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Comparison of LEM2 and a Dynamic Reduct Classification Algorithm Ola Leifler olale@ida.liu.se IDA Comparison of LEM2 and a Dynamic Reduct Classification Algorithm p.1/90 Agenda Machine learning Comparison of LEM2 and a Dynamic Reduct

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SLIDE 1

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm

Ola Leifler

  • lale@ida.liu.se

IDA

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.1/90

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SLIDE 2

Agenda

Machine learning

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.2/90

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SLIDE 3

Agenda

Machine learning Task & Rationale

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.2/90

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SLIDE 4

Agenda

Machine learning Task & Rationale Rough Sets

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.2/90

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SLIDE 5

Agenda

Machine learning Task & Rationale Rough Sets Techniques used

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.2/90

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SLIDE 6

Agenda

Machine learning Task & Rationale Rough Sets Techniques used Evaluation

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.2/90

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SLIDE 7

Machine learning – Definition

Learning A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P , if its performance at tasks in T, as measured by P , improves with experience E.

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.3/90

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SLIDE 8

Machine learning – Figure

universe sample model

FILTER CONSTRUCT MODEL CLASSIFY EVALUATE

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.4/90

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SLIDE 9

Machine learning – Figure

universe sample model

FILTER CONSTRUCT MODEL CLASSIFY EVALUATE

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.5/90

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SLIDE 10

Machine learning – Figure

universe sample model

FILTER CONSTRUCT MODEL CLASSIFY EVALUATE

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.6/90

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SLIDE 11

Machine learning – Figure

universe sample model

FILTER CONSTRUCT MODEL CLASSIFY EVALUATE

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.7/90

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SLIDE 12

Machine learning – Figure

universe sample model

FILTER CONSTRUCT MODEL CLASSIFY EVALUATE

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.8/90

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SLIDE 13

Machine learning – Figure

universe sample model

FILTER CONSTRUCT MODEL CLASSIFY EVALUATE

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.9/90

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SLIDE 14

Machine learning – Figure

universe sample model

FILTER CONSTRUCT MODEL CLASSIFY EVALUATE

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.10/90

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SLIDE 15

Machine learning – Figure

universe sample model

FILTER CONSTRUCT MODEL CLASSIFY EVALUATE

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.11/90

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SLIDE 16

Machine learning – Figure

universe sample model

FILTER CONSTRUCT MODEL CLASSIFY EVALUATE

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.12/90

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SLIDE 17

Machine learning – Figure

model

FILTER CONSTRUCT MODEL CLASSIFY

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.13/90

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SLIDE 18

Task

Evaluate two machine learning approaches, or more accurately:

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.14/90

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SLIDE 19

Task

Evaluate two machine learning approaches, or more accurately: two filters

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.14/90

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SLIDE 20

Task

Evaluate two machine learning approaches, or more accurately: two filters

  • ne model construction algorithm

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.14/90

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SLIDE 21

Task

Evaluate two machine learning approaches, or more accurately: two filters

  • ne model construction algorithm

and three classifier algorithms

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.14/90

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SLIDE 22

Rationale

No previous comparisons done from scratch

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.15/90

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SLIDE 23

Rationale

No previous comparisons done from scratch in the same programming environment

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.15/90

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SLIDE 24

Rationale

No previous comparisons done from scratch in the same programming environment in the same machine learning framework

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.15/90

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SLIDE 25

Rationale

No previous comparisons done from scratch in the same programming environment in the same machine learning framework with the same statistical tools

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.15/90

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SLIDE 26

Rationale

No previous comparisons done from scratch in the same programming environment in the same machine learning framework with the same statistical tools for these algorithms

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.15/90

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SLIDE 27

Machine learning – Example

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.16/90

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SLIDE 28

Machine learning – Example

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.17/90

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SLIDE 29

Machine learning – Weka

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.18/90

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SLIDE 30

Machine learning – Weka

Java machine learning library

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.18/90

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SLIDE 31

Machine learning – Weka

Java machine learning library Available methods for:

