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Community Blog Using HybridDB/PostgreSQL to Find the Best Product Combination for Marketing

Using HybridDB/PostgreSQL to Find the Best Product Combination for Marketing

In this blog, we look at how statistical analysis can help enterprises determine the perfect product combination for marketing.

Background

Typically when talking about product combinations, you would think of products that are closely related in terms of form and function. For instance, in China, stuffed buns, soybean milk, and tea eggs are common breakfast items. So it wouldn't come as a surprise if these products are promoted together in a supermarket.

But then, you've probably heard of the infamous beer and diapers correlation. Why do these seemingly disparate items are the best product combination?

For these questions, we can find answers based on accumulated order data. The question "how to use PostgreSQL to find the best production combination" was raised by a friend in the PostgreSQL community during the PostgreSQL community activity on April 8.

In fact, this problem can also be solved by using a professional recommendation database that supports a variety of recommendation algorithms.

However, this article does not intend to use RecDB to solve this problem. Instead, this article uses the traditional statistics to reach a conclusion.

Limitation of the Statistical Method Described in This Article

The statistical method covered in this article can only be used to calculate the best combination of directly related items (data included in the same order).

To calculate the combination of indirectly associated items (for example, if user A bought item 1 and item 2 and user B bought item 2 and item 3, item 1 and item 3 have an indirect relationship), you need to use the recommendation algorithm in RecDB or use a similar graph search method.

Scenario Simulation

Assume that there is a total of 100,000 item IDs and simulate a batch of users' order or shopping cart records with each order or shopping cart record containing 5-10 items. Create a total of around 11 million of these records.

Create a table

postgres=# create unlogged table buy (pay_id int8, item_id int[]);  
CREATE TABLE  

Construct Data

Create a function that inserts data into the buy table (array of 5-10 items)

create or replace function f() returns void as 
$$
    
declare    
begin    
  for i in 5..15 loop    
    insert into buy (item_id) select array_agg((100000*random())::int8) from generate_series(1,i);    
  end loop;    
end;    

$$
 language plpgsql strict;

Use pgbench to generate 11 million records

vi test.sql    
select f();    
    
pgbench -M prepared -n -r -P 1 -f ./test.sql -c 100 -j 100 -t 10000    
  
transaction type: ./test.sql  
scaling factor: 1  
query mode: prepared  
number of clients: 100  
number of threads: 100  
number of transactions per client: 10000  
number of transactions actually processed: 1000000/1000000  
latency average = 1.155 ms  
latency stddev = 1.814 ms  
tps = 85204.625725 (including connections establishing)  
tps = 85411.351807 (excluding connections establishing)  
script statistics:  
 - statement latencies in milliseconds:  
         1.158  select f();  

Confirm that the data has been successfully written

postgres=# select count(*) from buy;  
  count     
----------  
 11000000  
(1 row)  
  
postgres=# select * from buy limit 10;  
 pay_id |                           item_id                              
--------+--------------------------------------------------------------  
        | {6537,76804,33612,75580,8021}  
        | {72437,66015,2939,56128,7056}  
        | {40983,79581,15954,21039,6702,90279}  
        | {93626,8337,13416,69371,4366,75868}  
        | {84611,56893,25201,74038,59337,62045,59178}  
        | {97422,48801,69714,77056,17059,79714,21598}  
        | {42997,50834,57214,52866,83656,76342,5639,93416}  
        | {53543,24369,31552,28654,38516,63657,86564,11483}  
        | {58873,23162,23369,55091,32046,29907,31895,65658,5487}  
        | {39916,6641,85068,55870,27679,91770,46150,12290,48662,71350}  
(10 rows)  

GIN Indexes

postgres=# create index idx_buy_item on buy using gin(item_id);  

Split Functions

The purpose of splitting is to split the array in an order into several sets. For example, an order containing five items can be split into 10 (4+3+2+1) sets of 2 items.

{6537,76804,33612,75580,8021}  

Split the order into the following sets

{6537,76804}  
  
{6537,33612}  
  
{6537,75580}  
  
{6537,8021}  
  
{76804,33612}  
  
{76804,75580}  
  
{76804,8021}  
  
{33612,75580}  
  
{33612,8021}  
  
{75580,8021}  

Create a function to complete the split work

Use a recursive query for recombination

Example

WITH RECURSIVE   
t(i) AS (  
  SELECT * FROM unnest('{A,B,C}'::char[])  
),   
cte AS (  
     SELECT i AS combo, i, 1 AS ct   
     FROM t   
   UNION ALL   
     SELECT cte.combo || t.i, t.i, ct + 1   
     FROM cte, t   
     WHERE ct <= 3 -- Combine 4 (3+1) times  
       AND position(t.i in cte.combo) = 0 -- Newly added characters are not included in existing characters  
)   
SELECT ARRAY(SELECT combo FROM cte ORDER BY ct, combo) AS result;  
  
                      result                         
---------------------------------------------------  
 {A,B,C,AB,AC,BA,BC,CA,CB,ABC,ACB,BAC,BCA,CAB,CBA}  
(1 row)  

