Spatial Data Mining: Three Case Studies

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Spatial Data Mining Three Case Studies

• Presented by Chang-Tien Lu
• Spatial Database Lab
• Department of Computer Science
• University of Minnesota
• ctlu_at_cs.umn.edu
• http//www.cs.umn.edu/research/shashi-group
• Group Members
• Shashi Shekhar, Weili Wu, Yan Huang, C.T. Lu

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Outline

• Introduction
• Case 1 Location Prediction
• Case 2 Spatial Association Co-location
• Case 3 Spatial Outlier Detection
• Conclusion and Future Directions

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Introduction spatial data mining

• Spatial Databases are too large to analyze
  manually
• NASA Earth Observation System (EOS)
• National Institute of Justice Crime mapping
• Census Bureau, Dept. of Commerce - Census Data
• Spatial Data Mining
• Discover frequent and interesting spatial
  patterns for post processing (knowledge
  discovery)
• Pattern examples spatial outliers, location
  prediction, clustering, spatial association,
  trends, ..
• Historical Example
• London, 1854
• Cholera water pump

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Framework

• Problem statement capture special needs
• Data exploration maps
• Try reusing classical methods
• data mining, spatial statistics
• Invent new methods if reuse is not applicable
• Develop efficient algorithms
• Validation, Performance tuning

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Case 1 Location Prediction

• 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)
• Open issues spatial accuracy vs. classification
  accurary
• Open issue performance - SAR learning is slow!

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Location Prediction
Given 1. Spatial Framework 2. Explanatory
functions 3. A dependent class 4. A family
of function mappings Find Classification
model Objectivemaximize classification_accurac
y Constraints Spatial Autocorrelation exists

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

• Linear Regression
• Spatial Autoregression Model (SAR)
• y ?Wy X? ?
• W models neighborhood relationships
• ? models strength of spatial dependencies
• ? error vector
• Mixed Spatial Autoregression Model (MSAR)
• y ?Wy X? WX? ?
• Consider the impact of the explanatory variables
  from the neighboring observations

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Measure ROC Curve

• Classification accuracy confusion matrix

• ROC Curve Locus of the pair (TPR,FPR) for each
  cut-off probability
• Receiver Operating Characteristic (ROC)
• TPR AnPn / (AnPn AnPnn)
• FPR AnnPn / (AnnPnAnnPnn)

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Evaluation Change Model

• Linear Regression
• Spatial Regression
• Spatial model is better

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Solution Procedures

• Spatial Autoregression Model (SAR)
• y ?Wy X? ?
• Solutions
• ? and ? - can be estimated using Maximum
  likelihood theory or Bayesian statistics.
• e.g., spatial econometrics package uses Bayesian
  approach using sampling-based Markov Chain Monte
  Carlo (MCMC) method.
• Maximum likelihood-based estimation requires
  O(n3) ops.

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Evaluation Chang measure

• Spatial accuracy (map similarity)

• New measure ADNP
• Average distance to nearest prediction

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Predicting Location using Map Similarity
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Predicting location using Map Similarity

• PLUMS components
• Map Similarity Avg. Distance to Nearest
  Prediction(ADNP) ,..
• Search Algorithm Greedy, gradient descent
• Function family generalized linear (GL)(logit,
  probit), non-linear,
• GL with auto-correlation
• Discretization of parameter space Uniform,
  non-uniform,
• multi-resolution,

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Association Rule

• Supermarket shelf management
• Goal To identify items that are bought together
  by sufficiently many customers
• Approach Process the point-of-scale data
  collected with barcode scanners to find
  dependencies among items (Transaction data)
• A classic rule
• If a customer buys diaper and milk, then he is
  very likely to buy beer
• So, dont be surprised if you find six-packs of
  beer stacked next to diapers!

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Association RulesSupport and confidence

• Item set I i1, i2, .ik
• Transactions T t1, t2, tn
• Association rule A -gt B
• Support S
• (A and B) occur in at least S percent of the
  transactions
• P (A U B)
• Confidence C
• Of all the transactions in which A occurs, at
  least C percent of them contains B
• P (BA)

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Case 2 Spatial Association Rule

• 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
• Classical data mining approach association rules
• But, No Transactions!!! No support measure!!
• Approach Work with continuous data without
  transactionizing it!
• Participation index (support) min. fraction of
  instances of a features in join result
• Confidence Pr.fire at s drought in N(s) and
  vegetation in N(s)
• new algorithm using spatial joins

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Co-location
Can you find co-location patterns from the
following sample dataset?
Answers and
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Co-location
Can you find co-location patterns from the
following sample dataset?
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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 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
Comparison with association rules

• Participation index
• Participation index minpr(fi, c)
• Participation ratio pr(fi, c) of feature fi in
  co-location c f1, f2, , fk
• Fraction of instances of fi with feature f1,
  f2, f i-1, f i1,, fk nearby.

