1. © Vipin Kumar CSci 8980 Fall 2002 1 CSci 8980: Data Mining (Fall 2002) Vipin Kumar Army High Performance Computing Research Center Department of Computer Science University of Minnesota http://www.cs.umn.edu/~kumar

2. © Vipin Kumar CSci 8980 Fall 2002 2 Rule-Based Classifiers l Classify instances by using a collection of “if…then…” rules l Rule: (Condition)  y –where Condition is a conjunctions of attributes and y is the class label –LHS: rule antecedent or condition –RHS: rule consequent –Examples of classification rules:  (Blood Type=Warm)  (Lay Eggs=Yes)  Birds  (Taxable Income < 50K)  (Refund=Yes)  Cheat=No

3. © Vipin Kumar CSci 8980 Fall 2002 3 Classifying Instances with Rules l A rule r covers an instance x if the attributes of the instance satisfy the condition of the rule Rule: r: (Age < 35)  (Status = Married)  Cheat=No Instances: x1: (Age=29, Status=Married, Refund=No) x2: (Age=28, Status=Single, Refund=Yes) x3: (Age=38, Status=Divorced, Refund=No) => Only x1 is covered by the rule r

4. © Vipin Kumar CSci 8980 Fall 2002 4 Rule-Based Classifiers l Rules may not be mutually exclusive –More than one rule may cover the same instance –Solution?  Order the rules  Use voting schemes l Rules may not be exhaustive –May need a default class

5. © Vipin Kumar CSci 8980 Fall 2002 5 Example of Rule-Based Classifier

6. © Vipin Kumar CSci 8980 Fall 2002 6 Advantages of Rule-Based Classifiers l As highly expressive as decision trees l Easy to interpret l Easy to generate l Can classify new instances rapidly l Performance comparable to decision trees

7. © Vipin Kumar CSci 8980 Fall 2002 7 Basic Definitions l Coverage of a rule: –Fraction of instances that satisfy the antecedent of a rule l Accuracy of a rule: –Fraction of instances that satisfy both the antecedent and consequent of a rule (Status=Single)  No Coverage = 40%, Accuracy = 50%

8. © Vipin Kumar CSci 8980 Fall 2002 8 Building Classification Rules l Generate an initial set of rules: –Direct Method:  Extract rules directly from data  e.g.: RIPPER, CN2, Holte’s 1R –Indirect Method:  Extract rules from other classification models (e.g. decision trees).  e.g: C4.5rules l Rules are pruned and simplified l Rules can be ordered to obtain a rule set R l Rule set R can be further optimized

9. © Vipin Kumar CSci 8980 Fall 2002 9 Indirect Method: From Decision Trees To Rules Rules are mutually exclusive and exhaustive Rule set contains as much information as the tree

10. © Vipin Kumar CSci 8980 Fall 2002 10 Rules Can Be Simplified Initial Rule: (Refund=No)  (Status=Married)  No Simplified Rule: (Status=Married)  No

11. © Vipin Kumar CSci 8980 Fall 2002 11 Indirect Method: C4.5rules l Extract rules from an unpruned decision tree l For each rule, r: A  y, –consider an alternative rule r’: A’  y where A’ is obtained by removing one of the conjuncts in A –Compare the pessimistic error rate for r against all r’s –Prune if one of the r’s has lower pessimistic error rate –Repeat until we can no longer improve the generalization error

12. © Vipin Kumar CSci 8980 Fall 2002 12 Indirect Method: C4.5rules l Instead of ordering the rules, order the subsets of rules –Each subset is a collection of rules with the same rule consequent (class) –Compute description length of each subset  Description length = L(error) + g L(model)  g is a parameter that takes into account the presence of redundant attributes in a rule set (default value = 0.5)

13. © Vipin Kumar CSci 8980 Fall 2002 13 Direct Method: Sequential Covering 1. Start from an empty rule 2. Find the conjunct (test condition on attribute) that optimizes certain objective criterion (e.g., entropy or FOIL’s information gain) 3. Remove instances covered by the conjunct 4. Repeat Step (2) and (3) until stopping criterion is met e.g., stop when all instances belong to same class or all attributes have same values.

