Positional Association Rules

1. Positional Association Rules Dr. Bernard Chen Ph.D. University of Central Arkansas Fall 2010

2. Motivation • In order to obtain the DNA/protein sequence motifs information, fixing the length of sequence segments is usually necessary. • Due to the fixed size, they might deliver a number of similar motifs simply shifted by several bases or including mismatches

3. Example • If there exists a biological sequence motif with length of 12 and we set the window size to 9, it is highly possible that we discovered two similar sequence motifs where one motif covers the front part of the biological sequence motif and the other one covers the rear part.

4. Positional Association Rules • The basic association rule gives the information of A => B • However, under the circumstances of the “order” involved with the appearance of items, the basic association rule is not powerful enough • we introduce another parameter called “distance assurance” to help identify frequent itemset with frequent distance

5. Positional Association Rules

6. Pseudocode of Positional Association Rule with the Apriori concept Algorithm: Positional Association Rule with the Apriori Concept Input: Database, D, (Protein sequences as Transactions and Sequence Motifs as items), min_support, min_confidence, and min_distance_assurance Output: P, positional association rules in D Method: L = find_frequent_itemsets(D, min_support) S = find_strong_association_rules(L, min_confidence) for (k=2; Sk ≠ Ø; k++ ) for each strong association rule, r Sk antecedent_motif = Apriori_Motif_Construct(r_ant) consequence_motif = Apriori_Motif_Construct(r_con) if antecident_motif == NULL or consequence_motif == NULL: goto Step (4) for each protein sequence, ps D for (ant_position=1; |ps| ; ant_position++) if antecedent_motif start appear on ps[ant_position]: r_ant_count++ for (con_position=1; |ps| ; con_position++) if consequent_motif start appear on ps[con_position]: distance = ant_position – con_position rdistance ++ Pk = { rdistance | rdistance > min_distance_assurance * r_ant_count } Apriori_Motif_Construct(itemset) if |itemset| == 1: return itemset else: for each positional association rules in P|itemset| if all items in the itemset appear in the positional association rule: return the new motif constructed by the positional association rule return NULL

7. Positional Association Rules Example

8. Positional Association Rules Example • minimum support = 60%, • minimum confidence = 80%, • minimum distance assurance = 60%

9. minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60% • Scan for C1 A: 3/5 A B: 5/5 B C: 2/5 => => AB, AD, BD D: 4/5 D E: 1/5

10. minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60% • Scan for C2 AB: 3/5 AB AD: 3/5 => AD => ABD BD: 4/5BD

11. minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60% • Scan for C3 ABD: 3/5 => ABD => no C4

12. minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60% • Therefore, the itemset that pass support: {AB, AD, BD, ABD} • Next, we need to compute their confidence

13. minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60% • First, we work on 2-itemset: {AB,AD,BD} A=>B: 3/3 B=>A: 3/5 A=>D: 3/3 D=>A: 3/4 B=>D: 4/5 D=>B: 4/4

14. minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60% • then, we work on 3-itemset: {ABD} A=>BD: 3/3 B=>AD: 3/5 D=>AB: 3/4 AB=>D: 3/3 AD=>B: 3/3 BD=>A: 3/4

15. minimum support = 60%, minimum confidence = 80%, minimum distance assurance = 60% • Thus, the strong association rules we have: 2-itemset 3-itemset A=>B A=>BD A=>D AB=>D B=>D AD=>B D=>B Next, we work on Positional Association rules…

16. Positional Association Rules D=>Bminimum distance assurance = 60% 1.= 3/4 3. =1/4 2. = 1/4

17. Positional Association Rules B=>Dminimum distance assurance = 60% 1.= 3/6 3. = 1/6 2. = 1/6

18. Positional Association Rules A=>Bminimum distance assurance = 60% 1.= 2/4 3. = 1/4 2. = 1/4 4. = 1/4

19. Positional Association Rules A=>Dminimum distance assurance = 60% 1.= 3/4 2. = 1/4

20. Positional Association Rules AD=>Bminimum distance assurance = 60% 1.= 2/3 2. = 1/3

21. Positional Association Rules AB=>Dminimum distance assurance = 60% NO Positional Association Rules on AB !!!

22. Positional Association Rules A=>BDminimum distance assurance = 60% 1.= 2/4 2. = 1/4

23. Strong Association Rules are not necessary interesting Dr. Bernard Chen Ph.D. University of Central Arkansas Fall 2010

24. Example 5.8 Misleading “Strong” Association Rule • Of the 10,000 transactions analyzed, the data show that • 6,000 of the customer included computer games, • while 7,500 include videos, • And 4,000 included both computer games and videos

25. Misleading “Strong” Association Rule • For this example: • Support (Game & Video) = 4,000 / 10,000 =40% • Confidence (Game => Video) = 4,000 / 6,000 = 66% • Suppose it pass our minimum support and confidence (30% , 60%, respectively)

26. Misleading “Strong” Association Rule • However, the truth is : “computer games and videos are negatively associated” • Which means the purchase of one of these items actually decreases the likelihood of purchasing the other. • (How to get this conclusion??)

27. Misleading “Strong” Association Rule • Under the normal situation, • 60% of customers buy the game • 75% of customers buy the video • Therefore, it should have 60% * 75% = 45% of people buy both • That equals to 4,500 which is more than 4,000 (the actual value)

28. From Association Analysis to Correlation Analysis • Lift is a simple correlation measure that is given as follows • The occurrence of itemset A is independent of the occurrence of itemset B if P(AUB) = P(A)P(B) • Otherwise, itemset A and B are dependent and correlated as events • Lift(A,B) = P(AUB) / P(A)P(B) • If the value is less than 1, the occurrence of A is negatively correlated with the occurrence of B • If the value is greater than 1, then A and B are positively correlated

29. Χ2 (chi-square) test