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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

• 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

• Dataset

Spatial feature A,B, C, and their instances
Support (A,B) 2 (B,C)2
Support (A,B)1 (B,C)2
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Spatial Co-location Patterns

• Reference feature approach Han SSD 95
• Use C as reference feature to get transactions
• Transactions (B1) (B2)
• Support (A,B) ?
• Note Neighbor relationship includes following
• pairs
• A1, B1
• A2, B1
• A2, B2
• B1, C1
• B2, C2

• Dataset

Spatial feature A,B, C, and their instances
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Spatial Co-location Patterns

• Our approach (Event Centric)
• Neighborhood instead of transactions
• Spatial join on neighbor relationship
• Support
• 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(3/2,3/2)1.5
• Support(B, C)min(2/2,2/2)1

• Dataset

Spatial feature A,B, C, and their instances
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Spatial Co-location Patterns

• Partition approach

• Our approach

• Dataset

Support(A,B)min(3/2,3/2)1.5
Support(B,C)min(2/2,2/2)1
Support A,B 2 B,C2
Spatial feature A,B, C, and their instances

• Reference feature approach

C as reference feature Transactions (B1)
(B2) Support (A,B) ?
Support A,B1 B,C2
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Case 3 Spatial Outliers Detection

• Spatial Outlier A data point that is extreme
  relative to it neighbors

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Application Domain Traffic Data
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Spatial Outlier Detection

• Given
• A spatial framework SF consisting of locations
  s1, s2, , sn
• An attribute function f si ? R
• (R set of real numbers)
• A neighborhood relationship N ? SF ? SF
• A neighborhood aggregation function RN ?
  R
• A difference function Fdiff R ? R ? R
• Statistic test function ST R ? True, False
• Test is based on Fdiff (f, (f, N)
• 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

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An example of Spatial outlier
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Spatial Outlier Detection Zs(x) approach
Function
If
Declare x as a spatial outlier
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Evaluation of Statistical Assumption

• Distribution of traffic station attribute f(x)
  looks normal
• Distribution of
  looks normal too!

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Different Spatial Outlier Test

• Spatial Statistic Approach
• Scatter plot approach(Luc Anselin 94)
• Moran scatter plot approach (Luc Anselin 95)
• Variogram cloud approach (Graphic)

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Scatter plot approach

• Given
• An attribute function f(x)
• A neighborhood relationship N(x)
• An aggregation function
• A difference function
• Fdiff ? E(x) (m ? f(x) b)
• Detect spatial outlier by
• Statistic test function
• ST

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Graphical Spatial Outlier Test
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Graphical Spatial Tests
Original Data
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A Unified Algorithm

• Separate two phases
• Model building
• Testing (a node or a set of nodes)
• Computation structure of model building
• Key insights
• Spatial self join using N(x) relationship
• Algebraic aggregate functions can be computed in
  one disk scan of spatial join
• Computation structure of testing
• Single node spatial range query
• Get-All-Neighbors(x) operation

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An example Scatter plot

• Model building
• An attribute function f(x)
• Neighborhood aggregate function
• Distributive aggregate functions
• Algebraic aggregate functions
• where
  ,
• Testing
• Difference function
• where
• Statistic test function

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Outlier Stations Detected
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Outlier Station Detected
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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., outliers vs.
  spatial outliers
• data exploration maps and albums
• Open Issues
• patterns hot-spots, spatial trends,
• metrics spatial accuracy (predicted locations),
  spatial contiguity(clusters)
• spatio-temporal dataset spatial-temporal
  outliers
• scale and resolutions sentivity of patterns
• geo-statistical confidence measure for mined
  patterns

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Reference

• 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, 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, C.T. Lu, P. Zhang, Detecting
  Graph-based Saptial Outlier, Intelligent Data
  Analysis, To appear in Vol. 6(3), 2002
• 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, 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
• 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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http//www.cs.umn.edu/research/shashi-group
Thank you !!!