向量数据库：PGVector
一、PGVector 介绍
PGVector 是一个基于 PostgreSQL 的扩展插件，为用户提供了一套强大的向量存储和查询的功能：
- 精确和近似最近邻搜索
- 单精度（Single-precision）、半精度（Half-precision）、二进制（Binary）和稀疏向量（Sparse Vectors）
- L2 距离（L2 Distance）、内积（Inner Product）、余弦距离（Cosine Distance）、L1 距离（L1 Distance）、汉明距离（Hamming Distance）和 Jaccard 距离（Jaccard Distance）
- 支持 ACID 事务、点时间恢复、JOIN 操作，以及 Postgres 所有的其他优秀特性
二、安装 PGVector
2.1 安装 PostgreSQL
PGVector是基于PostgreSQL的扩展插件，要使用PGVector需要先安装PostgreSQL(支持Postgres 12以上)，PostgreSQL具体安装操作可参考：PostgreSQL基本操作。
2.2 安装 PGVector
# 1.下载
git clone --branch v0.7.0 https://github.com/pgvector/pgvector.git
# 2.进入下载目录
cd pgvector# 3.编译安装
make && make install
2.3 启用 PGVector
登录PostgreSQL数据库，执行以下命令启用PGVector：
CREATE EXTENSION IF NOT EXISTS vector;
三、PGVector 日常使用
3.1 存储数据
创建向量字段：
#建表时，创建向量字段
CREATE TABLE items (id bigserial PRIMARY KEY, embedding vector(3));
#已有表，新增向量字段
ALTER TABLE items ADD COLUMN embedding vector(3);
插入向量数据：
INSERT INTO items (embedding) VALUES ('[1,2,3]'), ('[4,5,6]');
更新向量数据：
UPDATE items SET embedding = '[1,2,3]' WHERE id = 1;
删除向量数据：
DELETE FROM items WHERE id = 1;
3.2 查询数据
| 操作符 | 函数 | 距离类型 |
|---|---|---|
| <-> | l2_distance | 两个向量相减得到的新向量的长度 |
| <#> | vector_negative_inner_product | 两个向量内积的负值 |
| <=> | cosine_distance | 两个向量夹角的cos值 |
| <+> |
Get the nearest neighbors to a vector
SELECT * FROM items ORDER BY embedding <-> '[3,1,2]' LIMIT 5;
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;
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;
Average vectors
SELECT AVG(embedding) FROM items;
Average groups of vectors
SELECT category_id, AVG(embedding) FROM items GROUP BY category_id;
3.3 HNSW 索引
HNSW索引创建了一个多层图。在速度-召回权衡方面，它的查询性能优于IVFFlat，但构建时间较慢且占用更多内存。另外，由于没有像IVFFlat那样的训练步骤，可以在表中没有数据的情况下创建索引。
Supported types are:
- vector - up to 2,000 dimensions
- halfvec - up to 4,000 dimensions (added in 0.7.0)
- bit - up to 64,000 dimensions (added in 0.7.0)
- sparsevec - up to 1,000 non-zero elements (added in 0.7.0)
L2 distance
CREATE INDEX ON items USING hnsw (embedding vector_l2_ops);
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 - added in 0.7.0
CREATE INDEX ON items USING hnsw (embedding vector_l1_ops);
Hamming distance - added in 0.7.0
CREATE INDEX ON items USING hnsw (embedding bit_hamming_ops);
Jaccard distance - added in 0.7.0
CREATE INDEX ON items USING hnsw (embedding bit_jaccard_ops);
3.4 IVFFlat 索引
IVFFlat索引将向量划分为列表，然后搜索最接近查询向量的那些列表的子集。它的构建时间比HNSW快，且占用更少内存，但查询性能（就速度-召回权衡而言）较低。
Supported types are:
- vector - up to 2,000 dimensions
- halfvec - up to 4,000 dimensions (added in 0.7.0)
- bit - up to 64,000 dimensions (added in 0.7.0)
L2 distance
CREATE INDEX ON items USING ivfflat (embedding vector_l2_ops) WITH (lists = 100);
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 - added in 0.7.0
CREATE INDEX ON items USING ivfflat (embedding bit_hamming_ops) WITH (lists = 100);