Mining for Spatial Patterns
Shashi Shekhar
Department of Computer Science
University of Minnesota
http://www.cs.umn.edu/~shekhar
Collaborators: V. Kumar, G. Karypis, C.T. Lu, W. Wu, Y. Huang, V. Raju,
P. Zhang, P. Tan, M. Steinbach
This work was partially funded by NASA and Army High Performance Computing Center
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Spatial Data Mining(SDM) - Examples
Historical Examples:
London Asiatic Cholera 1854 (Griffith)
Dental health and fluoride in water, Colorado early 1900s
Current Examples:
Cancer clusters (CDC), Spread of disease (e.g. Nile virus)
Crime hotspots (NIJ CML, police petrol planning)
Environmental justice (EPA), fair lending practices
Upcoming Applications: Location aware services
Defense: Sensor networks, Mobile ad-hoc networks
Civilian: Mortgage PMI determination based on location
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Army Relevance of SDM
Strategic
Predicting global hot spots (FORMID)
Army land: endangered species vs. training and war games
Search for local trends in massive simulation data
Critical infra-structure defense (threat assessment)
Tactical
Inferring enemy tactics (e.g. flank attack) from blobology
Detection of lost ammunition dumps (Dr. Radhakrishnan)
Operational
Interpretation of maps: map matching (locating oneself on map)
• identify terrain feature, e.g. ravines, valleys, ridge, etc.
Locating enemy (e.g. sniper in a haystack, sensor networks)
Avoiding friendly fire
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Spatial Data Mining(SDM) - Definition
Search of implicit, interesting patterns in geo-spatial data
Ex. Reconnaissance, Vector maps(NIMA, TEC), GPS, Sensor networks
Data Mining vs. Statistics:
Primary vs. Secondary analysis
Global vs. local trends
Spatial Data Mining vs. Data Mining:
Spatial Autocorrelation
Continuous vs. Discrete data types
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Background
Spatial Data Mining
Spatial statistics in Geology, Regional Economics
NSF workshop on GIS and DM (3/99)
NSF workshop on spatial data analysis (5/02)
Spatial patterns:
Spatial outliers
Location prediction
Associations, colocations
Hotspots, Clustering, trends, …
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Framework
2 Approaches to mining Spatial Data
1. Pick spatial features; use classical DM methods
2. Use novel data mining techniques
Our Approach:
Define the problem: capture special needs
Explore data using maps, other visualization
Try reusing classical DM methods
If classical DM perform poorly, try new methods
Evaluate chosen methods rigourously
Performance tuning if needed
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Spatial Association Rule
Citation: Symp. On Spatial Databases 2001
Problem: Given a set of boolean spatial features
find subsets of co-located features, e.g. (fire, drought, vegetation)
Data - continuous space, partition not natural, no reference feature
Classical data mining approach: association rules
But, Look Ma! No Transactions!!! No support measure!
Approach: Work with continuous data without
transactionizing it!
confidence = Pr.[fire at s | drought in N(s) and vegetation in N(s)]
support: cardinality of spatial join of instances of fire, drought, dry
veg.
participation: min. fraction of instances of a features in join result
new algorithm using spatial joins and apriori_gen filters
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Event Definition
Convert the time series into sequence of events at
each spatial location.
time
y
t1
AK
M
A
B
AB
D
DF
CM
ABE
G
AB
G
DL
J
x
AB
D
AB
DEF
EG
K
BCD
CE
F
EG
M
BCE
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t3
t2
DK
L
AB
GL
CFM
AB
E
Grid Cell (x,y)
(1,1)
(1,2)
(1,3)
(1,4)
(2,1)
(2,2)
(2,3)
(2,4)
(3,1)
(3,2)
(3,3)
(3,4)
(4,1)
(4,2)
(4,3)
(4,4)
Mining For Spatial Patterns
t1
Æ
{A, B, D}
Æ
{A, K, M}
{B, C, E}
Æ
Æ
{A, B}
Æ
{A, B, G}
{C, M}
Æ
Æ
Æ
Æ
Æ
t2
Æ
{D, L, J}
{A, B, E, G}
Æ
{E, G, M}
{C, E, F}
Æ
{D, F}
Æ
Æ
Æ
Æ
Æ
{D, K, L}
Æ
{A, B}
t3
Æ
Æ
{B, C, D}
Æ
{C, F, M}
{A, B, G, L}
Æ
{A, B, D}
Æ
{A, B, E}
Æ
Æ
Æ
Æ
{E, G, K}
{D, E, F}
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Interesting Association Patterns
Use domain knowledge to eliminate uninteresting
patterns.
A pattern is less interesting if it occurs at random
locations.
Approach:
Partition the land area into distinct groups (e.g., based on landcover type).
For each pattern, find the regions for which the pattern can be
applied.