14. © Vipin Kumar CSci 8980 Fall 2002 14 Example of Sequential Covering

15. © Vipin Kumar CSci 8980 Fall 2002 15 Example of Sequential Covering…

16. © Vipin Kumar CSci 8980 Fall 2002 16 Method for Adding Conjuncts l CN2: –Start from an empty conjunct: {} –Add conjuncts that minimizes the entropy measure: {A}, {A,B}, … –Determine the rule consequent by taking the majority class of instances covered by the rule l RIPPER: –Start from an empty rule: {} => class –Add conjuncts that maximizes FOIL’s information gain measure:  R0: {} => class (empty rule)  R1: {A} => class  Gain(R0, R1) = t [ log (p1/(p1+n1)) – log (p0/(p0 + n0)) ]  where t: number of positive instances covered by both R0 and R1 p0: number of positive instances covered by R0 n0: number of negative instances covered by R0 p1: number of positive instances covered by R1 n1: number of negative instances covered by R1

17. © Vipin Kumar CSci 8980 Fall 2002 17 Direct Method: Sequential Covering… l Use a general-to-specific search strategy l Greedy approach l Unlike decision tree (which uses simultaneous covering), it does not explore all possible paths –Search only the current best path –Beam search: maintain k of the best paths l At each step, –decision tree chooses among several alternative attributes for splitting –Sequential covering chooses among alternative attribute-value pairs

18. © Vipin Kumar CSci 8980 Fall 2002 18 Direct Method: RIPPER l For 2-class problem, choose one of the classes as positive class, and the other as negative class –Learn rules for positive class –Negative class will be default class l For multi-class problem –Order the classes according to increasing class prevalence (fraction of instances that belong to a particular class) –Learn the rule set for smallest class first, treat the rest as negative class –Repeat with next smallest class as positive class

19. © Vipin Kumar CSci 8980 Fall 2002 19 Direct Method: RIPPER l Growing a rule: –Start from empty rule –Add conjuncts as long as they improve FOIL’s information gain –Stop when rule no longer covers negative examples –Prune the rule immediately using incremental reduced error pruning –Measure for pruning: v = (p-n)/(p+n)  p: number of positive examples covered by the rule in the validation set  n: number of negative examples covered by the rule in the validation set –Pruning method: delete any final sequence of conditions that maximizes v

20. © Vipin Kumar CSci 8980 Fall 2002 20 Direct Method: RIPPER l Building a Rule Set: –Use sequential covering algorithm  finds the best rule that covers the current set of positive examples  eliminate both positive and negative examples covered by the rule –Each time a rule is added to the rule set, compute the description length  stop adding new rules when the new description length is d bits longer than the smallest description length obtained so far

21. © Vipin Kumar CSci 8980 Fall 2002 21 Direct Method: RIPPER l Optimize the rule set: –For each rule r in the rule set R  Consider 2 alternative rules: –Replacement rule (r*): grow new rule from scratch –Revised rule(r’): add conjuncts to extend the rule r  Compare the rule set for r against the rule set for r* and r’  Choose rule set that minimizes MDL principle –Repeat rule generation and rule optimization for the remaining positive examples

22. © Vipin Kumar CSci 8980 Fall 2002 22 Example

23. © Vipin Kumar CSci 8980 Fall 2002 23 C4.5 versus C4.5rules versus RIPPER C4.5rules: (Give Birth=No, Can Fly=Yes)  Birds (Give Birth=No, Live in Water=Yes)  Fishes (Give Birth=Yes)  Mammals (Give Birth=No, Can Fly=No, Live in Water=No)  Reptiles ( )  Amphibians RIPPER: (Live in Water=Yes)  Fishes (Have Legs=No)  Reptiles (Give Birth=No, Can Fly=No, Live In Water=No)  Reptiles (Can Fly=Yes,Give Birth=No)  Birds ()  Mammals

24. © Vipin Kumar CSci 8980 Fall 2002 24 C4.5 versus C4.5rules versus RIPPER C4.5 and C4.5rules: RIPPER: