Mining%20Fuzzy%20Spatial%20Association%20Rules%20from%20Image%20Data

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Mining Fuzzy Spatial Association Rules from Image
Data

• G. Brannon Smith
• Mississippi State University
• 6 June 2001

2
Contents

• Introduction
• Motivation
• Brief Background
• Fuzzy Relative Position
• Object Co-occurence

• Theory
• Aggregate
• Traditional
• Experiments
• Conclusion
• Future Work
• Selected References
• Acknowledgements

3
Introduction

• Operating on raster image data image space
• Images can be partitioned into regions or objects
  (groups of like pixels)
• Like objects compose classes
• Would like to know general spatial, i.e.,
  directional, arrangement of these

Depends on DSK
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Introduction (cont.)

• Association Rules seem appropriate but not made
  for raster data, so
• Need an approach for finding generalized fuzzy
  association rules on object spatial relations
  pulled from image space

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Motivation

• GENERAL Periodic collection of vast amounts of
  data tedious for human to analyze
• SPECIFIC OKEANOS project sponsored by NAVO
  collects many seafloor images
• Data Mining/Knowledge Discovery helps

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Background

• Fuzzy Set Theory (Zadeh)
• Fuzzy Relative Position (Bloch)
• Association Rules (Agrawal et al.)
• Fuzzy Association Rules (Kuok, Fu Wong)
• Spatial Data Mining (Koperski Han)
• Object co-occurrence rules (Ordoñez Omiecinski)

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Fuzzy Spatial Relations

• I. Bloch applies fuzzy sets to spatial relations
• Fuzzy concepts of position right of is fuzzy
• Morphology (shape size) has effect

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Fuzzy Spatial Relations (cont.)

• Objects described as fuzzy sets (crisp OK)
• Ex. ?A(x) and ?R(x) , x?S
• Landscape ??(R)(x) is whole image S in relation
  to R in direction ?
• Relation want ?A(x) and ??(R)(x) overlap

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Fuzzy Landscape (single)
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Membership Interval

• Bloch algorithm on all points in objects
• Result 3 stats per relation, M?N,?

Captures imprecision
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Fuzzy Relation Stats
N0.9959, M0.9999, ? 1.0000
N0.7557, M0.9079, ? 1.0000
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Image Data Mining

• Ordoñez and Omiecinski have done preliminary work
  in image space
• Used Blobworld to convert images to transactions,
  objects to item meta-data
• ARM to find simple co-occurrence rules

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Hypothesis

• Unified system of above can be made
• Raster Image data input (KH)
• Fuzzy Spatial Relation metadata (Bloch)
• Fuzzy Assoc Rule mining (Agrawal et al., KFW)
• Result useful fuzzy rules describing
  generalities of object spatial relations

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Main Problem

• How to get from Fuzzy Relation metadata tuples
  (Bloch) to useful rules?
• What are rule forms?
• What are Support and Confidence or analogs
  thereof?
• Time? Space? Usefulness?

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Theory

• A pre-emptive approach
• By aggregating objects into classes first, can do
  pseudo-mining right away
• PRO Few landscapes, small, quick, no mining per
  se
• CON lost info (e.g., no more indiv objs)

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Fuzzy Landscape (multi)
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Theory (cont.)

• Class-class or Pixel-Pixel rule form
• S C

For any pixel x of class A and any given pixel y
of class B, it is implied that y is in direction
? of x, with some degree of confidence supported
by some portion of the (meta) database.
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Theory (cont.)

• Prev. ex.

alpha RC OC N M ?
0.0 H G 0.9959 0.9999 1.0000
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Theory (cont.)

• More traditional (aggreg loses obj id)
• Given relations for all obj pairs in 4 dirs
• 1.

For any object x of class A, there exists some
object y of class B, such that that y is in
direction ? of x, with some degree of confidence
supported by some portion of the (meta) database.

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Theory (cont.)

• Prev. ex. (same source objs)

alpha RO RC OO OC N M ?
0.0 1 H 4 G 0.6887 0.7590 0.8233
0.0 1 H 5 G 0.9959 0.9999 1.0000
0.0 2 H 4 G 0.9959 0.9999 1.0000
0.0 2 H 5 G 0.6904 0.7603 0.8242
0.0 3 H 4 G 0.6887 0.7590 0.8233
0.0 3 H 5 G 0.4842 0.5434 0.6019
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Theory (cont.)

