关于向量的基础概念，可以参考：向量数据库学习笔记（1） —— 基础概念-CSDN博客

一、 pgvector简介

       pgvector 是一款开源的、基于pg的、向量相似性搜索 插件，将您的向量数据与其他数据统一存储在pg中。支持功能包括：

• 精确与近似最近邻搜索
• 单精度/半精度浮点向量、二进制向量及稀疏向量
• 多种距离度量：L2距离、内积、余弦距离、L1距离、汉明距离、杰卡德距离
• 支持所有具有Postgres客户端的编程语言
• 同时继承PostgreSQL全部核心优势

二、 安装与启用

https://github.com/pgvector/pgvector

下载并解压安装包

cd pgvector
make
make install

插件安装（注意它叫vector，不叫pgvector）

CREATE EXTENSION vector;

三、 简单用法

1. 建表与增删改

Create a new table with a vector column

CREATE TABLE items (id bigserial PRIMARY KEY, embedding vector(3));

add a vector column to an existing table

ALTER TABLE items ADD COLUMN embedding vector(3);

Insert vectors

INSERT INTO items (embedding) VALUES ('[1,2,3]'), ('[4,5,6]');

load vectors in bulk using COPY

COPY items (embedding) FROM STDIN WITH (FORMAT BINARY);

Upsert vectors

INSERT INTO items (id, embedding) VALUES (1, '[1,2,3]'), (2, '[4,5,6]')
    ON CONFLICT (id) DO UPDATE SET embedding = EXCLUDED.embedding;

Update vectors

UPDATE items SET embedding = '[1,2,3]' WHERE id = 1;

Delete vectors

DELETE FROM items WHERE id = 1;

2. 向量查询

Get the nearest neighbors to a vector

SELECT * FROM items ORDER BY embedding <-> '[3,1,2]' LIMIT 5;

Supported distance functions are:

• <-> - L2 distance
• <#> - (negative) inner product
• <=> - cosine distance
• <+> - L1 distance
• <~> - Hamming distance (binary vectors)
• <%> - Jaccard distance (binary vectors)

Get the nearest neighbors to a row

SELECT * FROM items WHERE id != 1 ORDER BY embedding <-> (SELECT embedding FROM items WHERE id = 1) LIMIT 5;

Get rows within a certain distance

SELECT * FROM items WHERE embedding <-> '[3,1,2]' < 5;

Note: Combine with ORDER BY and LIMIT to use an index

3. 距离查询

Get the distance

SELECT embedding <-> '[3,1,2]' AS distance FROM items;

For inner product, multiply by -1 (since <#> returns the negative inner product)

SELECT (embedding <#> '[3,1,2]') * -1 AS inner_product FROM items;

For cosine similarity, use 1 - cosine distance

SELECT 1 - (embedding <=> '[3,1,2]') AS cosine_similarity FROM items;

4. 聚合查询

Average vectors

SELECT AVG(embedding) FROM items;

Average groups of vectors

SELECT category_id, AVG(embedding) FROM items GROUP BY category_id;

四、索引

pgvector支持两类索引，即前面提到过的两类算法 —— HNSW（默认） 与 IVFFlat。

1. HNSW索引

       HNSW索引会构建一个多层图结构。相比IVFFlat索引，它具有更优的查询性能（在搜索速度与召回率的权衡方面），但构建时间更长且内存占用更高。此外，由于不需要像IVFFlat那样的训练步骤，该索引可以在表内尚无数据时直接创建。

创建各类距离索引

L2 distance

CREATE INDEX ON items USING hnsw (embedding vector_l2_ops);

Note: Use halfvec_l2_ops for halfvec and sparsevec_l2_ops for sparsevec (and similar with the other distance functions)

Inner product

CREATE INDEX ON items USING hnsw (embedding vector_ip_ops);

Cosine distance

CREATE INDEX ON items USING hnsw (embedding vector_cosine_ops);

L1 distance

CREATE INDEX ON items USING hnsw (embedding vector_l1_ops);

Hamming distance

CREATE INDEX ON items USING hnsw (embedding bit_hamming_ops);

Jaccard distance

CREATE INDEX ON items USING hnsw (embedding bit_jaccard_ops);

Supported types are:

• vector - up to 2,000 dimensions
• halfvec - up to 4,000 dimensions
• bit - up to 64,000 dimensions
• sparsevec - up to 1,000 non-zero elements

2. IVFFlat索引

       IVFFlat索引的工作原理是将向量划分为多个聚类列表，仅搜索距离查询向量最近的若干列表。相较于HNSW索引，它具有更快的构建速度和更低的内存占用，但在查询性能（速度与召回率的平衡）方面表现稍逊。

       IVFFlat索引实现高召回率需把握三个关键要点：

• 数据准备：建议在表中已存有数据后再创建索引

• 列表数量设定：

  • 数据量≤100万条时，建议初始值为行数/1000

  • 数据量＞100万条时，建议采用行数的平方根值

• 查询调优：设置合适的探测数量（probes参数）

  • 较高值提升召回率，较低值加快查询速度

  • 建议初始值为列表数量的平方根值

创建各类距离索引

L2 distance

CREATE INDEX ON items USING ivfflat (embedding vector_l2_ops) WITH (lists = 100);

Note: Use halfvec_l2_ops for halfvec (and similar with the other distance functions)

Inner product

CREATE INDEX ON items USING ivfflat (embedding vector_ip_ops) WITH (lists = 100);

Cosine distance

CREATE INDEX ON items USING ivfflat (embedding vector_cosine_ops) WITH (lists = 100);

Hamming distance

CREATE INDEX ON items USING ivfflat (embedding bit_hamming_ops) WITH (lists = 100);

Supported types are:

• vector - up to 2,000 dimensions
• halfvec - up to 4,000 dimensions
• bit - up to 64,000 dimensions

五、 最佳实践

橙色是探针节点，越多越准确

参考

部分内容来自AI回答

https://github.com/pgvector/pgvector?tab=readme-ov-file#hnsw

在 PostgreSQL 中为生成式 AI 应用程序查询向量数据的最佳实践_哔哩哔哩_bilibili