Constraint-Based Mining: Where Data Management Meets Optimization

1. CPS 196.03: Information Management and Mining Constraint-based Mining, First programming project

2. Where we are headed • First programming project: • On constraint-based association rule mining • Month-long, demo and report, 15% of grade • Due: March 2 • Data warehousing • Multi-billion dollar industry, fast growing • Web data management and mining

3. Constraint-based (Query-Directed) Mining • Let us start with an example • Sales(customer_id, item_id, date) • Lives_in(customer_id, city, state) • Items(item_id, group, price)

4. Constraint-based (Query-Directed) Mining • Finding all the patterns in a database autonomously? — unrealistic! • The patterns could be too many but not focused! • Data mining should be an interactive process • User directs what to be mined using a data mining query language (or a graphical user interface) • Constraint-based mining • User flexibility: provides constraints on what to be mined • System optimization: explores such constraints for efficient mining—constraint-based mining

5. Constraints in Data Mining • Knowledge type constraint: • classification, association, etc. • Data constraint • find product pairs sold to Chicago customers in 2004 • Dimension/level constraint • in relevance to region, price, brand, customer category • Rule (or pattern) constraint • small sales (price < $10) trigger big sales (sum > $200) • Interestingness constraint • strong rules: min_support  3%, min_confidence  60%

6. Constrained Mining vs. Constraint-Based Search • Constrained mining vs. constraint-based search/reasoning • Both are aimed at reducing search space • Finding all patterns satisfying constraints vs. finding some (or one) answer in constraint-based search in AI or optimization • Constrained mining vs. query processing in DBMS • Constrained pattern mining shares a similar philosophy as pushing selections deeply in query processing

7. Anti-Monotonicity in Constraint Pushing TDB (min_sup=2) • Anti-monotonicity • When an itemset S violates the constraint, so does any of its superset • sum(S.Price)  v is anti-monotone • sum(S.Price)  v is not anti-monotone • Example. C: range(S.profit)  15 is anti-monotone • Itemset ab violates C • So does every superset of ab

8. Monotonicity for Constraint Pushing TDB (min_sup=2) • Monotonicity • When an itemset S satisfies the constraint, so does any of its superset • sum(S.Price)  v is monotone • min(S.Price)  v is monotone • Example. C: range(S.profit)  15 • Itemset ab satisfies C • So does every superset of ab

9. Succinctness • Succinctness: • Given A1, the set of items satisfying a succinctness constraint C, then any set S satisfying C is based on A1 , i.e., S contains a subset belonging to A1 • Idea: Without looking at the transaction database, whether an itemset S satisfies constraint C can be determined based on the selection of items • min(S.Price) v is succinct • sum(S.Price)  v is not succinct • Optimization: If C is succinct, C is pre-counting pushable

10. The Apriori Algorithm — Example Database D L1 C1 Scan D C2 C2 L2 Scan D L3 C3 Scan D

11. Naïve Algorithm: Apriori + Constraint Database D L1 C1 Scan D C2 C2 L2 Scan D L3 C3 Constraint: Sum{S.price} < 5 Scan D

12. The Constrained Apriori Algorithm: Push an Anti-monotone Constraint Deep Database D L1 C1 Scan D C2 C2 L2 Scan D L3 C3 Constraint: Sum{S.price} < 5 Scan D

13. The Constrained Apriori Algorithm: Push a Succinct Constraint Deep Database D L1 C1 Scan D C2 C2 L2 Scan D not immediately to be used L3 C3 Constraint: min{S.price } <= 1 Scan D

14. Converting “Tough” Constraints TDB (min_sup=2) • Convert tough constraints into anti-monotone or monotone by properly ordering items • Examine C: avg(S.profit)  25 • Order items in value-descending order • <a, f, g, d, b, h, c, e> • If an itemset afb violates C • So does afbh, afb* • It becomes anti-monotone!

15. Strongly Convertible Constraints • avg(X)  25 is convertible anti-monotone w.r.t. item value descending order R: <a, f, g,d, b, h, c, e> • If an itemset af violates a constraint C, so does every itemset with af as prefix, such as afd • avg(X)  25 is convertible monotone w.r.t. item value ascending order R-1: <e, c, h, b, d, g, f, a> • If an itemset d satisfies a constraint C, so does itemsets df and dfa, which having d as a prefix • Thus, avg(X)  25 is strongly convertible

16. Can Apriori Handle Convertible Constraints? • A convertible, not monotone nor anti-monotone nor succinct constraint cannot be pushed deep into the an Apriori mining algorithm • Within the level wise framework, no direct pruning based on the constraint can be made • Itemset df violates constraint C: avg(X)>=25 • Since adf satisfies C, Apriori needs df to assemble adf, df cannot be pruned • But it can be pushed into frequent-pattern growth framework!

17. Mining With Convertible Constraints • C: avg(X) >= 25, min_sup=2 • List items in every transaction in value descending order R: <a, f, g, d, b, h, c, e> • C is convertible anti-monotone w.r.t. R • Scan TDB once • remove infrequent items • Item h is dropped • Itemsets a and f are good, … • Projection-based mining • Imposing an appropriate order on item projection • Many tough constraints can be converted into (anti)-monotone TDB (min_sup=2)

18. Recall • Traversal of Itemset Lattice

19. Handling Multiple Constraints • Different constraints may require different or even conflicting item-ordering • If there exists an order R s.t. both C1 and C2 are convertible w.r.t. R, then thereis no conflict between the two convertible constraints

20. What Constraints Are Convertible?

21. Constraint-Based Mining—A General Picture

22. Monotone Antimonotone Strongly convertible Succinct Convertible anti-monotone Convertible monotone Inconvertible A Classification of Constraints

23. Visualization of Association Rules: Plane Graph

24. Visualization of Association Rules: Rule Graph

25. Visualization of Association Rules (SGI/MineSet 3.0)

26. First Programming Project • Individual project, 15 Points in final grade • Sales(customer_id, item_id, item_group, item_price, purchase_date) • Will be provided as a file during demo and for generating performance numbers for project report • Task 1: 5 Points • Interface to enter MIN_SUPPORT (% of customers) • Find frequent itemsets using Apriori (set of item_id’s) • Task 2: 5 Points (Section 5.5 in the textbook) • Interface to enter two constraint types (e.g., SUM(item_price) op const) • Use the constraints in Apriori as effectively as possible, study and demonstrate performance improvement • Task 3: 5 Points • Extension of your choice. Examples include (i) association rules, (ii) complex constraints, (iii) sequential patterns, (iv) variants of apriori, (v) FP-growth

27. First Programming Project: Milestones • Feb 3: Project announced • Feb 17: Mid-project report due • Describe progress and planned extensions • Describe detailed algorithms for all three tasks • Feb 17: Sample data file will be provided for generating performance results for project report • March 2: Submit code, README file to run code, code documentation, and final project report • March 2-4: Project demos (random assignment) • March 6: Spring break. Second project announced

28. Finalized Grading Criteria for Class • Homeworks: 15 points • Programming projects: 40 points • Midterm: 20 points • Note: Midterm is on Feb 19 (Thu) in class • Final: 25 Points