Function 1 That Returns a Specified Number of Sets

Assume that the array doesn't include replicate elements

create or replace function array_regroup(  
  i_arr int[], -- Enter an array  
  i_elems int -- Scramble into sets of fixed length  
) returns setof int[] as 
$$
  
declare  
  v_arr_len int := array_length(i_arr, 1); -- The length of the array that has been entered  
begin  
  -- Protection  
  if i_elems > v_arr_len then  
    raise notice 'you cann''t return group len % more then %', i_elems, v_arr_len;  
    return;  
  elsif i_elems = v_arr_len then  
    return next i_arr;  
    return;  
  elsif i_elems = 1 then  
    return query select array(select i) from unnest(i_arr) t(i);  
    return;  
  end if;  
  
  return query  
  WITH RECURSIVE   
  t(i) AS (  
      select array(select i) from unnest(i_arr) t(i)  
  ),   
  cte AS (  
     SELECT i AS combo, i, 1 AS ct   
     FROM t   
   UNION ALL   
     SELECT array(select i from (select unnest(array_cat(cte.combo, t.i)) order by 1) t(i)), t.i, ct + 1   
     FROM cte, t   
     WHERE cte.ct <= i_elems-1 -- Combine any times  
       AND (not cte.combo @> t.i) -- Newly added values are not included in existing value sets  
  )   
  SELECT combo FROM cte where array_length(combo,1)=i_elems group by combo;   
  
  return;  
end;  

$$
 language plpgsql strict;  
postgres=# select array_regroup(array[1,2,3],2);  
 array_regroup   
---------------  
 {2,3}  
 {1,2}  
 {1,3}  
(3 rows)  

Function 2 That Returns All Sets

create or replace function array_regroup(  
  i_arr int[], -- Enter an array  
) returns setof int[] as 
$$
  
declare  
  v_arr_len int := array_length(i_arr, 1); -- The length of the array that has been entered  
begin  
  
  return query  
  WITH RECURSIVE   
  t(i) AS (  
      select array(select i) from unnest(i_arr) t(i)  
  ),   
  cte AS (  
     SELECT i AS combo, i, 1 AS ct   
     FROM t   
   UNION ALL   
     SELECT array(select i from (select unnest(array_cat(cte.combo, t.i)) order by 1) t(i)), t.i, ct + 1   
     FROM cte, t   
     WHERE cte.ct <= v_arr_len-1 -- Combine any times  
       AND (not cte.combo @> t.i) -- Newly added values are not included in existing value sets  
  )   
  SELECT combo FROM cte group by combo;   
  
  return;  
end;  

$$
 language plpgsql strict;  
postgres=# select array_regroup(array[1,2,3]);  
 array_regroup   
---------------  
 {2}  
 {2,3}  
 {1,2}  
 {1}  
 {1,2,3}  
 {3}  
 {1,3}  
(7 rows)  

Function 3 That Returns a Specified Number of Sets and That Only Displays Sets Containing Certain Elements (For Example, Arrays That Contain the Bread ID)

create or replace function array_regroup(  
  i_arr int[], -- Enter an array  
  i_elems int -- Scramble into sets of fixed length  
  i_arr_contain int[] -- Arrays that contain specified item IDs  
) returns setof int[] as 
$$
  
declare  
  v_arr_len int := array_length(i_arr, 1); -- The length of the array that has been entered  
begin  
  -- Protection  
  if i_elems > v_arr_len then  
    raise notice 'you cann''t return group len % more then %', i_elems, v_arr_len;  
    return;  
  elsif i_elems = v_arr_len then  
    return next i_arr;  
    return;  
  elsif i_elems = 1 then  
    return query select array(select i) from unnest(i_arr) t(i);  
    return;  
  end if;  
  
  return query  
  WITH RECURSIVE   
  t(i) AS (  
      select array(select i) from unnest(i_arr) t(i)  
  ),   
  cte AS (  
     SELECT i AS combo, i, 1 AS ct   
     FROM t   
   UNION ALL   
     SELECT array(select i from (select unnest(array_cat(cte.combo, t.i)) order by 1) t(i)), t.i, ct + 1   
     FROM cte, t   
     WHERE cte.ct <= i_elems-1 -- Combine any times  
       AND (not cte.combo @> t.i) -- Newly added values are not included in existing value sets  
       AND (cte.combo @> i_arr_contain)  
  )   
  SELECT combo FROM cte where array_length(combo,1)=i_elems group by combo;   
  
  return;  
end;  

$$
 language plpgsql strict;  
postgres=# select array_regroup(array[1,2,3,4,5],2,array[1]);  
 array_regroup   
---------------  
 {1,2}  
 {1,3}  
 {1,4}  
 {1,5}  
(4 rows)  
  
Time: 1.150 ms  

Find the One Best Combination Item for a Single Item

For example, find the best combination item for bread.