Object based
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Theory (cont.)

• 2.

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Theory (cont.)

object
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Time ? Parallel

• Landscape generation/Relation extraction
  independent for given RO,?
• Embarrassingly Parallel
• mpiShell by Wooley shortens development time,
  allows user to exploit parallel
• Not linear 16CPU ? 4? BUT very useful
  considering min implementation effort

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Simple Hand Constructed
3 classes
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Hand graph
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ExperimentsSynthetic Data Sample Graphs

• Scatter plots of rules mined from
• synthetic images with a
• fuzzy spatial relation extractor, using
• Obj-Obj rules

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Synthetic Data

• Synthetic Data Generator to produce images with
  bias loaded images
• Can we extract rules that reflect the bias?
• Regular
• Extended
• Half

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Side Effects

• Edge Effect image edges
• Counterbias wrong direction
• Spillover - other classes benefit
• Probability bias is NOT a guarantee

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Sample random 2 (6 classes)
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R2 graph
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Sample 4
RG, AH of 6 classes, bias90 Extended, ?0
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4 graph
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Sample 2
RG, AH of 6 classes, bias80 Extended, ?0
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2 graph
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Sample 10
RG, AH of 6 classes, bias95, ?0
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10 graph
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Half
AI of 6 classes, bias85 Half, ?0
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Half graph
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Seafloor
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Seafloor graph
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Seafloor Rule 148
?
?
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Conclusions

• Fairly recent discovery of Association Rules
  (1993) has enjoyed much growth. (Agrawal)
• Expansion into categorical, fuzzy , etc.
  (Srikant, Kuok/Fu/Wong, et al.)
• Many have done work with Spatial Databases in
  Object Space (Koperski Han)
• BUT

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Conclusions

• Preliminary investigation on image object
  co-occurrence rules by Ordonez and Omiecinski
  aside
• Very little work done in Association Rule Mining
  in (raster) Image Space, esp. fuzzy
• We have endeavored to fill this gap

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Conclusions

• Used Bloch Fuzzy Spatial Relations as tool for
  meta-data generation
• Used techniques inspired by (not implemented)
  Kuok, Fu Wong
• Showed that we can find interesting and useful
  rules both loaded and unknown

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Future Work

• Better exploitation of fuzzy membership interval
• Application of thresholding typical to most AR to
  prune low fuzzy values
• Addition of a distance measure attribute
• Exploration of different kinds of rules such as
  Spatial Relation Co-occurence

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Summary

• Introduction
• Motivation
• Brief Background
• Fuzzy Relative Position
• Object Co-occurence

• Theory
• Aggregate
• Traditional
• Experiments
• Conclusion
• Future Work
• Selected References
• Acknowledgements

48
Selected References

• Agrawal, R., T. Imielinski, and A. Swami. 1993.
  Mining associations between sets of items in
  massive databases. In Proceedings of the 1993 ACM
  SIGMOD Intl Conferences on Management of Data
  held in Washington, DC, May 26-28, 1993, 207-216.
  New York ACM Press.
• Bloch, I. 1999. Fuzzy relative position between
  objects in image processing A morphological
  approach. IEEE Transactions on Pattern Analysis
  and Machine Intelligence 21(7)657-664.
• Fayyad, U. M., G. Piatetsky-Shapiro, P. Smyth,
  and R. Uthurusamy (Eds.). 1996. Advances in
  knowledge discovery and data mining. Menlo Parks,
  CA AAAI/MIT Press.
• Knorr, E. M., and R. T. Ng. 1996. Finding
  aggregate proximity relationships and
  commonalities in spatial data mining. IEEE
  Transactions on Knowledge and Data Engineering
  8(6)884-897.

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Selected References (cont.)

• Koperski, K., J. Adhikary, and J. Han. 1996.
  Knowledge discovery in spatial databases
  Progress and challenges. In Proceedings of the
  1996 ACM SIGMOD Workshop on Research Issues on
  Data Mining and Knowledge Discovery (DMKD96)
  held in Montréal, June 2, 1996, 55-70.
  IRIS/Precarn.
• Kuok, C. M., A. W.-C. Fu, and M. H. Wong. 1998.
  Mining fuzzy association rules in databases.
  SIGMOD Record 27(1)41-46.
• Luo, J. and S. M. Bridges. 2000. Mining fuzzy
  association rules and frequency episodes for
  intrusion detection. International Journal of
  Intelligent Systems 15(8)687-703.
• Ordonez, C. and E. Omiecinski. 1999. Discovering
  association rules based on image content.
  Proceedings of the 1999 IEEE Forum on Research
  and Technology Advances in Digital Libraries held
  in Baltimore, MD, May 19-21, 1999, 38-49. IEEE.

