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Rule discovery strategies LERS & ERID

Rule discovery strategies LERS & ERID. System LERS ( L earning from E xamples based on R ough S ets). I nput data is represented as a decision table. In the decision table examples are described by values of attributes and characterized by a value of a decision .

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Rule discovery strategies LERS & ERID

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  1. Rule discovery strategies LERS & ERID Lecture 2

  2. System LERS (Learning from Examples based onRoughSets) Input data is represented as a decision table. In the decision table examples are described by values of attributes and characterized by a value of a decision. All examples with the same value of the decision belong to the same concept. This system looks for regularities in the decision table. Lecture 2

  3. System LERS (Learning from Examples based onRoughSets) • The first implementation of LERS was done byJohn S. Dean and Douglas J. Sikora in 1988. • Other important steps were: • -adding two modules of LEM (Learning from Examples Module): module LEM1, module LEM2, • -improvements in the basic algorithm, • -implementation, and the fundamental • implementation. Lecture 2

  4. System LERS (Learning from Examples based onRoughSets) • has two main options of rule induction, which are: • a basic algorithm, invoked by selecting Induce Rules from the menu Induce Rule Set (LEM 2). • This algorithm works on the level of attribute-value pairs. A local covering for each of the concepts is computed Lecture 2

  5. System LERS (Learning from Examples based onRoughSets) has two main options of rule induction, which are: 2. the option Induce Rules Using Priorities on Concept Level,of the menu Induce Rule Set working on entire attributes (LEM 1). Lecture 2

  6. Algorithm (LEM 1) Letbe the information system. Lecture 2

  7. Algorithm (LEM 1) Letbe the information system. Classification attributes Lecture 2

  8. Algorithm (LEM 1) Letbe the information system. Decision attribute Lecture 2

  9. Algorithm (LEM 1) Letbe the information system. The partitions of X, generated by single attributes are: Let C be the set containing of one attribute {f}: Lecture 2

  10. Algorithm (LEM 1) Letbe the information system. The partitions of X, generated by single attributes are: Let C be the set containing of one attribute {f}: None of the sets is a subset of {f}* Lecture 2

  11. Algorithm (LEM 1) Letbe the information system. forming two item sets: Lecture 2

  12. Algorithm (LEM 1) Letbe the information system. marked Lecture 2

  13. Algorithm (LEM 1) Letbe the information system. marked, but not covering of f Lecture 2

  14. Algorithm (LEM 1) Letbe the information system. All of the sets are marked! The coverings of C are: Lecture 2

  15. How tofind rules fromcoverings ? Lecture 2

  16. Algorithm (LEM 1) Letbe the information system. Covering {a,b} marked Lecture 2

  17. Algorithm (LEM 1) Letbe the information system. Covering {a,b} marked Lecture 2

  18. Algorithm (LEM 1) Letbe the information system. Covering {a,b} Certain rules, obtained from marked items: Lecture 2

  19. Algorithm (LEM 1) Letbe the information system. Covering {a,b} Possible rules, obtained from non-marked items: with confidence ½ with confidence ½ with confidence ½ with confidence ½ Lecture 2

  20. New Rule Discovery Method for Incomplete IS New strategy for discovering rules from incomplete information systems We allow to use not only sets of attribute values as values of an object but also we allow to assign a weight to each value in such set. Lecture 2

  21. New Rule Discovery Method for Incomplete IS New strategy for discovering rules from incomplete information systems We allow to use not only sets of attribute values as values of an object but also we allow to assign a weight to each value in such set. the confidence that object x has blue eyes is 2/3, whereas the confidence that x has brown eyes is1/2 Lecture 2

  22. Definition 2.2 2 • Incomplete Information Systemis a triple (X, A, V) where: • X is a nonempty, finite set of objects, • A is a nonempty, finite set of attributes, • is a set of values of attributes, • where Vais a set of values of attribute a, for any • We assume that for each attribute and Null value assigned to an object is interpreted as all possible values of an attribute with equal confidence assigned to all of them. Lecture 2

  23. X a b c d e x1 x2 x3 x4 x5 x6 x7 x8 Extract rules from S describing attribute e in terms of attributes {a,b,c,d} ( following a strategy similar to LERS) Lecture 2

  24. X a b c d e x1 x2 x3 x4 x5 x6 x7 x8 Algorithm ERID (Extracting Rules from partially Incomplete Information System(Database)) Goal: Describe e in terms of {a,b,c,d} Lecture 2

  25. X a b c d e x1 x2 x3 x4 x5 x6 x7 x8 Algorithm ERID for Extracting Rules from partially Incomplete Information System Goal: Describe e in terms of {a,b,c,d} Lecture 2

  26. X a b c d e x1 x2 x3 x4 x5 x6 x7 x8 Algorithm ERID for Extracting Rules from partially Incomplete Information System Goal: Describe e in terms of {a,b,c,d} For the values of the decision attribute we have: Lecture 2

  27. X a b c d e x1 x2 • Check the relationship “ ” between values of classification attributes {a,b,c,d} and values • of decision attribute e x3 x4 x5 x6 x7 x8 Algorithm ERID for Extracting Rules from partially Incomplete Information System Goal: Describe e in terms of {a,b,c,d} Lecture 2

  28. X a b c d e x1 x2 x3 x4 x5 x6 x7 x8 Algorithm ERID for Extracting Rules from partially Incomplete Information System Goal: Describe e in terms of {a,b,c,d} Let , . We say that: support iff and confidence of the rule are above some threshold values. Lecture 2

  29. X a b c d e x1 x2 x3 x4 x5 x6 x7 x8 Algorithm ERID for Extracting Rules from partially Incomplete Information System Goal: Describe e in terms of {a,b,c,d} How to define support and confidence of a rule ? Let , . We say that: support iff and confidence of the rule are above some threshold values. Lecture 2

  30. Definition of Support and Confidence (by example) To define support and confidence of the rule a1 e3we compute: Support of the rule: Support of the term a1: Confidence of the rule: Lecture 2

  31. X a b c d e x1 x2 x3 x4 x5 x6 x7 x8 Extracting Rules from partially Incomplete Information System(Algorithm ERID(λ1, λ2)) Goal: Describe e in terms of {a,b,c,d} Thresholds (provided by user): Minimal support (λ1 = 1) Minimal confidence (λ2 = ½) - marked negative - marked negative - marked positive Lecture 2

  32. X a b c d e x1 x2 x3 x4 x5 x6 x7 x8 Extracting Rules from partially Incomplete Information System(Algorithm ERID(λ1, λ2)) but but but but but but but but but Lecture 2

  33. X a b c d e x1 x2 x3 x4 x5 x6 x7 x8 Extracting Rules from partially Incomplete Information System(Algorithm ERID(λ1, λ2)) but but but but but but but but but They all are not marked Lecture 2

  34. X a b c d e x1 x2 x3 x4 x5 x6 x7 x8 Extracting Rules from partially Incomplete Information System(Algorithm ERID(λ1, λ2)) and and Lecture 2

  35. X a b c d e x1 x2 x3 x4 x5 x6 x7 x8 Extracting Rules from partially Incomplete Information System(Algorithm ERID(λ1, λ2)) and and They all are marked positive Lecture 2

  36. X a b c d e x1 x2 x3 x4 x5 x6 x7 x8 Extracting Rules from partially Incomplete Information System(Algorithm ERID(λ1, λ2)) and and They all are marked positive They all are marked negative Lecture 2

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