Graph-Based Concept Learning

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Graph-Based Concept Learning
Jesus A. Gonzalez, Lawrence B. Holder, and Diane
J. Cook Department of Computer Science and
Engineering University of Texas at Arlington Box
19015, Arlington, TX 76019-0015 gonzalez,holder,c
ook_at_cse.uta.edu http//cygnus.uta.edu/subdue/
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MOTIVATION AND GOAL

• Need for non-logic-based relational concept
  learner
• Empirical and theoretical comparisons of
  relational learners
• Logic-based relational learners (ILP)
• FOIL Quinlan et al.
• Progol Muggleton et al.
• Graph-based relational learner
• SUBDUE

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SUBDUE KNOWLEDGE DISCOVERY SYSTEM

• SUBDUE discovers patterns (substructures) in
  structural data sets
• SUBDUE represents data as a labeled graph.
• Vertices represent objects or attributes
• Edges represent relationships between objects
• Input Labeled graph
• Output Discovered patterns and instances

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SUBDUE EXAMPLE
Input
Output
shape
triangle
object
shape
square
on
object
4 instances of
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SUBDUES SEARCH

• Starts with a single vertex and repeatedly
  expands by one edge
• Computationally-constrained beam search
• Polynomially-constrained inexact graph matching
• Search space is all sub-graphs of input graph
• Guided by compression heuristic
• Minimum description length

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EVALUATION CRITERION MINIMUM DESCRIPTION LENGTH

• Minimum Description Length (MDL) principle
• The best theory to describe a set of data is the
  one that minimizes the DL of the entire data
  set.
• DL of the graph the number of bits necessary
  to completely describe the graph.
• Search for the substructure that results in the
  maximum compression.

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CONCEPT LEARNING SUBDUE

• Modify Subdue for concept learning (SubdueCL)
• Accept positive and negative graphs as input
  examples
• Find substructure describing positive examples,
  but not negative examples
• Learn multiple rules (DNF)

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CONCEPT LEARNING SUBDUE

• Evaluation criteria based on number of positive
  examples covered without covering negative
  examples
• Substructure value 1 - Error

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CONCEPT LEARNING SUBDUE EXAMPLE

• Examples in graph format (chess domain)

a) Board Configuration b) Graph Representation
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PRELIMINARY RESULTS

• Comparison with FOIL and Progol
• Significance test p for the Vote domain
• Significance test p for the Chess domain

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RELATED THEORY

• Galois lattice reference?
• Subdues search space is similar to the Galois
  lattice
• Polynomial convergence results for the Galois
  lattice apply to Subdue
• PAC analysis of conceptual graphs reference?
• Subdues representation is a superset of
  conceptual graphs
• PAC sample complexity results for conceptual
  graphs apply to Subdue

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CONCLUSIONS

• Empirical results indicate Subdue is competitive
  with ILP systems
• More empirical comparisons are necessary
• Theoretical results on Galois lattice and
  conceptual graphs apply to Subdue
• Need to identify specific components of the
  theory directly applicable to Subdue
• Expand theories where needed