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Mining Fuzzy Spatial Association Rules from Image Data

Mining Fuzzy Spatial Association Rules from Image Data. G. Brannon Smith Mississippi State University 6 June 2001. Introduction Motivation Brief Background Fuzzy Relative Position Object Co-occurence. Theory Aggregate Traditional Experiments Conclusion Future Work

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Mining Fuzzy Spatial Association Rules from Image Data

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  1. Mining Fuzzy Spatial Association Rules from Image Data G. Brannon Smith Mississippi State University 6 June 2001

  2. Introduction Motivation Brief Background Fuzzy Relative Position Object Co-occurence Theory Aggregate Traditional Experiments Conclusion Future Work Selected References Acknowledgements Contents

  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

  4. 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

  5. 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

  6. 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)

  7. R A R A Fuzzy Spatial Relations • I. Bloch applies fuzzy sets to spatial relations • Fuzzy concepts of position: right of is fuzzy • Morphology (shape & size) has effect…

  8. 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

  9. H G Reference Object #2 OO#4 Background; Empty Space F Test Image Landscape RO#2, =0 Fuzzy Landscape (single)

  10. Membership Interval • Bloch algorithm on all points in objects • Result: 3 stats per relation, M[N,]: Captures imprecision

  11. R A R A Fuzzy Relation Stats N=0.9959, M=0.9999,  = 1.0000 N=0.7557, M=0.9079,  = 1.0000

  12. 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

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

  14. 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?

  15. 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)

  16. Reference Object #7 Background; Empty Space Test Image Landscape RO#7, =0 Fuzzy Landscape (multi)

  17. 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.

  18. Theory (cont.) • Prev. ex.:

  19. 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.

  20. Theory (cont.) • Prev. ex. (same source objs):

  21. Theory (cont.) Object based

  22. Theory (cont.) • 2.

  23. Theory (cont.) object

  24. 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…

  25. Experiments:Synthetic Data Sample Graphs Scatter plots of rules mined from synthetic images with a fuzzy spatial relation extractor, using Obj-Obj rules

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

  27. Side Effects • Edge Effect – image edges • Counterbias – wrong direction • “Spillover” - other classes benefit • Probability – bias is NOT a guarantee

  28. Sample random 2 (6 classes)

  29. R2 graph

  30. Sample 4 R=G, A=H of 6 classes, bias=90% Extended, =0

  31. 4 graph

  32. Sample 2 R=G, A=H of 6 classes, bias=80% Extended, =0

  33. 2 graph

  34. Sample 10 R=G, A=H of 6 classes, bias=95%, =0

  35. 10 graph

  36. R=H, A=I R=J, A=I Half A=I of 6 classes, bias=85% Half, =0

  37. Half graph

  38. Seafloor

  39. Seafloor graph

  40. Seafloor Rule #148  

  41. 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…

  42. 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

  43. 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

  44. 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

  45. Introduction Motivation Brief Background Fuzzy Relative Position Object Co-occurence Theory Aggregate Traditional Experiments Conclusion Future Work Selected References Acknowledgements Summary

  46. 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 Int’l 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.

  47. 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 (DMKD’96) 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.

  48. Selected References (cont.) Wooley, B. 2000. mpiShell Documentation. http://www.cs.msstate.edu/~bwooley/software/mpiShellDoc.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.

  49. 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

  50. 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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