Simultaneous row and column partitioning: Evaluation of an heuristic

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Djamel A. Zighed and Nicolas Nicoloyannis ERIC
Laboratory University of Lyon 2
(France) zighed_at_univ-lyon2.fr
Prague Sept. 04
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About Computer science dep.

• In Lyon, there are 3 universities, 100000
  students
• Lumière university Lyon 2, has 22000 students,
• Lyon 2, is mainly a liberal art university
• The faculty of economic has tree departments,
  among them the computer science one
• We belong to this department
• We have Bachelor, Master and PhD programs for 300
  students

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ERIC Lab at the University
Faculties of university of Lyon 2
Economic
Sociology
Linguistic
Law
ERIC
Research centers of the university
Knowledge Engineering Research Center
- The budget of ERIC doesnt depend from the
university, its given par The national ministry
of education - We have a large autonomy in
decision making
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ERIC Lab

• Born in 1995,
• 11 professors (N. Nicoloyannis, director)
• 15 PhD Students
• GrantscontractsWK200K/year
• Research topics
• Data mining (theory, tools and applications)
• Data warehouse management (T,T,A)

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Data Mining (T,T,A)

• Theory
• Induction graphs
• Learning and classification
• Tools
• SIPINA Plate form for data mining
• Applications
• Medical fields
• Chemical applications
• Human science

Data mining TTA for complex data
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Data mining on complex data

• An example Breast cancer diagnosis

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Motivations
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Motivations
Association measure It measures the strength
of the relationship between X and Y





Contingency table




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Motivations
Association measure It measures the strength
of the relationship between X and Y





Contingency table




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Motivations
Association measure It measures the strength
of the relationship between X and Y
According to a specific association measure, may
we improve the strength of the relationship by
merging some rows and/or some columns ?





Contingency table




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Motivations
According to a specific association measure, may
we improve the strength of the relation ship by
merging some rows and/or some columns ?





Contingency table




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An example
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Goal Find the groupings that maximize the
association between attributes
Yes, we can improve the association by reducing
the size of the contingency table
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Extension
According to a specific association measure, may
we find the optimal reduced contingency table ?





Contingency table




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Optimal solution (exhaustive search)
Goal Find the best cross partition on T
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Optimal solution (exhaustive search)
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Optimal solution (exhaustive search)
According to a specific association measure, may
we find the optimal reduced contingency table ?
Yes, but the solution is intractable in real word
because of the high time complexity
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Heuristic
Proceed successively to the grouping of 2 (row or
column) values that maximizes the increase in the
association criteria.
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Complexity
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Simulation
Goal How far is the quasi-optimal solution from
the true optimum? Comparison tractable for
tables not greater than 6 6.
Simulation Design
Randomly generate 200 tables Analysis of the
distribution of the deviations between optima
and quasi-optima.
Generating the Tables
10000 cases distributed in the cxr cells of the
table with an uniform distribution (worst case).
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Quasi-optimal solution
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Quasi-optimal solution
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Conclusion

• Implementation for new approach induction
  decision tree.
• Zighed, D.A., Ritschard, G., W. Erray and V.-M.
  Scuturici (2003), Abogodaï,a New approach for
  Decision Trees, in Lavrac, N., D.Gamberger, L.
  Todorovski and H. Blockeel (eds), Knowledge
  Discovery in databases PKDD 2003 , LNAI 2838,
  Berlin Springer, 495--506.
• Zighed D. A., Ritschard G., Erray W., Scuturici
  V.-M. (2003), Decision tree with optimal join
  partitioning, To appear in Journal of Information
  Intelligent Systems, Kluwer (2004).
• Divisive top-down approach
• Extension to multidimensionnal case