Flowers

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05/2009
Large-Scale Graph Mining Using Backbone
Refine-ment Classes
Andreas Maunz1, Christoph Helma1,2, and Stefan
Kramer3 1) FDM Universität Freiburg (D)2)
in-silico toxicology Basel (CH) 3) Technische
Universität München (D)
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BACKBONE REFINEMENT CLASS MINING

• Efficient diverse substructure mining from a
  large class-labelled graph database

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BBRC Rationale
Typical substructure frequencies for databases of
small molecules
Trees are most frequent substructure type yet
efficiently enumerable. However

• Excessively large result sets are obtained even
  for high correlation and minimum frequency
  constraints.

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BBRC Definitions
GASTON (GrAph, Sequence and Tree ExtractiON) by
Nijssen and Kok1

• Backbone of a tree longest path with the lowest
  sequence (assuming canonical sequence ordering).

• Since every tree has exactly one backbone,
  backbones partition the partial order of trees
  disjointly.

• Pre-order (depth-first) traversal is used within
  each partition to refine structures.

Backbone Refinement Class (BBRC) All tree
refinements growing from a specific backbone.
1 Nijssen S. Kok J.N. A Quickstart in
Frequent Structure Mining can make a Difference,
KDD 04 Proceedings of the tenth ACM SIGKDD
International Conference on Knowledge Discovery
and Data Mining, New York, NY, USA ACM 2004
647652.
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BBRC Example
Backbones in gray
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BBRC Properties (1)
Some Properties

• Two types of BBRCs
• within a backbone not disjoint(see figure on
  the left)
• across backbones disjoint

• A given backbone spans a maximum search tree. No
  node may be added without changing the backbone.

• BBRCs partition the search space structurally
  (as opposed to occurrence-based methods, such as
  open/closed features).

Search space for two BBRCs within the same
backbone.
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BBRC Properties (2)
The Number of BBRCs
? The number of Backbone Refinement Classes is
governed by the (recursive)branches on this
backbone.
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BBRC Properties (3)
The Number of BBRCs (unpublished)
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BBRC Properties (4)
Summary of Feature Counts
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BBRC Implementation
Idea Use paths as candidate backbones. Mine
BBRCs and represent each BBRC by the most
(?2-)significant member.

• In case of several most significant members, use
  the most general one.

• ?2 thresholds can not be used for anti-monotonic
  pruning, however an upper bound for ?2 values of
  refinements of a pattern exists1 (Statistical
  Metric Pruning).

Dynamic Upper Bound Pruning ?2 threshold may be
increased during depth-first traversal since we
only search for the max. elements of classes.
1 S. Morishita and J. Sese. Traversing Itemset
Lattices with Statistical Metric Pruning. In
Symposium on Principles of Database Systems,
pages 226236, 2000.
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BBRC Experiments (1)
Investigation of BBRCs regarding time efficiency,
feature set sizes and expressiveness

• Class-Balanced CPDB datasets
• Salmonella Mutagenicity (SM, 388 active / 810
  compounds)
• Rat Carcinogenicity (RC, 459 active / 1145
  compounds)
• Mouse Carcinogenicity (MoC, 428 active / 927
  compounds)
• Multicell Call (MuC, 553 active / 1067
  compounds).

• Significant Trees all trees that are frequent
  and significant.

• BBRC Representatives most significant
  representatives of the backbone refinement
  classes.

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BBRC Experiments (2)
Feature Set Sizes
Minimum frequency 6
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BBRC Experiments (3)
Time Efficiency
Minimum frequency 6
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BBRC Experiments (4)
Instance-based predictions all all
predictions AD top 80 confidence
predictions wt. predictions weighted by
confidence
Accuracy, Sensitivity, Specificity
Black Sign. Trees Dark Gray BBRC-R. Light Gray
Open Trees
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Large-Scale Analysis (1)
Large Scale Analysis

• NCI Yeast Anticancer Drug Screen datasets (April
  2002 release)
• AC-One (stage 0) 87,264 compounds, 12,068
  active
• AC-All (stage 0) 87,264 compounds, 5,777
  active
• AC-All (stage 1) 10,924 compounds, 5,433 active

To the best knowledge of the authors, 1. and 2.
are the largest labelled datasets that have been
considered in correlated graph mining.
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Large-Scale Analysis (2)
Effects of Minimum Frequency on Dataset Coverage
AC-One (stage 0) 87,264 comp
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Large-Scale Analysis (3)
Feature Count for Balanced datasets (downsampling)
Max. Trees the positive border as implied by
minimum frequency and significance constraints1.
1 M. Al Hasan et.al. Origami Mining
Representative Orthogonal Graph Patterns. ICDM
2007. Seventh IEEE International Conference on
Data Mining, pages 153162, Oct. 2007.
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Large-Scale Analysis (4)
Time Efficiency
Time efficiency (Mining)
Open Treesmining times of 4-12h
Time efficiency (Prediction)
Open Treesprediction times of gt60simpractical
RAM demand.
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BBRC Experiments (5)
Euclidean embedding based on Co-Occurrences and
Entropy1
Active / Inactive compounds Activating /
Deactivatingfeatures
Differently colored features nearly perfectly
separated
Features are well distributed with few clusters
1 Hannes Schulz, Christian Kersting, Andreas
Karwath, ILP, the Blind, and the Elephant
Euclidean Embedding of Co-Proven Queries
(Proceedings of the 19th International Conference
on Inductive Logic Programming (ILP 2009)
(forthcoming)).
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SUMMARY
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Summary (1)
Backbone Refinement Class Representatives

• Structurally heterogeneous descriptors,
  compression by structural invariant (backbone
  constraint)

• Good dataset coverage, robust against increasing
  minimum frequencies

• Applicable to large-scale graph databases
  through a novel statistical pruning technique

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Summary (2)
Backbone Refinement Class Representatives

• Compression of 90 compared to all trees and 31
  compared to open trees

• Time efficiency improved by 85 and 83 versus
  no statistical pruning and static upper bound
  pruning, respectively.

• Discriminative potential similar to complete set
  of trees, but significantly better than open
  trees.

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Acknowledgements
The authors would like to thank Björn Bringmann
for providing a binary and friendly cooperation
in dataset testing, and Ulrich Rückert for
providing datasets. The research was (partially)
supported by the EU seventh framework programme
under contract no Health-F5-2008-200787 (OpenTox).
http//www.opentox.org
C implementation http//www.maunz.de/libfminer-
doc
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