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.18/90

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SLIDE 32

Machine learning – Weka

Java machine learning library Available methods for: Filtering

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.18/90

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SLIDE 33

Machine learning – Weka

Java machine learning library Available methods for: Filtering Model construction/Classification

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.18/90

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SLIDE 34

Machine learning – Weka

Java machine learning library Available methods for: Filtering Model construction/Classification Evaluation

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.18/90

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SLIDE 35

Rough Sets

Rough sets describe the notion of sets in terms of mathematical relations between objects.

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.19/90

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SLIDE 36

Rough Sets

Rough sets describe the notion of sets in terms of mathematical relations between objects. These relations are used to reason about approximate knowledge

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.19/90

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SLIDE 37

Rough Sets

Rough sets describe the notion of sets in terms of mathematical relations between objects. These relations are used to reason about approximate knowledge The “Indiscernibility relation” describes what makes two objects seem like the same object.

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.19/90

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SLIDE 38

Indiscernibility

Given a set B

A and a decision system S U A d

the indiscernibility relation is defined as

INDS B u u U2 : a B a u a u INDS B is an equivalence relation.

skip example

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.20/90

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SLIDE 39

Indiscernibility – Example

Occupation Age Shoesize Credibility u2

doctor 45 44 Medium

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.21/90

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SLIDE 40

Indiscernibility – Example

Occupation Age Shoesize Credibility u2

doctor 45 44 Medium

u6

doctor 49 44 Low

u7

doctor 49 44 Low Let B be the set Occupation .

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.22/90

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SLIDE 41

Indiscernibility – Example

Occupation Age Shoesize Credibility u2

doctor 45 44 Medium

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.23/90

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SLIDE 42

Indiscernibility – Example

Occupation Age Shoesize Credibility u2

doctor 45 44 Medium

u6

doctor 49 44 Low

u7

doctor 49 44 Low Given the attribute set Occupation , u2 u6 & u7 are indiscernible from each other.Relative Reducts

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.23/90

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SLIDE 43

Lower approximation – Definition

Let

X x : Credibility x Low

and

B Shoesize . Then the lower approximation to X w.r.t. B is the set of objects that are certainly in X, given the

information in B. skip example

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.24/90

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SLIDE 44

Lower Approximation – Example

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.25/90

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SLIDE 45

Lower Approximation – Example

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.26/90

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SLIDE 46

Lower Approximation – Example

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.27/90

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SLIDE 47

Lower Approximation – Example

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.28/90

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SLIDE 48

Lower Approximation – Example

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.29/90

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SLIDE 49

Upper Approximation – Definition

Let X and B be as before. Then the upper approxim- ation to X is the set of objects that are possibly in X, given the information in B. skip example

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.30/90

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SLIDE 50

Upper Approximation – Example

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.31/90

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SLIDE 51

Upper Approximation – Example

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.32/90

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SLIDE 52

Reduct

We want to find a more compact description of the data,

  • r a reduced set of attributes describing the things we

are interested in (for instance the concept of having high Credibility)

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.33/90

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SLIDE 53

Reduct – Definition

A superreduct B is a set of attributes in an information system such that INDS A

INDS B . If B is a su-

perreduct such that if one of the attributes is removed from B, the number of objects that are indiscernible from each other (are in the INDS B relation with each

