Spatial Data Mining:
Three Case Studies
Shashi Shekhar, University of Minnesota
Presented to UCGIS Summer Assembly 2001
For additional details
www.cs.umn.edu/~shekhar/problems.html
Background
• NSF workshop on GIS and DM (3/99)
• Spatial data[1, 8] - traffic, bird habitats,
global climate, logistics, ...
• For spatial patterns - outliers, location
prediction, associations, sequential
associations, trends, …
Framework
• Problem statement: capture special needs
• Data exploration: maps, new methods
• Try reusing classical methods
– from data mining, spatial statistics
• If reuse is not possible, invent new methods
• Validation, Performance tuning
Case 1: Spatial Outliers
• Problem: stations different from neighbors [SIGKDD 2001]
• 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
Spatial outlier detection[4]
Spatial outlier
A data point that is extreme relative to
it neighbors
Given
A spatial graph G={V,E}
A neighbor relationship (K neighbors)
An attribute function f: V -> R
An aggregation function f aggr : R k -> R
Confidence level threshold 
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
Attribute value is normally distributed
Computation cost dominated by I/O op.
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)
Spatial outlier and its neighbors
S(x)
Spatial outlier detection
Results
1. CCAM achieves higher
clustering efficiency (CE)
2. CCAM has lower I/O cost
3. Higher CE leads to lower
I/O cost
4. Page size improves CE for
all methods
Cell-Tree
CE value
I/O cost
CCAM
Z-order
Case 2: Location Prediction
• Citations: 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 auto-correlation !
– Spatial auto-regression (SAR), Markov random field bayesian
classifier
– Open issues: spatial accuracy vs. classification accurary
– Open issue: performance - SAR learning is slow!
Location Prediction[6, 7, 8]
Given:
1. Spatial Framework
S  {s1 ,...sn }
f Xk : S  R
2. Explanatory functions:
fY : S  {0,1}
3. A dependent function
4. A family  of function mappings:
R  ...  R  {0,1}
Find: A function
fˆy  
Nest locations
Objective:maximize
classification_accuracy
Distance to open water
( fˆy , f y )
Constraints:
Spatial Autocorrelation exists
Vegetation durability
Water depth
Evaluation: Changing Model
• Linear Regression y  X  
• Spatial Regression y  Wy  X  
• Spatial model is better
Evaluation: Changing measure
New measure:
ADNP( A, P)   dist ( Ak , Ak .nearest ( P))
k
Case 3: Spatial Association Rules
• 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
Co-location Patterns[2, 3]
Can you find co-location patterns from the following sample dataset?
Answers:
and
Co-location Patterns
Can you find co-location patterns from the following sample dataset?
Co-location Patterns
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
Reference Feature Centric
Find
Tc = subsets of T frequently co-located
Objective
Correctness
Completeness
Efficiency
Constraints
R is symmetric and reflexive
Monotonic prevalence measure
Window Centric
Event Centric
Co-location Patterns
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
Conclusions & 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
References
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, Y. Huang, and H. Xiong, “Performance Evaluation of Co-location Miner”, the IEEE International Conference on Data
Mining (ICDM’01), Nov. 2001. (submitted)
4.
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.
5.
S. Shekhar, S. Chawla, the book “Spatial Database: Concepts, Implementation and Trends”. (To be published in 2001)
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”, IEEE Transactions on Multimedia, 2001. (Submitted)
Some papers are available on the Web sites: http://www.cs.umn.edu/research/shashi-group/