gbs_final.ppt

Mining Fuzzy Spatial Mining Fuzzy Spatial Association Rules from Association Rules from

Image DataImage Data

G. Brannon Smith

Mississippi State University

6 June 2001

ContentsContents

• Introduction

• Motivation

• Brief Background– Fuzzy Relative

Position– Object Co-occurence

• Theory– Aggregate– Traditional

• Experiments• Conclusion• Future Work• Selected References• Acknowledgements

IntroductionIntroduction

• 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

Introduction (cont.)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

MotivationMotivation

• 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

BackgroundBackground

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)

Fuzzy Spatial RelationsFuzzy Spatial Relations

• I. Bloch applies fuzzy sets to spatial

relations

• Fuzzy concepts of position: right of is fuzzy

• Morphology (shape & size) has effect…

AR A R

Fuzzy Spatial Relations (cont.)Fuzzy Spatial Relations (cont.)

• Objects described as fuzzy sets (crisp OK)

Ex. µA(x) and µR(x) , x∈S

• Landscape: µα(R)(x) is whole image S in

relation to R in direction α

• Relation: want µA(x) and µα(R)(x) overlap

Fuzzy Landscape (single)Fuzzy Landscape (single)

Test Image Landscape RO#2, α=0

ReferenceObject #2

Background;Empty Space

OO#4H G

F

Membership IntervalMembership Interval

• Bloch algorithm on all points in objects

• Result: 3 stats per relation, M∈[N,Π]:

∑

∏

∈

∈

∈

=

−=

=

SxA

R

ASx

R

ASx

xRxA

A

xxRsA

xxRt

M

N))(()(

1)(Mean

)](1),)(([inf)(Necessity

)](),)(([sup(A)yPossibilitR

αα

αα

αα

µµ

µµ

µµ

membership average)(Mean

membership minimum)(Necessity

membership maximum(A)yPossibilitR

=

=

=∏

A

A

MN

R

R

α

α

α

Captures imprecision

Fuzzy Relation StatsFuzzy Relation Stats

N=0.9959, M=0.9999, Π = 1.0000

N=0.7557, M=0.9079, Π = 1.0000

R A R A

Image Data Mining 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

HypothesisHypothesis

• 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

Main ProblemMain 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?

TheoryTheory

• 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)

Fuzzy Landscape (multi)Fuzzy Landscape (multi)

Test Image Landscape RO#7, α=0

ReferenceObject #7

Background;Empty Space

Theory (cont.)Theory (cont.)

• “Class-class” or “Pixel-Pixel” rule form:

• S & C

),,(),(),(

)()()()(,

yxinDirByinCAxinC

ypBcxpAcyx

α⇒∧

∧∧∧∧∀∀

NPNPNPSumS BA ),(=

yPossibilitC

MeanC

NecessityC

M

N

===

ΠNPNPNPMaxSNPNPNPMinS

BA

BA

),(),(

3

2

==

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


• Prev. ex.:

),,0(),(),(

)()()()(,

yxinDirGyinCGxinC

ypGcxpHcyx

⇒∧

∧∧∧∧∀∀

%33.83=S

%100

%99.99

%59.99

===

ΠC

C

C

M

N

1.00000.99990.9959GH0.0

∏MNOC#RC#alpha

%00.50%33.33

3

2

==

SS


• More traditional… (aggreg loses obj id)

• Given: relations for all obj pairs in 4 dirs

• 1.

),,(),()()(),()()(,

yxinDirByinCBcyoAxinCAcxoyx

α∧∧∧∧∧∧∃∀

NONONOSumS BA ),(=( )

{ }Π∈

=∑∈ ∈

,,

),,(inDirmax

MNi

NO

yx

CA

Axi

Byi

α

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


• Prev. ex. (same source objs):

0.60190.54340.4842G5H30.0

0.82330.75900.6887G4H30.0

0.82420.76030.6904G5H20.0

1.00000.99990.9959G4H20.0

1.00000.99990.9959G5H10.0

0.82330.75900.6887G4H10.0

∏MNOC#OO#RC#RO#alpha


),,0()183,()183()()255,()255()(,

yxinDiryinCcyoxinCcxoyx

∧∧∧∧∧∧∃∀

%33.83=S

%11.94

%96.91

%35.89

===

ΠC

C

C

M

N

Object based


• 2.