  • ther) will increase, then B is a reduct, or proper reduct

skip example

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.34/90

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SLIDE 54

Reduct – Example 1

Let B

Shoesize

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.35/90

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SLIDE 55

Reduct – Example 1

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.36/90

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SLIDE 56

Reduct – Example 1

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.37/90

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SLIDE 57

Reduct – Example 1

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.38/90

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SLIDE 58

Reduct – Example 1

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.39/90

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SLIDE 59

Reduct – Example 1

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.40/90

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SLIDE 60

Reduct – Example 2

Let B

Age Shoesize

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.41/90

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SLIDE 61

Reduct – Example 2

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.42/90

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SLIDE 62

Reduct – Example 2

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.43/90

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SLIDE 63

Reduct – Example 2

Occupation Age Shoesize Credibility u1

thief 35 42 High

u2

doctor 45 44 Medium

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.44/90

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SLIDE 64

Relative Reduct – Definition

A relative reduct B

A is a minimal set of attrib-

utes in a decision system S

U A d

such that

INDS d INDS B

skip example

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.45/90

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SLIDE 65

Relative Reduct – Example

Let B

Shoesize . Remove u2 from S

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.46/90

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SLIDE 66

Relative Reduct – Example

Occupation Age Shoesize Credibility u1

thief 35 42 High

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.47/90

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SLIDE 67

Relative Reduct – Example

Occupation Age Shoesize Credibility u1

thief 35 42 High

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.48/90

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SLIDE 68

Relative Reduct – Example

Occupation Age Shoesize Credibility u1

thief 35 42 High

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.49/90

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SLIDE 69

Relative Reduct – Example

Occupation Age Shoesize Credibility u1

thief 35 42 High

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.50/90

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SLIDE 70

Relative Reduct – Example

Occupation Age Shoesize Credibility u1

thief 35 42 High

u3

thief 35 41 Low

u4

farmer 23 46 High

u5

thief 53 46 High

u6

doctor 49 44 Low

u7

doctor 49 44 Low

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.51/90

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SLIDE 71

Dynamic Reducts

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.52/90

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SLIDE 72

Dynamic Reducts

Reducts that occur in subtables are good (conjecture)

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.53/90

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SLIDE 73

Dynamic Reducts

Reducts that occur in subtables are good (conjecture) Find the ones that occur in most subtables

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.53/90

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SLIDE 74

Dynamic Reducts

Reducts that occur in subtables are good (conjecture) Find the ones that occur in most subtables and are also reducts of the whole table.

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.53/90

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SLIDE 75

Dynamic Reducts

Reducts that occur in subtables are good (conjecture) Find the ones that occur in most subtables and are also reducts of the whole table. The frequency is called stability

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.53/90

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SLIDE 76

Filtering techniques

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.54/90

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SLIDE 77

Filtering techniques

Replace missing values

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.55/90

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SLIDE 78

Filtering techniques

Replace missing values Discretization

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.55/90

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SLIDE 79

Filtering techniques

Replace missing values Discretization MD-heuristic

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.55/90

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SLIDE 80

Filtering techniques

Replace missing values Discretization MD-heuristic Dynamic reducts

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.55/90

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SLIDE 81

Discretization – Example

Suppose we have a number of objects with different values on the numerical attribute Age.

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.56/90

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SLIDE 82

Discretization – Example

We want to construct a limited number of intervals.

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.57/90

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SLIDE 83

Discretization – MD-heuristics

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.58/90

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SLIDE 84

Discretization – MD-heuristics

  • 1. Get the cut that discerns most object-pairs with

different decisions from each other.

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.58/90

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SLIDE 85

Discretization – MD-heuristics

  • 1. Get the cut that discerns most object-pairs with

different decisions from each other.

  • 2. Separate the data w.r.t. that cut

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.58/90

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SLIDE 86

Discretization – MD-heuristics

  • 1. Get the cut that discerns most object-pairs with

different decisions from each other.

  • 2. Separate the data w.r.t. that cut
  • 3. If the data in each part does not belong to single

decision classes, go to 1.

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.58/90

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SLIDE 87

Discretization – Dynamic Reducts

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.59/90

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SLIDE 88

Discretization – Dynamic Reducts

  • 1. Convert the original dataset into a new set with

binary attributes. See example

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.60/90

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SLIDE 89

Discretization – Dynamic Reducts

  • 1. Convert the original dataset into a new set with

binary attributes. See example

  • 2. Divide this set of data into subsets (suitable

number of sets of suitable size)

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.61/90

slide-90
SLIDE 90

Discretization – Dynamic Reducts

  • 1. Convert the original dataset into a new set with

binary attributes. See example

  • 2. Divide this set of data into subsets (suitable

number of sets of suitable size)

  • 3. Extract a number of relative reducts from the table
  • btained in step 1.