If the pattern occurs mostly in a certain group of land areas, then it
is potentially interesting.
If the pattern occurs frequently in all groups of land areas, then it
is less interesting.
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Association Rules
Intra-zone non-sequential Patterns
FPAR-Hi  NPP-Hi (support  10)
Shrubland regions
• Region corresponds to semi-arid grasslands, a type of vegetation, which is able to
quickly take advantage of high precipitation than forests.
• Hypothesis: FPAR-Hi events could be related to unusual precipitation conditions.
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Co-location
Can you find co-location patterns from the following sample dataset?
Answers:
Shashi Shekhar
and
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Co-location
Spatial Co-location
A set of features frequently co-located
Given
A set T of K boolean spatial feature
types
T={f1,f2, … , fk}
A set P of N locations P={p1, …, pN } in
a spatial frame work S, pi P is of
some spatial feature in T
A neighbor relation R over locations in S
Find
Reference Feature Centric
Tc = subsets of T frequently co-located
Objective
Correctness
Completeness
Efficiency
Constraints
R is symmetric and reflexive
Monotonic prevalence measure
Window Centric
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Mining For Spatial Patterns
Event Centric
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Co-location
Comparison with association rules
Association rules
Co-location rules
underlying space
discrete sets
continuous space
item-types
item-types
events /Boolean spatial features
collections
transactions
neighborhoods
prevalence measure
support
participation index
conditional probability
measure
Pr.[ A in T | B in T ]
Pr.[ A in N(L) | B at L ]
Participation index
Participation ratio pr(fi, c) of feature fi in co-location c = {f1, f2, …, fk}: fraction of instances of fi
with
feature {f1, …, fi-1, fi+1, …, fk} nearby 2.Participation index = min{pr(fi, c)}
Algorithm
Hybrid Co-location Miner
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Spatial Co-location Patterns
Dataset
• Spatial feature A,B,C and their instances
• Possible associations are (A, B), (B, C), etc.
• Neighbor relationship includes following pairs:
•A1, B1
•A2, B1
•A2, B2
•B1, C1
•B2, C2
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Spatial Co-location Patterns
Dataset
Partition approach[Yasuhiko, KDD 2001]
•Support not well defined,i.e. not independent of execution
trace
•Has a fast heuristic which is hard to analyze for
correctness/completeness
Spatial feature A,B, C,
and their instances
Support A,B =2 B,C=2
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Mining For Spatial Patterns
Support A,B=1 B,C=2
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Spatial Co-location Patterns
Dataset
Reference feature approach [Han SSD 95]
•C as reference feature to get transactions
•Transactions: (B1) (B2)
•Support (A,B) = Ǿ from Apriori algorithm
Spatial feature A,B, C,
and their instances
Shashi Shekhar
•Note: Neighbor relationship includes following pairs:
•A1, B1
•A2, B1
•A2, B2
•B1, C1
•B2, C2
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Spatial Co-location Patterns
Dataset
Spatial feature A,B, C,
and their instances
Our approach (Event Centric)
• Neighborhood instead of transactions
• Spatial join on neighbor relationship
• Support  Prevalence
•Participation index = min. p_ratio
•P_ratio(A, (A,B)) = fraction of instance of
A participating in join(A,B, neighbor)
•Examples
Support(A,B)=min(2/2,3/3)=1
Support(B,C)=min(2/2,2/2)=1
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Spatial Co-location Patterns
Dataset
Partition approach
Our approach
Support(A,B)=min(2/2,3/3)=1
Support(B,C)=min(2/2,2/2)=1
Spatial feature A,B, C,
and their instances
Support A,B =2 B,C=2
Reference feature
approach
C as reference feature
Transactions: (B1) (B2)
Support (A,B) = Ǿ
Support A,B=1 B,C=2
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Spatial Outliers
Spatial Outlier: A data point that is extreme relative
to it neighbors
Case Study: traffic stations different from neighbors
[SIGKDD 2001, JIDA 2002]
Data - space-time plot, distr. Of f(x), S(x)
Distribution of base attribute:
spatially smooth
frequency distribution over value domain: normal
Classical test - Pr.[item in population] is low
Q? distribution of diff.[f(x), neighborhood agg{f(x)}]
Insight: this statistic is distributed normally!
Test: (z-score on the statistics) > 2
Performance - spatial join, clustering methods
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Spatial Outlier Detection
Given
A spatial graph G={V,E}
A neighbor relationship (K neighbors)
An attribute function f : V -> R
An aggregation function : Faggr :R k -> R
A comparison function Fdiff ( f , Faggr )
Confidence level threshold 
Statistic test function ST: R ->{T, F}
Find
O = {vi | vi V, vi is a spatial outlier}
Objective
Correctness: The attribute values of vi
is extreme, compared with its neighbors
Computational efficiency
Constraints
Fdiff and ST are algebraic aggregate
functions of f and Faggr
Computation cost dominated by I/O op.
