余弦相似度的SQL计算

Question

假设您在数据库中按以下方式构造了一个表：

create table data (v int, base int, w_td float);
insert into data values (99,1,4);
insert into data values (99,2,3);
insert into data values (99,3,4);
insert into data values (1234,2,5);
insert into data values (1234,3,2);    
insert into data values (1234,4,3);

为了清楚起见，select * from data应输出：

v   |base|w_td
--------------
99  |1   |4.0
99  |2   |3.0
99  |3   |4.0
1234|2   |5.0
1234|3   |2.0
1234|4   |3.0

请注意，由于向量存储在数据库中，因此我们仅需要存储非零条目。在此示例中，我们只有两个向量$ v_ {99} =（4,3,4,0）$和$ v_ {1234}
=（0,5,2,3）$都在$ \ mathbb {R}中^ 4 $。

这些向量的余弦相似度应为$ \ displaystyle \ frac {23} {\ sqrt {41 \ cdot 38}} =
0.5826987807288609 $。

如何仅使用近乎余量来计算余弦相似度SQL？

我之所以这么说sqrt，是因为您将需要在基本SQL实现中并不总是提供的功能，例如，在sqlite3！中并没有提供该功能。

Answer 1

with norms as (
    select v,
        sum(w_td * w_td) as w2
    from data
    group by v
)
select 
    x.v as ego,y.v as v,nx.w2 as x2, ny.w2 as y2,
    sum(x.w_td * y.w_td) as innerproduct,
    sum(x.w_td * y.w_td) / sqrt(nx.w2 * ny.w2) as cosinesimilarity
from data as x
join data as y
    on (x.base=y.base)
join norms as nx
    on (nx.v=x.v)
join norms as ny
    on (ny.v=y.v)
where x.v < y.v
group by 1,2,3,4
order by 6 desc

产量

ego|v   |x2  |y2  |innerproduct|cosinesimilarity
--------------------------------------------------
99 |1234|41.0|38.0|23.0        |0.5826987807288609