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.62/90

slide-91
SLIDE 91

Discretization – Dynamic Reducts

  • 4. Of these, choose the one that most frequently

appear the tables obtained in step 2. (most stable reduct)

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.63/90

slide-92
SLIDE 92

Discretization – Dynamic Reducts

  • 4. Of these, choose the one that most frequently

appear the tables obtained in step 2. (most stable reduct)

  • 5. Convert this reduct into a set of cuts on the old

table (revert the process in step 1)

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.64/90

slide-93
SLIDE 93

Discretization – Dynamic Reducts

  • 4. Of these, choose the one that most frequently

appear the tables obtained in step 2. (most stable reduct)

  • 5. Convert this reduct into a set of cuts on the old

table (revert the process in step 1)

  • 6. Use these cuts to discretize the table (see

example) Continue

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.65/90

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SLIDE 94

Binary table – Example

Discretize the data (on a reduced table) w.r.t. age

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.66/90

slide-95
SLIDE 95

Binary table – Example

Age Credibility u1

35 High

u2

45 Medium

u3

35 Low

u4

23 High

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.67/90

slide-96
SLIDE 96

Binary table – Example

Create cutpoints 29 40 on Age between the values of the instances in the set and make new binary attributes

Age29 Age40 for each of these cutpoints: Agex u

if Age u

x 1

if Age u

x

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.68/90

slide-97
SLIDE 97

Binary table – Example

Age29 Age40 Credibility u1

1 High

u2

1 1 Medium

u3

1 Low

u4

High return

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.69/90

slide-98
SLIDE 98

Discretized table – Example

Age29 Age40 Credibility u1

1 High

u2

1 1 Medium

u3

1 Low

u4

High

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.70/90

slide-99
SLIDE 99

Discretized table – Example

Age Credibility u1 29 40

High

u2 40 ∞

Medium

u3 29 40

Low

u4 ∞ 29

High return

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.71/90

slide-100
SLIDE 100

Model construction

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.72/90

slide-101
SLIDE 101

Model construction

Our internal model is represented as a set of decision rules:

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.73/90

slide-102
SLIDE 102

Model construction

Our internal model is represented as a set of decision rules:

Occupation thief Shoesize 42 Credibility High

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.73/90

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SLIDE 103

LEM2 – sketch of the algorithm

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.74/90

slide-104
SLIDE 104

LEM2 – sketch of the algorithm

For each lower/upper approximation to each decision class do:

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.74/90

slide-105
SLIDE 105

LEM2 – sketch of the algorithm

For each lower/upper approximation to each decision class do:

  • 1. Create rules by adding pairs of attributes and

values and use a heuristic measure for determining which pairs to choose

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.74/90

slide-106
SLIDE 106

LEM2 – sketch of the algorithm

For each lower/upper approximation to each decision class do:

  • 1. Create rules by adding pairs of attributes and

values and use a heuristic measure for determining which pairs to choose

  • 2. Remove unnecessary pairs from the

generated rules

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.74/90

slide-107
SLIDE 107

LEM2 – sketch of the algorithm

For each lower/upper approximation to each decision class do:

  • 1. Create rules by adding pairs of attributes and

values and use a heuristic measure for determining which pairs to choose

  • 2. Remove unnecessary pairs from the

generated rules

  • 3. Repeat until stop criterion is met, then reduce

the set of rules by removing redundant ones.

Comparison of LEM2 and a Dynamic Reduct Classification Algorithm – p.74/90

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SLIDE 108

Classifying – The Voter

Use the decision table, no compressed model, during classification.

