SQL Server计算Jaccard系数—sim(i,j)

前些天，在Q群里面看到有人请教这样一个问题：在SQL Server中如何用SQL实现以下计算

由图得知，该问题是如何计算Jaccard系数。Jaccard系数，又称为Jaccard相似系数（Jaccard similarity coefficient）用于比较有限样本集之间的相似性与差异性。Jaccard系数值越大，样本相似度越高。

SQL Server通过intersect实现交集，union实现并集，如下：

intersect交集

计算交集代码段如下：(1 intersect 0 = null,1 intersect 1 = 1,0 intersect 0 = 0)

union并集

计算并集代码段如下：(1 union 0 = 1 0,1 union 1 = 1,0 union 0 = 0)

原理简介：

通过sys.columns表获取表的字段名与字段ID，循环字段名，并根据字段名去取到表中对应的值：如字段名为A，那么取ID为1的值：select A from test where id=1,取ID为2的值：select A from test where id=2，

然后将2个值进行交集与并集，字段循环结束后，得到@str_intersect，@str_union，计算比值：len(@str_intersect)*1.0/len(@str_union)

最终结果如下：

全部代码如下：(建表，见注释部分)

--create table Test(id int,A INT,B INT,C INT,D INT,E INT,F INT)--INSERT INTO TEST SELECT 1,1,1,1,0,0,0--INSERT INTO TEST SELECT 2,0,1,0,1,0,1--INSERT INTO TEST SELECT 3,1,1,1,1,0,1--INSERT INTO TEST SELECT 4,1,1,1,0,1,0--INSERT INTO TEST SELECT 5,0,1,0,1,1,1--INSERT INTO TEST SELECT 6,0,0,1,0,1,1--drop table Test_result--create table Test_result(id int,_1_ numeric(10,4),_2_ numeric(10,4),_3_ numeric(10,4),_4_ numeric(10,4),_5_ numeric(10,4),_6_ numeric(10,4))--insert into Test_result select 1,null,null,null,null,null,null--insert into Test_result select 2,null,null,null,null,null,null--insert into Test_result select 3,null,null,null,null,null,null--insert into Test_result select 4,null,null,null,null,null,null--insert into Test_result select 5,null,null,null,null,null,null--insert into Test_result select 6,null,null,null,null,null,nullSELECT name,column_id  into #test  FROM SYS.COLUMNS WHERE object_id =object_id('dbo.test')and column_id>1declare @id_1 int=0,@id_2 int=0,@str_union varchar(max),@a_union int,@sql_union varchar(max),@str_intersect varchar(max),@a_intersect int,@sql_intersect varchar(max)declare @name varchar(20),@column_id intcreate table #a_union(num int)create table #a_intersect(num int)declare @min_id int=0,@max_id int=0,@global_min_id int=0,@global_max_id int=0select @min_id=min(id),@max_id=max(id),@global_min_id=min(id),@global_max_id=max(id) from Testwhile(@min_id<=@max_id)beginselect @id_1=@min_id,@id_2=@global_min_idwhile @id_2<=@global_max_idbeginselect @str_union='',@str_intersect=''while(select count(1) from #test)>0 beginselect top 1 @name=name,@column_id=column_id from #test order by column_idselect @sql_union='select CASE '+'WHEN (select count(1) from (SELECT '+@name+' FROM TEST WHERE ID='+convert(varchar,@id_1)+'union SELECT '+@name+' FROM TEST WHERE ID='+convert(varchar,@id_2)+') as a)>1 THEN 1'+' WHEN ISNULL((SELECT '+@name+' FROM TEST WHERE ID='+convert(varchar,@id_1)+' UNION  SELECT '+@name+' FROM TEST WHERE ID='+convert(varchar,@id_2)+'),0)=0 THEN 0 ELSE 1 END'insert into #a_unionexec(@sql_union)SELECT @a_union=num from #a_uniondelete from #a_unionif(@a_union=1)select @str_union+=@nameselect @sql_intersect='select CASE WHEN ISNULL((SELECT '+@name+' FROM TEST WHERE ID='+convert(varchar,@id_1)+' INTERSECT  SELECT '+@name+' FROM TEST WHERE ID='+convert(varchar,@id_2)+'),0)=0 THEN 0 ELSE 1 END'insert into #a_intersectexec(@sql_intersect)SELECT @a_intersect=num from #a_intersectdelete from #a_intersectif(@a_intersect=1)select @str_intersect+=@namedelete from #test where @name=name and @column_id=column_idendinsert into #test SELECT name,column_id FROM SYS.COLUMNS WHERE object_id =object_id('dbo.test')and column_id>1--select @str_union,@str_intersect,@column_id,@id_1,@id_2if(@id_2=1)    update Test_result set _1_= convert(numeric(10,4),len(@str_intersect)*1.0/len(@str_union)) where id=@id_1if(@id_2=2)    update Test_result set _2_= convert(numeric(10,4),len(@str_intersect)*1.0/len(@str_union)) where id=@id_1if(@id_2=3)    update Test_result set _3_= convert(numeric(10,4),len(@str_intersect)*1.0/len(@str_union)) where id=@id_1if(@id_2=4)    update Test_result set _4_= convert(numeric(10,4),len(@str_intersect)*1.0/len(@str_union)) where id=@id_1if(@id_2=5)    update Test_result set _5_= convert(numeric(10,4),len(@str_intersect)*1.0/len(@str_union)) where id=@id_1if(@id_2=6)    update Test_result set _6_= convert(numeric(10,4),len(@str_intersect)*1.0/len(@str_union)) where id=@id_1   set @id_2=@id_2+1endset @min_id=@min_id+1enddrop table #testdrop table #a_uniondrop table #a_intersect-------------create table test_str_column(id int,str_columns varchar(max))--insert into test_str_column select 1,null--insert into test_str_column select 2,null--insert into test_str_column select 3,null--insert into test_str_column select 4,null--insert into test_str_column select 5,null--insert into test_str_column select 6,nullselect * into #temp_test_table from testselect name,column_id into #tmp_test_columns from sys.columns where object_id=object_id('dbo.test') and column_id>1declare @id int,@col_name varchar(20),@col_id int,@string_columns varchar(max),@sql_rs varchar(max),@num_1 intcreate table #tmp_rs(num int)while (select count(1) from #temp_test_table)>0beginselect top 1 @id=id from #temp_test_table order by idset @string_columns=''while(select count(1) from #tmp_test_columns)>0beginselect top 1 @col_name=name,@col_id=column_id from #tmp_test_columns order by column_idselect @sql_rs='select '+@col_name+' from test where id='+convert(varchar,@id)insert into #tmp_rsexec(@sql_rs)select @num_1=num from #tmp_rsif(@num_1=1)set @string_columns=@string_columns+@col_namedelete from #tmp_test_columns where @col_name=name and @col_id=column_iddelete from #tmp_rsendinsert into #tmp_test_columns select name,column_id  from sys.columns where object_id=object_id('dbo.test') and column_id>1update test_str_column set str_columns=@string_columns where id =@iddelete from #temp_test_table where @id=idenddrop table  #temp_test_tabledrop table #tmp_test_columnsdrop table #tmp_rsselect * from testselect * from test_str_columnselect * from Test_result