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Selected References (cont.)

• Wooley, B. 2000. mpiShell Documentation.
  http//www.cs.msstate.edu/bwooley/software/mpiShe
  llDoc.html (Accessed 02 May 2001.
• Zadeh, L.A. 1965. Fuzzy sets. Information and
  Control 8(3)338-353.
• Zimmerman, H.-J. 1996. Fuzzy set theory and its
  applications (3rd ed.). Boston Kluwer Academic
  Publishers.

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Acknowledgements

• Thanks to
• Dr. Susan Bridges (Major Professor) for being a
  great editor of a very long document
• Bruce Wooley for creating mpiShell
• Sean Taylor for code review

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Acknowledgements

• Grants from NAVO Research group based at Stennis
  Space Center in Bay St. Louis, MS
• National Science Foundation Grant 9818489
• ONR EPSCoR Grant N00014-96-1-1276
• Naval Oceanographic Office via NASA Stennis
  NAS1398033 DO92

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URL for Thesis Materials

• http//www.cs.msstate.edu/smithg/thesis/
• Includes this presentation, previous
  presentations (proposal, seminar, etc.), proposal
  text and thesis text in PostScript and PDF formats

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Questions and Comments?

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Fuzzy Set Theory

• Classical/Crisp set membership is TOTAL or NULL
• Can describe with characteristic function - map
  universe onto 0,1, a set itself
• OK, for definite sets, e.g. Turing winners

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Fuzzy Set Theory (cont.)

• PROBLEM imprecise sets such as TALL
• Where is NOT TALL/TALL boundary?
• Zadeh proposed set membership function
• ?A(x) mapping to 0,1 (interval), so 0.7 OK
• Exact membership function at user discretion
  domain specific

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Fuzzy Set Theory (cont.)

• Classical operator analogs complement,
  cardinality, etc.
• Union Intersection typically max min
  respectively (there are others)
• Still give proper results for crisp sets

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Association Rules

• Rules of Agrawal et al. usually of form
• antecedent X ? consequent Y (s,c)
• XY is set of items in a transaction and
• X?Y ? i.e., disjoint
• Ex. Beer ? Chips (support3,conf87)

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Association Rules (cont.)

• Notions of support and confidence
• Support of ALL transactions with both X Y -
  high support large
• Measures importance (freq) in database
• Confidence of X transactions with Y
• Strength of relationship between X and Y

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Association Rules (cont.)

• Rules use binary/boolean attributes
• Ex. Transaction includes chips/Trans. does NOT
  include chips
• Classical Set Theory
• But what about range data (e.g., Price or Age)?

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Association Rules (cont.)

• Srikant Agrawal offer mapping to Quantitative
  Rules to use range
• Can map values from range to booleans
• Ex. Price 700/Price ? 700
• Price ?500,999/Price?500,999
• Still use boolean algorithms

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Association Rules (cont.)

• Kuok, Fu Wong complaint interval boundaries
  (like TALL vs. NOT TALL)
• SOLUTION Use fuzzy set intervals
• 20,25 becomes Young Adult
• Attribute values have degrees of membership in
  several fuzzy sets

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Association Rules (cont.)

• KFW rule X is A ? Y is B (s,c)
• A and B are sets of fuzzy sets for attribs
• s,c are fuzzy analogs of supp and conf
• Significance and Certainty
• Weighted by fuzzy vals

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Spatial Data Mining

• Koperski Han leaders adapting General DM to
  Spatial Data specifically Spatial DB
• Spatial DB stores spatial data, object attribs,
  does spatial ops, e.g., Spatial Join
• Object Space
• This work does NOT use a Spatial DB

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Spatial Data Mining (cont.)

• But Koperski Han do acknowledge Raster Image
  Data (not in Spatial DB)
• Kind of bridge between strict SDM and Image
  Processing