Assume that the item ID of bread is 6537.

postgres=# select item_id from buy where item_id @> array[6537];  
......  
 {60573,17248,6537,77857,43349,66208,13656}  
 {97564,50031,79924,24255,6537,21174,39117}  
 {24026,78667,99115,87856,64782,8344,73169,41478,63091,29609,6537,71982,75382}  
 {53094,97465,26156,54181,6537}  
(1101 rows)  
Time: 5.791 ms  
  
postgres=# explain select item_id from buy where item_id @> array[6537];  
                                   QUERY PLAN                                      
---------------------------------------------------------------------------------  
 Bitmap Heap Scan on buy  (cost=457.45..51909.51 rows=55000 width=60)  
   Recheck Cond: (item_id @> '{6537}'::integer[])  
   ->  Bitmap Index Scan on idx_buy_item  (cost=0.00..443.70 rows=55000 width=0)  
         Index Cond: (item_id @> '{6537}'::integer[])  
(4 rows)  

Split order data into sets and find the sets that have the highest occurrence of this item ID.

postgres=# select count(*), array_regroup(item_id,2,array[6537]) from buy where item_id @> array[6537] group by 2 order by 1 desc;  
 count | array_regroup   
-------+---------------  
     3 | {6537,55286}  
     3 | {6537,48661}  
     3 | {6537,78337}  
     3 | {6537,72623}  
     3 | {6537,81442}  
     3 | {6537,66414}  
     3 | {6537,35346}  
     3 | {6537,79565}  
     3 | {3949,6537}  
......  
  
Time: 286.859 ms  

Find the Two Best Combination Items for a Single Item

For example, find the two best combination items for bread.

postgres=# select count(*), array_regroup(item_id,3,array[6537]) from buy where item_id @> array[6537] group by 2 order by 1 desc;  
 count |   array_regroup      
-------+--------------------  
     1 | {32,999,6537}  
     1 | {6537,49957,91533}  
     1 | {6537,49957,88377}  
     1 | {6537,49957,57887}  
     1 | {6537,49957,55192}  
     1 | {6537,49952,95266}  
     1 | {6537,49952,56916}  
     1 | {6537,49945,60492}  
     1 | {6537,49940,92888}  
......  
  
Time: 1055.414 ms  

Find the One Best Combination Item throughout the Network

This may take a long time.

select count(*), array_regroup(item_id,2) from buy group by 2 order by 1 desc limit 10;  

Find the N Best Combination Items throughout the Network

This may take a long time.

select count(*), array_regroup(item_id, n) from buy group by 2 order by 1 desc limit 10;  

Summary

1.  This case doesn't require highly technical methods, and only splits arrays by recommendation level to count the number of occurrences.

The following database features are used in this case:

1.1.  Support for the array type

1.2.  PL/pgSQL programming on the service side

1.3.  Retrieval of array elements by index (containing a specific element)

1.4.  The MPP distributed database architecture for computation performance enhancement For more information, refer to Alibaba Cloud HybridDB for PostgreSQL.

2.  Note that the statistical method in this article has a limitation.

The statistical method covered in this article can only be used to calculate the best combination of directly related items (data included in the same order).

To calculate the combination of indirectly associated items (for example, if user A bought item 1 and item 2 and user B bought item 2 and item 3, item 1 and item 3 have an indirect relationship), you need to use the recommendation algorithm in RecDB or use a similar graph search method.

3.  Alibaba Cloud HybridDB for PostgreSQL provides the MPP feature to support horizontal scaling, which is very suitable for OLAP scenarios. For example, the "group by" operation which is used many times in this case can result in significant performance improvement.

4.  The CPU-based multi-core parallel computing is added in PostgreSQL 9.6 and can significantly improve performance in OLAP scenarios. For example, the "group by" operation which is used many times in this case can have significant performance improvement.

References

https://github.com/DataSystemsLab/recdb-postgresql

https://www.ibm.com/developerworks/cn/web/1103_zhaoct_recommstudy1/index.html

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