Association Rule Mining Constraint Based Association Rule Mining

1. Association Rule MiningConstraint Based Association Rule Mining S.P.Vimal Assistant Lecturer CSIS/BITS-Pilani vimalsp@bits-pilani.ac.in

2. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 2 To discuss� Constraint Based Association Rule Mining Concepts Metarule-Guided Rule mining Constraint pushing Types of rule constraints antimonotonic monotonic succinct convertible inconvertible

3. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 3 Constraint Based Rule Mining - Concepts Constraints ? Users expectation or intuition helps confine the search space Forms of constraints Knowledge type constraints Data constraints Dimension / Level constraints Interestingness constraints Rule constraints

4. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 4 Constraint Based Rule Mining - Concepts Rule constraints ? Specify the �form of the rules� Rules take the form Rule Template / Meta Rule Set/subset relationships of attributes mined, aggregates etc. �Mining query optimizer� must be incorporated in the mining process to exploit the constraints specified

5. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 5 Constraint Based Rule Mining - Metarule-Guided Specifies the syntactic form of the rules, interested Syntactic forms serves as the constraint Based on analysts experience, expectation, or intuition regarding data To analyze the customers traits leading to the purchase of office software, meta rule will be P1(X,Y) ? P2(X,Z) ? buys (X, �office software�) where P1,P2 are the predicates on customer X

6. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 6 Constraint Based Rule Mining - Metarule-Guided Data mining system searches for the rule of the form that matches the meta rule given For ex. The rule generated matching the given metarule is age (X, �30..40�) ? income (X, �30K..50K�) ? buys (X, �office software�)

7. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 7 Constraint Based Rule Mining - Metarule-Guided Consider the template P1 ? P2 ? � ? Pl ? Q1 ? Q2 ?� ? Qr Each Pi�s and Qj�s are predicates (instantiated / variables) and l + r = p To mine for the rules satisfying this template Find all frequent p-predicate sets, Lp Find support & confidence of Lp

8. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 8 Constraint Based Rule Mining - Constraint Pushing Allows pushing constraints deep into mining process to confine the search space, assuring the completeness of the result as well Rule constraints specified as expected set/subset relationship of the variables involved, aggregate functions etc Can be used in conjunction with metarule-guided mining

9. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 9 Constraint Based Rule Mining - Constraint Pushing Look at the following scenario A datawarehouse with Fact table : sales (cust_name, item_name, TID) Dimension Tables : lives_in (cust_name, region, city) item (item_name, region, city) transaction (TID, day, month, year) And the mining query �Find the sales of which cheap items (price<100$) promote sales of expensive items (price>500$) of the same group for delhi customers in 2004�

10. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 10 Constraint Based Rule Mining - Constraint Pushing The DMQL query above case would be mine association as lives_in(C,_, �delhi�) ? sales+ (C, ?{ I}, {S}) ? sales+ (C, ?{ I}, {S} ) from sales where S.year=2004 and T.year=2004 and I.group=J.group group by C, I.group having sum(I.price) < 100 and min (J.price)>500 with support threshold = 1% with confidence threshold = 50%

11. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 11 Constraint Based Rule Mining - Constraint Pushing From this DMQL Query we can deduce the following constraints specified Meta Rule : Line 2 Knowledge constraint : Line 1 Data constraint : Line 3, line2 Level constraint : Line 2 Rule constraint : Line 4 and Line6 Interestingness Constraint : Line 8

12. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 12 Constraint Based Rule Mining - Types of Rule Constraints Rule constraints can be categorized as antimonotonic monotonic succinct convertible inconvertible Ensures completeness of result while pushing these rules deep into the mining process

13. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 13 Constraint Based Rule Mining - Types of Rule Constraints antimonotonic �if a itemset does not satisfy the rule constraint, then none of its supersets satisfy� , property of antimonotonic rules example : sum ( I.price >100) count ( I ) < 100 avg ( I ) < 250 is not antimonotonic Note, apriori property is antimonotonic.

14. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 14 Constraint Based Rule Mining - Types of Rule Constraints monotonic �if a itemset satisfy the rule constraint, then all of its supersets satisfy� , property of monotonic rules Example : sum (I.price) > 100 v ? S min(S) = V is not monotonic Once the subset satisfies this property, further testing for this rule is redundant

15. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 15 Constraint Based Rule Mining - Types of Rule Constraints succinct �All and only those set guaranteed to satisfy the rule can be enumerated� Property of succinct rules The itemsets can be generated that satisfy the rule even before the support count starts Once such subset is generated, iterative testing for the constraint can be effectively avoided Example : min(J.price) > 500 max(S) < 120 avg(S) > v , avg(S) <v are not succinct

16. 15/Sep/2006 04:00 PM S.P.Vimal, CS IS Group, BITS-Pilani 16 Constraint Based Rule Mining - Types of Rule Constraints convertible constraints Constraints not satisfying to any of antimonotonic, monotonic, succinct can be made to satisfy antimonotonic, monotonic constraints by changing order of elements in the set Ex : Avg(price) < 100 Inconvertible Constraints which are not convertible Ex : Sum(S) < v , sum (S) > V , element of set S could be any real value