CSE4334/5334 DATA MINING CSE4334/5334 Data Mining, Fall 2014 Lecture 15: Association Rule Mining (2) Department of Computer Science and Engineering, University of Texas at Arlington Chengkai Li (Slides courtesy of Vipin Kumar and Jiawei Han) Pattern Evaluation Pattern Evaluation Association rule algorithms tend to produce too many rules many of them are uninteresting or redundant Redundant if {A,B,C} {D} and {A,B} {D} have same support & confidence Interestingness measures can be used to prune/rank the derived patterns In the original formulation of association rules, support & confidence are the only measures used 3
There are lots of measures proposed in the literature Some measures are good for certain applications, but not for others What criteria should we use to determine whether a measure is good or bad? What about Aprioristyle support based pruning? How does it affect these measures? 4 Computing Interestingness Measure Given a rule X Y, information needed to compute rule interestingness can be obtained from a contingency table Contingency table for X Y Y
Y X f11 f10 f1+ X f01 f00 fo+ f+1 f+0 |T| f11: count of X and Y f10: count of X and Y f01: count of X and Y f00: count of X and Y Used to define various measures support, confidence, lift, Gini, J-measure, etc.
5 Drawback of Confidence Coffee Coffee Tea 15 5 20 Tea 75 5 80 90 10 100 Association Rule: Tea Coffee Confidence= P(Coffee|Tea) = 0.75 but P(Coffee) = 0.9
Although confidence is high, rule is misleading P(Coffee|Tea) = 0.9375 6 Statistical Independence Population of 1000 students 600 students know how to swim (S) 700 students know how to bike (B) 420 students know how to swim and bike (S,B) P(SB) = 420/1000 = 0.42 P(S) P(B) = 0.6 0.7 = 0.42 P(SB) = P(S) P(B) => Statistical independence P(SB) > P(S) P(B) => Positively correlated P(SB) < P(S) P(B) => Negatively correlated 7 Statistical-based Measures Measures that take into account statistical dependence
conf ( X Y ) P (Y | X ) Lift sup(Y ) P (Y ) Interest _ factor coefficient P( X , Y ) P ( X ) P (Y ) = 1, independent > 1, positively correlated < 1, negatively correlated = 0, independent P ( X , Y ) P ( X ) P (Y ) > 0, positively correlated P ( X )[1 P ( X )]P (Y )[1 P (Y )]< 0, negatively correlated 8 Example: Lift/Interest Coffee Coffee Tea 15 5
20 Tea 75 5 80 90 10 100 Association Rule: Tea Coffee Confidence= P(Coffee|Tea) = 0.75 but P(Coffee) = 0.9 Lift = 0.75/0.9= 0.8333 (< 1, therefore is negatively associated) 9 Drawback of Lift & Interest Y Y X 10
0 10 X 0 90 90 10 90 100 0.1 Lift 10 (0.1)(0.1) Y Y X 90 0
90 X 0 10 10 90 10 100 0.9 Lift 1.11 (0.9)(0.9) Statistical independence: If P(X,Y)=P(X)P(Y) => Lift = 1 10 Example: -Coefficient Coffee Coffee Tea 15 5
20 Tea 75 5 80 90 10 100 Association Rule: Tea Coffee 0.15 0.9 0.2 0.9 0.1 0.2 0.8 0.25(< 0, therefore is negatively correlated) 11 Drawback of -Coefficient Y Y X
60 10 70 X 10 20 30 70 30 100 0.6 0.7 0.7 0.7 0.3 0.7 0.3 0.5238 Y Y X 20 10
30 X 10 60 70 30 70 100 0.2 0.3 0.3 0.7 0.3 0.7 0.3 0.5238 Coefficient is the same for both tables 12