),,(),()()(),()()(,

yxinDirByinCBcyoAxinCAcxoyx

α⇒∧∧

∧∧∧∀∀

formulae C)-(C above usingpixels OR objs with dealcan S''

{ }Π∈+

=∑∑∈ ∈

,,

),,(inDir

MNi

NONO

yx

CBA

Ax Byi

i

α


),,0()183,()183()()255,()255()(,

yxinDiryinCcyoxinCcxoyx

⇒∧∧

∧∧∧∀∀

%33.83=oS

%54.84

%36.80

%73.75

===

ΠC

C

C

M

N

object

%50%33.33

3

2

==

o

o

SS

Time Time ⇒⇒ Parallel Parallel

• Landscape generation/Relation extraction independent for given RO,α

• “Embarrassingly Parallel”

• mpiShell by Wooley shortens development time, allows user to exploit parallel

• Not linear: 16CPU → 4×; BUT very useful considering min implementation effort…

Simple Hand Constructed Simple Hand Constructed

3 classes

Hand graphHand graph

)66.9991.6986.15 85.71,)(,,0(),()()(),()()(,

≤≤∧∧∧∧∧∧∃∀

yxinDirGyinClassGCyoFxinClassFCxoyx

)100100100 85.71,)(,,(),()()(),()()(,

≤≤∧∧∧∧∧∧∃∀

yxinDirFyinClassFCyoGxinClassGCxoyx

π

Experiments:Experiments:Synthetic Data Sample GraphsSynthetic Data Sample Graphs

Scatter plots of rules mined from

synthetic images with a

fuzzy spatial relation extractor, using

Obj-Obj rules

Synthetic DataSynthetic Data

• Synthetic Data Generator to produce images with bias – “loaded” images

• Can we extract rules that reflect the bias?

• Regular

• Extended

• Half

Side EffectsSide Effects

• Edge Effect – image edges

• Counterbias – wrong direction

• “Spillover” - other classes benefit

• Probability – bias is NOT a guarantee

Sample random 2 (6 classes)Sample random 2 (6 classes)

R2 graphR2 graph

Sample 4Sample 4

R=G, A=H of 6 classes, bias=90% Extended, α=0

4 graph4 graph

Sample 2Sample 2

R=G, A=H of 6 classes, bias=80% Extended, α=0

2 graph2 graph

Sample 10Sample 10

R=G, A=H of 6 classes, bias=95%, α=0

10 graph10 graph

R=H, A=I

R=J, A=I

HalfHalf

A=I of 6 classes, bias=85% Half, α=0

Half graphHalf graph

SeafloorSeafloor

Seafloor graphSeafloor graph

Seafloor Rule #148Seafloor Rule #148

)10096.4394.50 63.43,(

),,23(

),()()(),()()(,

≤≤

∧Γ∧Γ∧∧Φ∧Φ∧∃∀

yxinDir

yinClassCyoxinClass

Cxoyx

π ΦΓ

ConclusionsConclusions

• 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…


• 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


• 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

Future WorkFuture 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

SummarySummary

• Introduction

• Motivation

• Brief Background– Fuzzy Relative

Position– Object Co-occurence

• Theory– Aggregate– Traditional

• Experiments• Conclusion• Future Work• Selected References• Acknowledgements

Selected ReferencesSelected 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.

Selected References (cont.)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.

Selected References (cont.)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.

http://www.cs.msstate.edu/~bwooley/software/mpiShellDoc.html

AcknowledgementsAcknowledgements

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

AcknowledgementsAcknowledgements

• 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

URL for Thesis MaterialsURL 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

Questions and Comments?Questions and Comments?

Fuzzy Set TheoryFuzzy 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

Fuzzy Set Theory (cont.)Fuzzy Set Theory (cont.)

• PROBLEM: imprecise sets such as TALL

• Where is NOT TALL/TALL boundary?

• Zadeh proposed set membership function

µA(x) mapping to [0,1] (interval), so 0.7 OK

• Exact membership function at user

discretion – domain specific

Fuzzy Set Theory (cont.)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

Association RulesAssociation 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 (support:3%,conf:87%)

Association Rules (cont.)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


• 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)?


• 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


• 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


• 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

Spatial Data MiningSpatial 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

Spatial Data Mining (cont.)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

gbs_final.ppt

Documents

useful fuzzy rules

fuzzy spatial relations

fuzzy association rules

image data mining ordoez

useful rules

pixel x of class

object x of class

image spacemotivationgeneral