Spatial Data Mining: Three Case Studies

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Spatial Data MiningThree Case Studies
For additional details www.cs.umn.edu/shekhar/p
roblems.html
Shashi Shekhar, University of Minnesota Presented
to UCGIS Summer Assembly 2001
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Background

• NSF workshop on GIS and DM (3/99)
• Spatial data1, 8 - traffic, bird habitats,
  global climate, logistics, ...
• For spatial patterns - outliers, location
  prediction, associations, sequential
  associations, trends,

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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

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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
  aggf(x)
• Insight this statistic is distributed normally!
• Test (z-score on the statistics) gt 2
• Performance - spatial join, clustering methods

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Spatial outlier detection4

• Spatial outlier
• A data point that is extreme relative to
• it neighbors
• Given
• A spatial graph GV,E
• A neighbor relationship (K neighbors)
• An attribute function f V -gt R
• An aggregation function f aggr R k -gt 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.

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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 gt ?
• Hypothesis
• I/O cost determined by clustering efficiency

f(x)
S(x)
Spatial outlier and its neighbors
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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

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

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Location Prediction6, 7, 8

• Given
• 1. Spatial Framework
• 2. Explanatory functions
• 3. A dependent function
• 4. A family of function mappings
• Find A function
• Objectivemaximize
• classification_accuracy
• Constraints
• Spatial Autocorrelation exists

Nest locations
Distance to open water
Water depth
Vegetation durability
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Evaluation Changing Model

• Linear Regression
• Spatial Regression
• Spatial model is better

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Evaluation Changing measure
New measure
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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

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Co-location Patterns2, 3
Can you find co-location patterns from the
following sample dataset?
Answers and
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Co-location Patterns
Can you find co-location patterns from the
following sample dataset?
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Co-location Patterns

• Spatial Co-location
• A set of features frequently co-located
• Given
• A set T of K boolean spatial feature types
  Tf1,f2, , fk
• A set P of N locations Pp1, , 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
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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, fi1, , fk nearby
  2.Participation index minpr(fi, c)
• Algorithm
• Hybrid Co-location Miner

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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

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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. 1999.
• 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
  (ICDM01), Nov. 2001. (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, 2001.
  (Submitted)

Some papers are available on the Web sites
http//www.cs.umn.edu/research/shashi-group/