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Mining for Spatial Patterns

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NASA Ames Research Center: C. Potter. California State University, Monterey Bay: S. Klooster ... data exploration: maps and albums. Open Issues ... – PowerPoint PPT presentation

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Title: Mining for Spatial Patterns


1
Mining for Spatial Patterns
  • Shashi Shekhar
  • Department of Computer Science
  • University of Minnesota http//www.cs.umn.edu/s
    hekhar
  • Collaborators
  • U. of Minnesota V. Kumar, G. Karypis, C.T. Lu,
    W. Wu, Y. Huang, V. Raju, P. Zhang, P. Tan, M.
    Steinbach
  • NASA Ames Research Center C. Potter
  • California State University, Monterey Bay S.
    Klooster
  • This work was partially funded by NASA and Army
    High Performance Computing Center

2
Background
  • NSF workshop on GIS and DM (3/99)
  • Spatial data - traffic, bird habitats, global
    climate, logistics, ...
  • For spatial patterns - outliers, location
    prediction, associations, sequential
    associations, clustering, 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
Research Goals
  • Research Goals
  • modeling of ecological data
  • event modeling
  • zone modeling.
  • finding spatio-temporal patterns
  • associations
  • predictive models.

A key interest is finding connections between the
ocean and the land.
5
Sources of Earth Science Data
  • Before 1950, very sparse, unreliable data.
  • Since 1950, reliable global data.
  • Ocean temperature and pressure are based on data
    from ships.
  • Most land data, (solar, precipitation,
    temperature and pressure) comes from weather
    stations.
  • Since 1981, data has been available from Earth
    orbiting satellites.
  • FPAR, a measure related to plant
  • Since 1999 TERRA, the flagship of the NASA Earth
    Observing System, is providing much more detailed
    data.

6
Example Pattern Teleconnections
  • Teleconnections are the simultaneous variation in
    climate and related processes over widely
    separated points on the Earth.
  • For example, El Nino is the anomalous warming of
    the eastern tropical region of the Pacific, and
    has been linked to various climate phenomena.
  • Droughts in Australia and Southern Africa
  • Heavy rainfall along the western coast of South
    America
  • Milder winters in the Midwest

7
Net Primary Production (NPP)
  • Net Primary Production (NPP) is the net
    assimilation of atmospheric carbon dioxide (CO2)
    into organic matter by plants.
  • NPP is driven by solar radiation and can be
    constrained by precipitation and temperature.
  • NPP is a key variable for understanding the
    global carbon cycle and ecological dynamics of
    the Earth.
  • Keeping track of NPP is important because it
    includes the food source of humans and all other
    organisms.
  • Sudden changes in the NPP of a region can have a
    direct impact on the regional ecology.
  • An ecosystem model for predicting NPP, CASA (the
    Carnegie Ames Stanford Approach) provides a
    detailed view of terrestrial productivity.

8
Benefits of Data Mining
  • Data mining provides earth scientist with tools
    that allow them to spend more time choosing and
    exploring interesting families of hypotheses.
  • However, statistics is needed to provide methods
    for determining the statistical significance of
    results.
  • By applying the proposed data mining techniques,
    some of the steps of hypothesis generation and
    evaluation will be automated, facilitated and
    improved.
  • Association rules provide a new framework for
    detecting relationships between events.

9
Approaches
10
Clustering
  • Interested in relationships between regions, not
    points.
  • For land, clustering based on NPP or other
    variables, e.g., precipitation, temperature.
  • For ocean, clustering based on SST (Sea Surface
    Temperature).
  • When raw NPP and SST are used, clustering can
    find seasonal patterns.
  • Anomalous regions have plant growth patterns
    which reversed from those typically observed in
    the hemisphere in which they reside, and are easy
    to spot.

11
Clustering
El Nino Regions
SNN clusters of SST that are highly correlated
with El Nino indices.
12
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

13
Event Definition
  • Convert the time series into sequence of events
    at each spatial location.

14
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 land-cover 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.

15
Association Rules
  • Intra-zone non-sequential Patterns
  • 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.

16
Co-location
Can you find co-location patterns from the
following sample dataset?
Answers and
17
Co-location
Can you find co-location patterns from the
following sample dataset?
18
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
19
Co-location
Comparison with association rules
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
20
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

21
Spatial Co-location Patterns
  • Partition approachYasuhiko, 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,B1 B,C2
Support A,B 2 B,C2
22
Spatial Co-location Patterns
  • Dataset
  • Reference feature approach Han SSD 95
  • C as reference feature to get transactions
  • Transactions (B1) (B2)
  • Support (A,B) ? from Apriori algorithm
  • Note Neighbor relationship includes following
    pairs
  • A1, B1
  • A2, B1
  • A2, B2
  • B1, C1
  • B2, C2

Spatial feature A,B, C, and their instances
23
Spatial Co-location Patterns
  • 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
  • Dataset

Spatial feature A,B, C, and their instances
24
Spatial Co-location Patterns
  • Partition approach
  • Our approach
  • Dataset

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

C as reference feature Transactions (B1)
(B2) Support (A,B) ?
Support A,B1 B,C2
25
Spatial Outliers
  • Spatial Outlier A data point that is extreme
    relative to it neighbors
  • Case Study traffic 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

26
Spatial Outlier Detection
Given A spatial graph GV,E A neighbor
relationship (K neighbors) An attribute
function V -gt R An aggregation function
R k -gt R A comparison function
Confidence level threshold ? Statistic test
function ST R -gtT, 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
and ST are algebraic aggregate functions of
and Computation cost dominated by I/O op.
27
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)
28
Spatial Outlier Detection
Results 1. CCAM achieves higher clustering
efficiency (CE) 2. CCAM has lower I/O cost
3. High CE gt low I/O cost 4. Big Page gt high
CE
I/O cost
CE value
Z-order
CCAM
Cell-Tree
29
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
  • Algebric tests

Scatter Plot
Original Data
Our Approach
30
Graphical Spatial Tests
Moran Scatter Plot
Original Data
Variogram Cloud
31
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
    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!

32
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
Water depth
Vegetation durability
33
Motivation and Framework
34
Solution Procedures
  • 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.

35
Evaluation
  • Linear Regression
  • Spatial Regression
  • Spatial model is better

36
Solution Procedures
  • Markov Random Field based Bayesian Classifiers
  • Pr(li X, Li) Pr(Xli, 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(Xli, Li) can be estimated using kernel
    functions
  • Solutions
  • stochastic relaxation Geman
  • Iterated conditional modes Besag
  • Graph cut Boykov

37
Comparison
  • 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.

38
MRF vs. SAR
Confusion Matrix
Spatial Confusion Matrix
39
Experiment Design
40
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

41
Reference
  • 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, 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. Shekhar, S. Chawla, the book Spatial
    Database Concepts, Implementation and Trends,
    Prentice Hall, 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, 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.
  • 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)

42
Reference
  • S. Shekhar, C.T. Lu, P. Zhang, A Unified
    Approach to Spatial Outliers Detection, IEEE
    Transactions on Knowledge and Data Engineering
    (Submitted)
  • 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.
  • 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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