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SLIDE 109

Classifying – The Voter

Use the decision table, no compressed model, during classification. Match new objects to the objects in the table and use weighted voting among those that match the new object.

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SLIDE 110

Classifying – The Voter

Use the decision table, no compressed model, during classification. Match new objects to the objects in the table and use weighted voting among those that match the new object. Give high votes to those that match by the attributes in a relative reduct (indirectly).

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SLIDE 111

Classifying – Rule negotiation

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SLIDE 112

Classifying – Rule negotiation

There may be more than one rule matching an

  • bject

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SLIDE 113

Classifying – Rule negotiation

There may be more than one rule matching an

  • bject

Use negotiation methods between the classes of rules (one rule class = one decision value):

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SLIDE 114

Classifying – Rule negotiation

There may be more than one rule matching an

  • bject

Use negotiation methods between the classes of rules (one rule class = one decision value):

  • 1. Simple strength

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SLIDE 115

Classifying – Rule negotiation

There may be more than one rule matching an

  • bject

Use negotiation methods between the classes of rules (one rule class = one decision value):

  • 1. Simple strength
  • 2. Maximal strength

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SLIDE 116

Classifying – Rule negotiation

There may be more than one rule matching an

  • bject

Use negotiation methods between the classes of rules (one rule class = one decision value):

  • 1. Simple strength
  • 2. Maximal strength
  • 3. Stability strength (Dynamic reduct technique)

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SLIDE 117

Implementation

Written in Java

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SLIDE 118

Implementation

Written in Java 250 KiB of code on 8000 lines

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SLIDE 119

Implementation

Written in Java 250 KiB of code on 8000 lines Separate software package (weka.roughset)

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SLIDE 120

Implementation

Written in Java 250 KiB of code on 8000 lines Separate software package (weka.roughset) Licensed under the GPL

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SLIDE 121

Evaluation

Methods

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SLIDE 122

Evaluation

Methods Algorithms

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SLIDE 123

Evaluation

Methods Algorithms Datasets

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SLIDE 124

Evaluation

Methods Algorithms Datasets Results

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SLIDE 125

Evaluation – Methods

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SLIDE 126

Evaluation – Methods

  • 1. Divide the data into N equally sized chunks with

representation from all decision classes in each (hopefully)

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SLIDE 127

Evaluation – Methods

  • 1. Divide the data into N equally sized chunks with

representation from all decision classes in each (hopefully)

  • 2. Use N-1 of them to build a model

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SLIDE 128

Evaluation – Methods

  • 1. Divide the data into N equally sized chunks with

representation from all decision classes in each (hopefully)

  • 2. Use N-1 of them to build a model
  • 3. Test the model on the remaining part

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SLIDE 129

Evaluation – Methods

  • 1. Divide the data into N equally sized chunks with

representation from all decision classes in each (hopefully)

  • 2. Use N-1 of them to build a model
  • 3. Test the model on the remaining part
  • 4. Use

# correctly classified # objects in testing set as a quality measure

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SLIDE 130

Evaluation – Methods

  • 1. Divide the data into N equally sized chunks with

representation from all decision classes in each (hopefully)

  • 2. Use N-1 of them to build a model
  • 3. Test the model on the remaining part
  • 4. Use

# correctly classified # objects in testing set as a quality measure

  • 5. Repeat steps 2-4 for every chunk

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SLIDE 131

Evaluation – Methods

  • 1. Divide the data into N equally sized chunks with

representation from all decision classes in each (hopefully)

  • 2. Use N-1 of them to build a model
  • 3. Test the model on the remaining part
  • 4. Use

# correctly classified # objects in testing set as a quality measure

  • 5. Repeat steps 2-4 for every chunk
  • 6. Repeat steps 1-5 N times and average the results

