [
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] | p | It is common for AWS to abstract usage based pricing in the AWS marketplace, as there are too many factors to model when calculating billing from the AWS side. | [
"documentation",
"documentation/cloud",
"documentation/cloud/aws-marketplace"
] | 7,093 |
[
"AWS Marketplace - Qdrant",
"Billing"
] | /documentation/cloud/aws-marketplace/ | html > body > div:nth-of-type(1) > section > div > div > div:nth-of-type(2) > article > p:nth-of-type(4) | [
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