Paper study Application Of Variable Precision Rough Set Approach To Car Driver Assessment

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Paper study - Application Of Variable Precision
Rough Set Approach To Car Driver Assessment

• Presented by Lichun (Jack) Zhu
• Course 60-539
• Winter 2006
• Instructor Dr. Christie Ezeife
• University of Windsor

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Agenda

• Introduction
• Rough Set Theory
• Variable Precision Rough Set Theory
• Linear Hierarchy of Decision Table (HDTL)
  Algorithm
• How the data is prepared
• Result interpretation
• Summary and Conclusion
• Q A

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Introduction

• Problem Statement
• Need to find out unsafe car drivers based on
  history driving records.
• Driving records in the database are incomplete
  and inaccurate.
• Solution A new approach to analyze the data that
  contains inaccurate information
• Variable Precision Rough Set Theory
• Linear Hierarchy of Decision Table algorithm
• Classification

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Introduction to Rough Set Theory

• Background
• First introduced by Pawlak (1982)
• A mathematic method to describe the uncertainty
  and incompleteness
• Basic concept
• Terms Information System S, Universe U,
  Attributes A (condition attr, decision attr)
• S (U, A)

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Introduction to Rough Set Theory

• Domain Va With every attribute a of A, we
  associate a set Va as domain of a, Such as Vs
  Male, Female
• Indiscerniblity relation I(B) If B ? A, I(B) on
  U as (x,y) ? I(B), if and only if a(x) a(y) for
  every a ? B, where a(x) is the value of attribute
  a for turple x. We can see I(B) is a equivalence
  relation.
• B-elementary sets B1, Bi, the partition on
  the universe U/I(B) or simply U/B, we also define
  B(x) Bi x ? Bi

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Introduction to Rough Set Theory

• An example of Information System
• Table 1. U 1,2,3,4,5,6, AS, G, N, R

Let B S, G, N I(B) (1,1), (1,6), (2,2),
(3,3), (4,4), (5,5), (6,6) U/B 1,6, 2,
3, 4, 5 B1, B2, B3, B4, B5
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Introduction to Rough Set Theory

• Approximation
• For interest set X ? U, We define
• B-lower(X) ?x?U B(x) B(x) ? X,
• B-upper(X) ?x?U B(x) B(x) n X ? F
• BNR B (X) B-upper(X) B-lower(X)
• For example
• if X contains all turples with high risk, X
  2,3,4,6, then
• B-lower(X) 2,3,4,
• B-upper(X) 1,2,3,4,6
• BNR B (X) 1,6

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Introduction to Rough Set Theory
Figure 1. Rough Set Concept, U ?B1B14,
B-lower(X) Yellow Region, B-upper(X) Yellow
and Green Region BNR B (X) - Green Region
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Variable Precision Rough Set Theory

• Background Information
• Problem of Rough Set B-lower approximation will
  always be EMPTY if uncertainty widely exists.
• Solution use probability based approach
• presented by Ziarko(1993), Yao and Wong (1992),
  Slezak and Ziarko (2002) etc
• Definations
• lower limit l satisfying 0 l lt P(X) lt 1
• l-negative region of X NEG l (X) ?Bi
  P(XBi) l
• upper limit u satisfying 0 lt P(X) lt u 1.
• u-positive region of X POS u (X) ?Bi
  P(XBi) u
• (l,u)-boundary region of X BNR l,u (X) ?Bi
  l lt P(XBi) lt u

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Variable Precision Rough Set Theory

• For example

For data in Table 1, P(X) 4/6 2/30.67 If l
0.25 and u 0.75 then NEG 0.25 (X)5, POS
0.75 (X) 2,3,4, BNR 0.25,0.75
(X)1,6 Table 2. Sample Decision Table DT B,X
(U) with P(X) 0.67, l0.25, u0.75
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Variable Precision Rough Set Theory
Figure 2. VPRS Concept, U ?B1B17, NEG(X)
White Region, POS(X) Yellow Region BNR B (X)
Green Region
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Linear Hierarchy of Decision Table Algorithm
(Ziarko,2002)

• Corresponds to Tree-structured Hierarchy of
  Decision Table Algorithm

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Linear Hierarchy of Decision Table (HDTL)
Algorithm

• Linear Hierarchy of Decision Table (HDTL)
  Algorithm

• Advantage Linear Hierarchy of Decision Table
  algorithm effectively eliminates the exponential
  growth of the decision hierarchy size

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Linear Hierarchy of Decision Table (HDTL)
Algorithm (supervised approach)
Initialization 1.        U ? U, C ? C, D ?
D 2.        Compute POS u (X) and NEG l
(X) Iteration 3.        repeat 4.       
while (POS u (X) EMPTY and NEG l (X) EMPTY)
5.        C ? new(C, U) define new
condition attributes 6.        Compute POS u
(X) and NEG l (X) 7.       
Output DT C,X (U) output decision table based on
the union of the positive and negative
regions 8.        if POS u (X) ? NEG l (X) U
then exit. 9.        U ? U (POS u (X) ? NEG l
(X)) 10.     C ? new (C, U) define new
condition attributes 11.     D ? DU
restrict decision attributes to the current set
of data U 12.     Compute POS u (X) and NEG l
(X)

• There is a problem at this point. When defining
  the new condition attributes failed, the
  procedure should terminate.

Here embodies the linear approach of generating
the dataset for the subsequent layer.
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How the data is prepared

• Attributes
• Sex, Date-of-birth, City-population,
  Number-of-convictions, Number-of-past-accidents
  and Has-accident-in-last-year
• Data scale about 29,000 records
• Data normalization

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Result interpretation

• 5 test cycles, generating 5 first layer decision
  tables and 3 second layer decision tables.
• A problem can be found from the testing result
• In all the presented test cycles, the boundary
  sets of the first cycle all contain only one
  combination of attributes. Therefore the
  generated decision table hierarchy has no
  difference compared with the Tree-structured
  Hierarchy Decision Table algorithm at the first
  two layers. The author did not display his
  further investigation on the boundary sets that
  have more than one combination of attributes.

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Summary and Conclusion

• Strong points
• provides a valuable alternative solution that can
  be used in rule finding and classification based
  on inaccurate data.
• The HDTL algorithm can also avoid the exponent
  expansion of hierarchical data structures
• Weak point
• Incomplete of test results provided. The test
  results does not strong enough to testify the
  effectiveness and accuracy of Linear Hierarchy
  Decision Table algorithm.

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References

• Pawlak, Z, Decision Rules, Bayes Rule and Rough
  Sets, New Directions in Rough Sets, Data Mining,
  and Granular-Soft Computing, p.1-9, 7th
  International Workshop, RSFDGrC99, Yamaguchi,
  Japan, November 1999 Proceedings.
• Ziarko, W., Incremental Learning with Hierarchies
  of Rough Decision Tables, Proceedings of North
  American Fuzzy Information Processing Society
  Conf. (NAFIPS04), Banff, Alberta (2004)
  p.802-808.

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Q A

• Thanking You