SQL计算余弦相似度

假设数据库中有一个表，其构造如下：

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);

需要明确的是select * from data应该输出：

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，因此我们只需要存储非零条目。在此示例中，$\mathbb{R} 中只有两个向量 $v_{99} = (4,3,4,0)$ 和 $v_{1234} = (0,5,2,3)$ ^4$。

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

如何仅使用几乎来计算余弦相似度SQL?

我说几乎是因为你需要sqrt基本功能并不总是提供SQL实现，例如它不在sqlite3!

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

yields

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