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Spatial Outlier Detection
Spatial Outlier Detection Test
1. Choice of Spatial Statistic
S(x) = [f(x)–E y N(x)(f(y))]
Theorem: S(x) is normally distributed
if f(x) is normally distributed
2. Test for Outlier Detection
| (S(x) - s) / s | > 
Hypothesis
I/O cost determined by clustering efficiency
f(x)
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Mining For Spatial Patterns
S(x)
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Graphical Spatial Tests
Moran Scatter Plot
Original Data
Variogram Cloud
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A Unified Approach Spatial Outliers
•Tests : quantitative, graphical
•Results:
•Computation = spatial self-join
•Tests: algebraic functions of join
•Join predicate: neighbor relations
•I/O-cost: f(clustering efficiency)
•Our algorithm is I/O-efficient for
Algebraic tests
Scatter Plot
Original Data
Our Approach
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Spatial Outlier Detection
Results
1. CCAM achieves higher
clustering efficiency (CE)
2. CCAM has lower I/O cost
3. High CE => low I/O cost
4. Big Page => high CE
CE value
Cell-Tree
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CCAM
Mining For Spatial Patterns
I/O cost
Z-order
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Location Prediction
Citations: IEEE Tran. on Multimedia 2002, SIAM DM Conf. 2001,
SIGKDD DMKD 2000
Problem: predict nesting site in marshes
given vegetation, water depth, distance to edge, etc.
Data - maps of nests and attributes
spatially clustered nests, spatially smooth attributes
Classical method: logistic regression, decision trees, bayesian
classifier
but, independence assumption is violated ! Misses autocorrelation !
Spatial auto-regression (SAR), Markov random field bayesian
classifier
Open issues: spatial accuracy vs. classification accurary
Open issue: performance - SAR learning is slow!
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Location Prediction
Given:
1. Spatial Framework S  {s1 ,...sn }
2. Explanatory functions: f X : S  R
3. A dependent class: f C : S  C  {c1 ,...cM }
4. A family  of function
mappings: R ... R  C
k
Find: Classification model: fˆc  
Nest locations
Distance to open water
Objective:maximize
ˆ
classification_accuracy ( f c , f c )
Constraints:
Spatial Autocorrelation exists
Vegetation durability
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Mining For Spatial Patterns
Water depth
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Motivation and Framework
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Spatial AutoRegression (SAR)
•
Spatial Autoregression Model (SAR)
• y = Wy + X + 
• W models neighborhood relationships
•  models strength of spatial dependencies
•  error vector
• Solutions
•  and  - can be estimated using ML or Bayesian stat.
• e.g., spatial econometrics package uses Bayesian
approach using sampling-based Markov Chain Monte
Carlo (MCMC) method.
• Likelihood-based estimation requires O(n3) ops.
• Other alternatives – divide and conquer, sparse matrix,
LU decomposition, etc.
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Evaluation
Linear Regression y  X  
Spatial Regression y  Wy  X  
Spatial model is better
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MRF Bayesian
•
Markov Random Field based Bayesian Classifiers
• Pr(li | X, Li) = Pr(X|li, Li) Pr(li | Li) / Pr (X)
• Pr(li | Li) can be estimated from training data
• Li denotes set of labels in the neighborhood of si
excluding labels at si
• Pr(X|li, Li) can be estimated using kernel functions
• Solutions
• stochastic relaxation [Geman]
• Iterated conditional modes [Besag]
• Graph cut [Boykov]
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Experiment Design
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Prediction Maps(Learning)
Actual Nest Sites (Real Learning)
MRF-P Prediction (ADNP=3.36)
NZ=85
NZ=138
MRF-GMM Prediction (ADNP=5.88)
SAR Prediction (ADNP=9.80)
NZ=140
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NZ=130
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Prediction Maps(Testing)
Actual Nest Sites (Real Testing)
MRF-P Prediction (ADNP=2.84)
Actual Nest Sites (Real Learning)
NZ=30
NZ=80
MRF-GMM Prediction (ADNP=3.35)
NZ=76
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SAR Prediction (ADNP=8.63)
NZ=80
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Comparison (MRF-BC vs. SAR)
•
•
•
•
SAR can be rewritten as y = (QX)  + Q
• where Q = (I- W)-1 which can be viewed as a spatial
smoothing operation.
• This transformation shows that SAR is similar to linear
logistic model, and thus suffers with same limitations –
i.e., SAR model assumes linear separability of classes in
transformed feature space
SAR model also make more restrictive assumptions about the
distribution of features and class shapes than MRF
The relationship between SAR and MRF are analogous to the
relationship between logistic regression and Bayesian
classifiers.
