Apriori Itemset Generation With Oracle SQL

The Apriori Principle is given by the following description:

If an itemset is frequent, then all of its subsets must also be frequent. Conversely, if a subset is infrequent, then all of its supersets must be infrequent too.

In this article, I have tried to generate the most frequent items with Oracle SQL.

The data used in this article is given below:

First, I created a table named "APR_ITEMS_BOUGHT" with the following script and manually inserted the data into the table:

CREATE TABLE APR_ITEMS_BOUGHT
(
TID NUMBER,
ITEMS VARCHAR2(50)
)

After creating the table above, the itemsets are inserted in columns to a new table. The script for generating the table is:

CREATE TABLE APRIORI 
(
    TID NUMBER,
    ITEM_A varchar2(10),
    ITEM_B varchar2(10),
    ITEM_C varchar2(10),
    ITEM_D varchar2(10),
    ITEM_E varchar2(10),
    ITEM_F varchar2(10)
)

Finding the frequent itemsets has two steps:

• Generating candidate items set
• Generating frequent items set

Now the itemset generation can be started. The first candidate table "C1" is created in the following script;

create table C1 AS
SELECT ITEM ITEM_1, CNT, ALL_CNT FROM (
    select 'A' ITEM, SUM(CASE WHEN ITEM_A = 'A' THEN 1 ELSE 0 END) CNT, COUNT(*) ALL_CNT 
  from apriori
    UNION ALL
    select 'B' ITEM, SUM(CASE WHEN ITEM_B = 'B' THEN 1 ELSE 0 END) CNT, COUNT(*) ALL_CNT 
  from apriori
    UNION ALL
    select 'C' ITEM, SUM(CASE WHEN ITEM_C = 'C' THEN 1 ELSE 0 END) CNT, COUNT(*) ALL_CNT 
  from apriori
    UNION ALL
    select 'D' ITEM, SUM(CASE WHEN ITEM_D = 'D' THEN 1 ELSE 0 END) CNT, COUNT(*) ALL_CNT 
  from apriori
    UNION ALL
    select 'E' ITEM, SUM(CASE WHEN ITEM_E = 'E' THEN 1 ELSE 0 END) CNT, COUNT(*) ALL_CNT 
  from apriori
    UNION ALL
    select 'F' ITEM, SUM(CASE WHEN ITEM_F = 'F' THEN 1 ELSE 0 END) CNT, COUNT(*) ALL_CNT 
  from apriori    
)

Then the frequent itemset is created. I choose min support and min confidence values as:

• Min support %40
• Min confidence %60

create table F1 AS
SELECT ITEM_1, SUPPORT, CNT FROM (
    SELECT ITEM_1, CNT / ALL_CNT SUPPORT, CNT FROM C1
)
WHERE SUPPORT >= 0.4 --PRUNING

The result of both the "C1" and "F1" sets are shown below;

The C1 table has three columns: ITEM column gives the items in the market basket, CNT column gives how many transactions the item has, and ALL_CNT column gives all transactions count. After pruning with a %40 support value, we are left with the following frequent itemsets:

The F1 table has also three columns: the ITEM column, SUPPORT value for each column, and the transaction count in the CNT column.

For the second itemset generation and frequent itemset, the pruned F1 table will be used.

CREATE TABLE APRIORI_VERTICAL AS
SELECT TID, ITEM_A ITEM FROM APRIORI A
WHERE ITEM_A <> '0'
UNION ALL
SELECT TID, ITEM_B ITEM FROM APRIORI A
WHERE ITEM_B <> '0'
UNION ALL
SELECT TID, ITEM_C ITEM FROM APRIORI A
WHERE ITEM_C <> '0'
UNION ALL
SELECT TID, ITEM_D ITEM FROM APRIORI A
WHERE ITEM_D <> '0'
UNION ALL
SELECT TID, ITEM_E ITEM FROM APRIORI A
WHERE ITEM_E <> '0'
UNION ALL
SELECT TID, ITEM_F ITEM FROM APRIORI A
WHERE ITEM_F <> '0'

CREATE TABLE FREQ_ITEM_2 AS 
SELECT A.ITEM_1, B.ITEM_1 ITEM_2 
FROM F1 A , F1 B
WHERE A.ITEM_1 < B.ITEM_1

CREATE TABLE C2 AS
SELECT Z.ITEM_1 ITEM_1, Z.ITEM_2 ITEM_2, CNT, REC_CNT ALL_CNT, FIRST_INSTANCE_COUNT
FROM
(
    SELECT C.ITEM_1, C.ITEM_2, COUNT(DISTINCT C.TID) CNT
    FROM
    (
        SELECT * FROM FREQ_ITEM_2
    ) X
    INNER JOIN 
    (
        SELECT A1.TID, A1.ITEM ITEM_1, A2.ITEM ITEM_2
        FROM APRIORI_VERTICAL A1 CROSS JOIN APRIORI_VERTICAL A2 
        WHERE A1.TID = A2.TID
        AND A1.ITEM < A2.ITEM  
    ) C 
    ON X.ITEM_1 = C.ITEM_1 AND X.ITEM_2 = C.ITEM_2
    GROUP BY C.ITEM_1, C.ITEM_2
) Z
CROSS JOIN 
(
    SELECT COUNT(*) REC_CNT 
    FROM
    (
        SELECT * FROM FREQ_ITEM_2
    ) Z    
) D
INNER JOIN 
(
    SELECT A.ITEM_1, COUNT(DISTINCT TID) FIRST_INSTANCE_COUNT
    FROM FREQ_ITEM_2 A , APRIORI_VERTICAL B
    WHERE A.ITEM_1 = B.ITEM
    GROUP BY A.ITEM_1
) E ON Z.ITEM_1 = E.ITEM_1