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SLIDE 132

Evaluation – Methods

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SLIDE 133

Evaluation – Methods

Compared results to previous (original) experiment with similar setup

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SLIDE 134

Evaluation – Methods

Compared results to previous (original) experiment with similar setup Students t-test with 95% confidence limit used to test the significance of performance differences. Limit on t for 9 degrees of freedom = 1.83

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SLIDE 135

Evaluation – Algorithms used

Dynamic Approach The LEM2 Ap- proach Discretization Dynamic Discretiza- tion MD-heuristic Fayyad-Irani (stand- ard) Fayyad-Irani (standard) Model construction LEM2 LEM2 No rules (Voter)

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SLIDE 136

Evaluation – Algorithms used

Dynamic Ap- proach The LEM2 Ap- proach Classification – Rule Negotiation Stability strength Simple Strength Maximal Strength Classification – Vot- ing Voter N/A

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SLIDE 137

Evaluation – Algorithms used

10-12 combinations of algorithms for filtering, model construction and classification were used

  • n each dataset.

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SLIDE 138

Evaluation – Datasets

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SLIDE 139

Evaluation – Datasets

Breast Cancer Standard benchmarking dataset used

  • previously. Determine if a patients cancer will

return or not. The attributes represent the age of the patients, the size of the tumors etc. Some missing values occur.

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SLIDE 140

Evaluation – Datasets

Breast Cancer Standard benchmarking dataset used

  • previously. Determine if a patients cancer will

return or not. The attributes represent the age of the patients, the size of the tumors etc. Some missing values occur.

Lymphography Also medical dataset used

  • previously. Related to lymphography tests

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SLIDE 141

Evaluation – Datasets

Balance Scale Describes the concept of equilibrium.

Large dataset, only numerical values.

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SLIDE 142

Evaluation – Datasets

Balance Scale Describes the concept of equilibrium.

Large dataset, only numerical values.

Zoo Categorize animals at a zoo into families. Easy

to understand the models produced.

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SLIDE 143

Evaluation – Results

Setups with Rough Set filtering scored similar results to those with traditional filtering, though somewhat worse.

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SLIDE 144

Evaluation – Results

Setups with Rough Set filtering scored similar results to those with traditional filtering, though somewhat worse. The results did not match those obtained

  • riginally. Ours showed consistently lower

accuracy.

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SLIDE 145

Evaluation – Results

Algorithm Breast Cancer Lymphography Our LEM2 0.68 0.738

  • Orig. LEM2

0.70 0.81 Our Dyn. 0.6902 0.7373

  • Orig. Dyn.

0.772 0.843

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SLIDE 146

Evaluation – Results

No significant difference between the algorithms could be seen on the Breast Cancer (t = 1.31) and Lymphography datasets (t = 0.08)

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SLIDE 147

Evaluation – Results

No significant difference between the algorithms could be seen on the Breast Cancer (t = 1.31) and Lymphography datasets (t = 0.08) But the Dynamic Approach scored better on the Balance Scale set (t = 5.65)

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SLIDE 148

Evaluation – Results

No significant difference between the algorithms could be seen on the Breast Cancer (t = 1.31) and Lymphography datasets (t = 0.08) But the Dynamic Approach scored better on the Balance Scale set (t = 5.65) and the LEM2 Approach scored better on the Zoo dataset (t = 2.71)

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SLIDE 149

Discussion

Relaxations and differences in experiment setups

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SLIDE 150

Discussion

Relaxations and differences in experiment setups No exhaustive comparison between all possible ML-approaches

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SLIDE 151

Discussion

Relaxations and differences in experiment setups No exhaustive comparison between all possible ML-approaches No exhaustive comparison of all possible types of datasets

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SLIDE 152

Discussion

Relaxations and differences in experiment setups No exhaustive comparison between all possible ML-approaches No exhaustive comparison of all possible types of datasets Conclusion: No consistent support for the hypothesis that there is substantial difference between the approaches (in our experimental setup)

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SLIDE 153

Questions of Coffee?

And now it’s time for my opponent, or perhaps some coffee?

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