Our experimental results shows that MRF model yields better
spatial and classification accuracies than SAR predictions.
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MRF vs. SAR
Confusion Matrix:
Spatial Confusion Matrix:
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Conclusion and Future Directions
Spatial domains may not satisfy assumptions of classical
methods
data: auto-correlation, continuous geographic space
patterns: global vs. local, e.g. spatial outliers vs. outliers
data exploration: maps and albums
Open Issues
patterns: hot-spots, blobology (shape), spatial trends, …
metrics: spatial accuracy(predicted locations), spatial
contiguity(clusters)
spatio-temporal dataset
scale and resolutions sentivity of patterns
geo-statistical confidence measure for mined patterns
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Army Relevance and Collaborations
Relevance: “Maps are as important to soldiers as guns” - unknown
Joint Projects:
High Performance GIS for Battlefield Simulation (ARL Adelphi)
Spatial Querying for Battlefield Situation Assessment (ARL Adelphi)
Joint Publications:
w/ G. Turner (ARL Adelphi, MD) & D. Chubb (CECOM IEWD)
IEEE Computer (December 1996)
IEEE Transactions on Knowledge and Data Eng. (July-Aug. 1998)
Three conference papers
Visits, Other Collaborations
GIS group, Waterways Experimentation Station (Army)
Concept Analysis Agency, Topographic Eng. Center, ARL, Adelphi
Workshop on Battlefield Visualization and Real Time GIS (4/2000)
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Reference
1.
S. Shekhar, S. Chawla, S. Ravada, A. Fetterer, X. Liu and C.T. Liu, “Spatial Databases: Accomplishments and
Research Needs”, IEEE Transactions on Knowledge and Data Engineering, Jan.-Feb. 1999.
2.
S. Shekhar and Y. Huang, “Discovering Spatial Co-location Patterns: a Summary of Results”, In Proc. of 7th
International Symposium on Spatial and Temporal Databases (SSTD01), July 2001.
3.
S. Shekhar, C.T. Lu, P. Zhang, "Detecting Graph-based Spatial Outliers: Algorithms and Applications“, the
Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2001.
4.
S. Shekhar, C.T. Lu, P. Zhang, “Detecting Graph-based Saptial Outlier”, Intelligent Data Analysis, To appear in
Vol. 6(3), 2002
5.
S. Shekhar, S. Chawla, the book “Spatial Database: Concepts, Implementation and Trends”, Prentice Hall, 2002
6.
S. Chawla, S. Shekhar, W. Wu and U. Ozesmi, “Extending Data Mining for Spatial Applications: A Case Study in
Predicting Nest Locations”, Proc. Int. Confi. on 2000 ACM SIGMOD Workshop on Research Issues in Data
Mining and Knowledge Discovery (DMKD 2000), Dallas, TX, May 14, 2000.
7.
S. Chawla, S. Shekhar, W. Wu and U. Ozesmi, “Modeling Spatial Dependencies for Mining Geospatial Data”,
First SIAM International Conference on Data Mining, 2001.
8.
S. Shekhar, P.R. Schrater, R. R. Vatsavai, W. Wu, and S. Chawla, “Spatial Contextual Classification and Prediction
Models for Mining Geospatial Data”,To Appear in IEEE Transactions on Multimedia, 2002.
9.
S. Shekhar, V. Kumar, P. Tan. M. Steinbach, Y. Huang, P. Zhang, C. Potter, S. Klooster, “Mining Patterns in Earth
Science Data”, IEEE Computing in Science and Engineering (Submitted)
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Reference
10.
S. Shekhar, C.T. Lu, P. Zhang, “A Unified Approach to Spatial Outliers Detection”, IEEE Transactions on
Knowledge and Data Engineering (Submitted)
11.
S. Shekhar, C.T. Lu, X. Tan, S. Chawla, Map Cube: A Visualization Tool for Spatial Data Warehouses, as Chapter
of Geographic Data Mining and Knowledge Discovery. Harvey J. Miller and Jiawei Han (eds.), Taylor and
Francis, 2001, ISBN 0-415-23369-0.
12.
S. Shekhar, Y. Huang, W. Wu, C.T. Lu, What's Spatial about Spatial Data Mining: Three Case Studies , as Chapter
of Book: Data Mining for Scientific and Engineering Applications. V. Kumar, R. Grossman, C. Kamath, R.
Namburu (eds.), Kluwer Academic Pub., 2001, ISBN 1-4020-0033-2
13.
Shashi Shekhar and Yan Huang , Multi-resolution Co-location Miner: a New Algorithm to Find Co-location
Patterns in Spatial Datasets, Fifth Workshop on Mining Scientific Datasets (SIAM 2nd Data Mining Conference),
April 2002
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