F2 table

CREATE TABLE F2 AS
SELECT ITEM_1, ITEM_2, SUPPORT, CONFIDENCE, CNT FROM (
    SELECT ITEM_1, ITEM_2, TRUNC(CNT / ALL_CNT,2) SUPPORT, TRUNC(CNT / FIRST_INSTANCE_COUNT,2) CONFIDENCE, CNT FROM C2
)
WHERE SUPPORT >= 0.4 --PRUNING
OR CONFIDENCE >= 0.6 --PRUNING

After creating the F2 table, we are left with the following records, which means the most frequent couples:

The most frequent items for the third step:

CREATE TABLE FREQ_ITEM_3 AS
SELECT A.ITEM_1 ITEM_1, A.ITEM_2 ITEM_2, B.ITEM_2 ITEM_3  
FROM 
    F2 A, F2 B
WHERE A.ITEM_1 = B.ITEM_1
AND A.ITEM_2 < B.ITEM_2
order by A.ITEM_1, A.ITEM_2, B.ITEM_2

The 3rd C3 table:

create table C3 AS
SELECT Z.ITEM_1 ITEM_1, Z.ITEM_2 ITEM_2, Z.ITEM_3 ITEM_3, CNT, REC_CNT ALL_CNT, FIRST_INSTANCE_COUNT
FROM
(
    SELECT C.Item_1, C.ITEM_2, C.ITEM_3, COUNT(DISTINCT C.TID) CNT
    FROM
    (
        SELECT * FROM FREQ_ITEM_3
    ) X
    INNER JOIN 
    (
        SELECT A1.TID, a1.item ITEM_1, a2.item ITEM_2, A3.ITEM ITEM_3
        FROM APRIORI_VERTICAL A1 
        CROSS JOIN APRIORI_VERTICAL A2
        CROSS JOIN APRIORI_VERTICAL A3 
        where A1.TID = A2.TID
        AND A1.TID = A3.TID
        AND A1.ITEM < A2.ITEM
        AND A1.ITEM < A3.ITEM    
        AND A2.ITEM < A3.ITEM
    ) C 
    ON X.ITEM_1 = C.ITEM_1 AND X.ITEM_2 = C.ITEM_2 AND X.ITEM_3 = C.ITEM_3
    GROUP BY C.ITEM_1, C.ITEM_2, C.ITEM_3
) Z
CROSS JOIN 
(
    select COUNT(*) REC_CNT 
    FROM
    (
        SELECT * FROM FREQ_ITEM_3
    ) Z    
) D
INNER JOIN 
(
    SELECT A.ITEM_1, A.ITEM_2, COUNT(DISTINCT B.TID) FIRST_INSTANCE_COUNT
    FROM FREQ_ITEM_3 A , APRIORI_VERTICAL B, APRIORI_VERTICAL C 
    WHERE A.ITEM_1 = B.ITEM
    AND A.ITEM_2 = C.ITEM
    AND B.TID = C.TID
    GROUP BY A.ITEM_1, A.ITEM_2
) E ON Z.ITEM_1 = E.ITEM_1 AND Z.ITEM_2 = E.ITEM_2 

The 3rd pruning step for frequent itemsets, the F1 table:

create table F3 AS
SELECT ITEM_1, ITEM_2, ITEM_3, SUPPORT, CONFIDENCE, CNT FROM (
    SELECT ITEM_1, ITEM_2, ITEM_3, TRUNC(CNT / ALL_CNT,2) SUPPORT, TRUNC(CNT / FIRST_INSTANCE_COUNT,2) CONFIDENCE, CNT FROM C3
)
WHERE SUPPORT >= 0.4 --PRUNING
OR CONFIDENCE >= 0.6 --PRUNING

In the 4th step, there is no data in the frequent itemset table:

CREATE TABLE FREQ_ITEM_4 AS
SELECT A.ITEM_1 I1, A.ITEM_2 I2, a.ITEM_3, b.item_3 ITEM_4 
FROM 
    F3 A 
    , F3 B
WHERE A.ITEM_1 = B.ITEM_1
AND A.ITEM_2 = B.ITEM_2
AND A.ITEM_3 < B.ITEM_3
order by A.ITEM_1, A.ITEM_2, a.ITEM_3, b.item_3

So we can conclude that the most frequent itemsets are:

Let me know your thoughts in the comments below.