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Lecture 21 Rule discovery strategies LERS & ERID.

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1 Lecture 21 Rule discovery strategies LERS & ERID

2 Lecture 22 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. System LERS (Learning from Examples based on Rough Sets)

3 Lecture 23 System LERS (Learning from Examples based on Rough Sets) - The first implementation of LERS was done by John 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.

4 Lecture 24 has two main options of rule induction, which are: 1.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 System LERS (Learning from Examples based on Rough Sets)

5 Lecture 25 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). System LERS (Learning from Examples based on Rough Sets)

6 Lecture 26 Algorithm (LEM 1) Let be the information system. Xabcdf x100010 x201111 x300010 x401111 x511012 x611012 x722203 x822203

7 Lecture 27 Algorithm (LEM 1) Let be the information system. Classification attributes Xabcdf x100010 x201111 x300010 x401111 x511012 x611012 x722203 x822203

8 Lecture 28 Algorithm (LEM 1) Let be the information system. Decision attribute Xabcdf x100010 x201111 x300010 x401111 x511012 x611012 x722203 x822203

9 Lecture 29 Algorithm (LEM 1) Let be the information system. The partitions of X, generated by single attributes are: Let C be the set containing of one attribute {f}: Xabcdf x100010 x201111 x300010 x401111 x511012 x611012 x722203 x822203

10 Lecture 210 Algorithm (LEM 1) Let be 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}* Xabcdf x100010 x201111 x300010 x401111 x511012 x611012 x722203 x822203

11 Lecture 211 Algorithm (LEM 1) Let be the information system. Xabcdf x100010 x201111 x300010 x401111 x511012 x611012 x722203 x822203 forming two item sets:

12 Lecture 212 Algorithm (LEM 1) Let be the information system. Xabcdf x100010 x201111 x300010 x401111 x511012 x611012 x722203 x822203 marked

13 Lecture 213 Algorithm (LEM 1) Let be the information system. Xabcdf x100010 x201111 x300010 x401111 x511012 x611012 x722203 x822203 marked, but not covering of f

14 Lecture 214 Algorithm (LEM 1) Let be the information system. Xabcdf x100010 x201111 x300010 x401111 x511012 x611012 x722203 x822203 The coverings of C are: All of the sets are marked!

15 Lecture 215 How to find rules from coverings ?

16 Lecture 216 Algorithm (LEM 1) Let be the information system. Xabcdf x100010 x201111 x300010 x401111 x511012 x611012 x722203 x822203 Covering {a,b} marked

17 Lecture 217 Algorithm (LEM 1) Let be the information system. Xabcdf x100010 x201111 x300010 x401111 x511012 x611012 x722203 x822203 Covering {a,b} marked

18 Lecture 218 Algorithm (LEM 1) Let be the information system. Xabcdf x100010 x201111 x300010 x401111 x511012 x611012 x722203 x822203 Covering {a,b} Certain rules, obtained from marked items:

19 Lecture 219 Algorithm (LEM 1) Let be the information system. Xabcdf x100010 x201111 x300010 x401111 x511012 x611012 x722203 x822203 Covering {a,b} Possible rules, obtained from non-marked items: with confidence ½

20 Lecture 220 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.

21 Lecture 221 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 is 1 / 2

22 Lecture 222 Incomplete Information System is 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 V a is a set of values of attribute a, for any We assume that for each attribute and Definition 2.2 2 Null value assigned to an object is interpreted as all possible values of an attribute with equal confidence assigned to all of them.

23 Lecture 223 Extract rules from S describing attribute e in terms of attributes {a,b,c,d} ( following a strategy similar to LERS )

24 Lecture 224 Goal: Describe e in terms of {a,b,c,d} x8x8 x7x7 x6x6 x5x5 x4x4 x3x3 x2x2 x1x1 edcbaX Algorithm ERID (Extracting Rules from partially Incomplete Information System(Database))

25 Lecture 225 x8x8 x7x7 x6x6 x5x5 x4x4 x3x3 x2x2 x1x1 edcbaX Algorithm ERID for Extracting Rules from partially Incomplete Information System Goal: Describe e in terms of {a,b,c,d}

26 Lecture 226 Algorithm ERID for Extracting Rules from partially Incomplete Information System Goal: Describe e in terms of {a,b,c,d} x8x8 x7x7 x6x6 x5x5 x4x4 x3x3 x2x2 x1x1 edcbaX For the values of the decision attribute we have:

27 Lecture 227 x8x8 x7x7 x6x6 x5x5 x4x4 x3x3 x2x2 x1x1 edcbaX 2.Check the relationship “ ” between values of classification attributes {a,b,c,d} and values of decision attribute e Algorithm ERID for Extracting Rules from partially Incomplete Information System Goal: Describe e in terms of {a,b,c,d}

28 Lecture 228 x8x8 x7x7 x6x6 x5x5 x4x4 x3x3 x2x2 x1x1 edcbaX Let,. and confidence of the rule are above some threshold values. We say that: iff support Algorithm ERID for Extracting Rules from partially Incomplete Information System Goal: Describe e in terms of {a,b,c,d}

29 Lecture 229 Algorithm ERID for Extracting Rules from partially Incomplete Information System Goal: Describe e in terms of {a,b,c,d} x8x8 x7x7 x6x6 x5x5 x4x4 x3x3 x2x2 x1x1 edcbaX Let,. and confidence of the rule are above some threshold values. We say that: iff support How to define support and confidence of a rule ?

30 Lecture 230 Definition of Support and Confidence (by example) To define support and confidence of the rule a 1  e 3 we compute: Support of the rule: Support of the term a 1 : Confidence of the rule:

31 Lecture 231 Extracting Rules from partially Incomplete Information System (Algorithm ERID(λ 1, λ 2 )) x8x8 x7x7 x6x6 x5x5 x4x4 x3x3 x2x2 x1x1 edcbaX - marked negative - marked positive Thresholds (provided by user): Minimal support (λ 1 = 1) Minimal confidence (λ 2 = ½) - marked negative Goal: Describe e in terms of {a,b,c,d}

32 Lecture 232 x8x8 x7x7 x6x6 x5x5 x4x4 x3x3 x2x2 x1x1 edcbaX but Extracting Rules from partially Incomplete Information System (Algorithm ERID(λ 1, λ 2 ))

33 Lecture 233 x8x8 x7x7 x6x6 x5x5 x4x4 x3x3 x2x2 x1x1 edcbaX but They all are not marked Extracting Rules from partially Incomplete Information System (Algorithm ERID(λ 1, λ 2 ))

34 Lecture 234 x8x8 x7x7 x6x6 x5x5 x4x4 x3x3 x2x2 x1x1 edcbaX and Extracting Rules from partially Incomplete Information System (Algorithm ERID(λ 1, λ 2 ))

35 Lecture 235 Extracting Rules from partially Incomplete Information System (Algorithm ERID(λ 1, λ 2 )) x8x8 x7x7 x6x6 x5x5 x4x4 x3x3 x2x2 x1x1 edcbaX and They all are marked positive

36 Lecture 236 Extracting Rules from partially Incomplete Information System (Algorithm ERID(λ 1, λ 2 )) x8x8 x7x7 x6x6 x5x5 x4x4 x3x3 x2x2 x1x1 edcbaX and They all are marked positive They all are marked negative

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