1. Spatial Data Mining: Three Case Studies
For additional details
Shashi Shekhar, University of Minnesota
Presented to UCGIS Summer Assembly 2001

2. 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, …

3. 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

4. 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

5. Spatial outlier detection[4]
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.

6. 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)
S(x)
Spatial outlier and its neighbors

7. 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
CE value
I/O cost
Cell-Tree
CCAM
Z-order

8. 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!

9. Location Prediction[6, 7, 8]
Given:
1. Spatial Framework
2. Explanatory functions:
3. A dependent function
4. A family of function mappings:
Find: A function
Objective:maximize
classification_accuracy
Constraints:
Spatial Autocorrelation exists
Nest locations
Distance to open water
Vegetation durability
Water depth

10. Evaluation: Changing Model
Linear Regression
Spatial Regression
Spatial model is better

11. Evaluation: Changing measure
New measure:

12. 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

13. Co-location Patterns[2, 3]
Can you find co-location patterns from the following sample dataset?
Answers: and

14. Co-location Patterns
Can you find co-location patterns from the following sample dataset?

15. Co-location Patterns Spatial Co-location Given Find Objective
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
Tc = subsets of T frequently co-located
Objective
Correctness
Completeness
Efficiency
Constraints
R is symmetric and reflexive
Monotonic prevalence measure
Reference Feature Centric
Window Centric
Event Centric

16. Co-location Patterns Comparison with association rules
Co-location rules
underlying space
discrete sets
continuous space
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

17. 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

18. References
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
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.
S. Shekhar, Y. Huang, and H. Xiong, “Performance Evaluation of Co-location Miner”, the IEEE International Conference on Data Mining (ICDM’01), Nov (submitted)
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.
S. Shekhar, S. Chawla, the book “Spatial Database: Concepts, Implementation and Trends”. (To be published in 2001)
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.
S. Chawla, S. Shekhar, W. Wu and U. Ozesmi, “Modeling Spatial Dependencies for Mining Geospatial Data”, First SIAM International Conference on Data Mining, 2001.
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, (Submitted)
Some papers are available on the Web sites: