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类似倒排,以元素重叠度为基准的相似计算。广泛应用于数组、全文检索、字符串、文本特征值、多列任意组合查询的相似搜索。
代表的PostgreSQL插件如下
https://github.com/postgrespro/rum
https://www.postgresql.org/docs/devel/static/pgtrgm.html
http://sigaev.ru/git/gitweb.cgi?p=smlar.git;a=summary
《海量数据,海明(simhash)距离高效检索(smlar) - 阿里云RDS PosgreSQL最佳实践》
https://github.com/eulerto/pg_similarity
向量相似与元素重叠度计算,显然是不同的,基于元素的重叠度相似,可以利用倒排来实现,如上节描述。而基于元素向量相似,需要用到自定义的索引接口,典型的代表是GiST索引在空间距离上的计算,以及imgsmlr插件在图像特征值相似方面的计算。
https://github.com/postgrespro/imgsmlr
原理如下
64*64的图像,取16个区域的平均值,生成16个浮点数,作为图像特征值。
一个值求相似,相减绝对值最小。
2个值求相似,可以理解为平面坐标,求距离最小(GiST knn距离排序)。
3个值求相似,可以理解为3D坐标里面的点,求距离最小的点。
...
16个值求相似,与上类似。imgsmlr插件使用gist索引接口实现了16个元素的向量相似索引排序。
例子
postgres=# \d t_img Table "public.t_img" Column | Type | Collation | Nullable | Default --------+-----------+-----------+----------+--------- id | integer | | not null | sig | signature | | | Indexes: "t_img_pkey" PRIMARY KEY, btree (id) "idx_t_img_1" gist (sig)
数据量
postgres=# select count(*) from t_img; count ----------- 319964709 (1 row) Time: 698.075 ms
图像特征值搜索例子,速度杠杠的。(以上使用citus+postgres+128 shard)
postgres=# select * from t_img order by sig <-> '(3.539080, 0.243861, 1.509150, 1.781380, 8.677560, 4.232060, 8.979810, 1.665030, 1.294100, 4.449800, 9.200450, 1.859860, 5.440250, 7.788580, 0.514258, 8.424920)' limit 1; id | sig -----------+------------------------------------------------------------------------------------------------------------------------------------------------------------------ 148738668 | (2.554440, 0.310499, 2.322520, 0.478624, 7.816080, 4.360440, 8.287050, 1.011060, 2.114320, 3.541110, 9.166300, 1.922250, 4.488640, 7.897890, 1.600290, 7.462080) (1 row) Time: 337.301 ms
https://www.postgresql.org/docs/devel/static/cube.html
a <-> b float8 Euclidean distance between a and b. a <#> b float8 Taxicab (L-1 metric) distance between a and b. a <=> b float8 Chebyshev (L-inf metric) distance between a and b.
计算图片向量相似时,cube比imgsmlr性能稍差,因为cube使用的是float8,而imgsmlr使用的是float4。
例子
cube
postgres=# explain (analyze,verbose,timing,costs,buffers) select * from t_img0 order by sig::Text::cube <-> '(0.435404, 6.602870, 9.050220, 9.379750, 2.483920, 1.534660, 0.363753, 4.079670, 0.124681, 3.611220, 7.127460, 7.880070, 2.574830, 6.778820, 5.156320, 8.329430)' limit 1; QUERY PLAN ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Limit (cost=0.36..0.37 rows=1 width=76) (actual time=147.432..147.434 rows=1 loops=1) Output: id, sig, ((((sig)::text)::cube <-> '(0.435404, 6.60287, 9.05022, 9.37975, 2.48392, 1.53466, 0.363753, 4.07967, 0.124681, 3.61122, 7.12746, 7.88007, 2.57483, 6.77882, 5.15632, 8.32943)'::cube)) Buffers: shared hit=16032 -> Index Scan using idx_t_img0_1 on public.t_img0 (cost=0.36..13824.28 rows=754085 width=76) (actual time=147.430..147.430 rows=1 loops=1) Output: id, sig, (((sig)::text)::cube <-> '(0.435404, 6.60287, 9.05022, 9.37975, 2.48392, 1.53466, 0.363753, 4.07967, 0.124681, 3.61122, 7.12746, 7.88007, 2.57483, 6.77882, 5.15632, 8.32943)'::cube) Order By: (((t_img0.sig)::text)::cube <-> '(0.435404, 6.60287, 9.05022, 9.37975, 2.48392, 1.53466, 0.363753, 4.07967, 0.124681, 3.61122, 7.12746, 7.88007, 2.57483, 6.77882, 5.15632, 8.32943)'::cube) Buffers: shared hit=16032 Planning Time: 0.096 ms Execution Time: 148.905 ms (9 rows)
imgsmlr
postgres=# explain (analyze,verbose,timing,costs,buffers) select * from t_img0 order by sig <-> '(0.435404, 6.602870, 9.050220, 9.379750, 2.483920, 1.534660, 0.363753, 4.079670, 0.124681, 3.611220, 7.127460, 7.880070, 2.574830, 6.778820, 5.156320, 8.329430)' limit 2; QUERY PLAN ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ Limit (cost=0.36..0.37 rows=2 width=72) (actual time=40.284..48.183 rows=2 loops=1) Output: id, sig, ((sig <-> '(0.435404, 6.602870, 9.050220, 9.379750, 2.483920, 1.534660, 0.363753, 4.079670, 0.124681, 3.611220, 7.127460, 7.880070, 2.574830, 6.778820, 5.156320, 8.329430)'::signature)) Buffers: shared hit=2914 -> Index Scan using t_img0_sig_idx on public.t_img0 (cost=0.36..7032.36 rows=754085 width=72) (actual time=40.282..48.179 rows=2 loops=1) Output: id, sig, (sig <-> '(0.435404, 6.602870, 9.050220, 9.379750, 2.483920, 1.534660, 0.363753, 4.079670, 0.124681, 3.611220, 7.127460, 7.880070, 2.574830, 6.778820, 5.156320, 8.329430)'::signature) Order By: (t_img0.sig <-> '(0.435404, 6.602870, 9.050220, 9.379750, 2.483920, 1.534660, 0.363753, 4.079670, 0.124681, 3.611220, 7.127460, 7.880070, 2.574830, 6.778820, 5.156320, 8.329430)'::signature) Buffers: shared hit=2914 Planning Time: 0.091 ms Execution Time: 48.210 ms (9 rows)
cube相比imgsmlr的好处是:cube可以计算任意维度的向量相似,imgsmlr则仅用于计算16维(signation类型)的向量相似
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