IDENTIFYING PATTERNS IN
SPATIAL DATA
Xun Zhou
University of Iowa
September 5, 2014
OUTLINE
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Introduction
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Spatial Data and Models
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Statistical models
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Spatial Pattern Families
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Computational Challenges
WHAT IS SPATIAL DATA MINING (SDM)
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Identifying interesting, non-trivia, and useful patterns from large
spatial datasets
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“Spatial” is general – includes spatio-temporal
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Examples of spatial/spatio-temporal datasets:
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GPS traces
Facebook / Twitter check-ins
Climate observations (e.g., rainfall, temperature, etc).
Remotely sensed images (e.g., NASA products)
Crime reports
Disease maps and records
Traffic statistics and road networks
Sales/market price data, supply maps
WHY IS SDM IMPORTANT
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Location/time information brings rich context
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Support decision making
Understanding natural phenomenon
Improve the quality of knowledge
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London Cholera 1854 – John Snow
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Modern examples
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Predict land cover type with limited samples
Which animals often live in the same area?
Detect outbreaks of diseases/crimes
Find anomalous climate events
Picture Courtesy: Prof. Shashi Shekhar @ UMN
WHAT IS “SPECIAL” ABOUT “SPATIAL”
Traditional Data Mining
Spatial Data Mining
Data Types
Age, salary, text…
(in addition) Location, shape, time …
Relationships
Arithmetic,
Ordering,
Subset…
Topological,
directional,
metric…
Statistical models
Data follows i.i.d.
Data is auto-correlated & heterogeneous
Output pattern
Diaper + beer = frequent
set
Diaper + beer only frequent in blue-collar
neighborhoods
Computation
…
…
Picture Source: [1]
SPATIAL DATA MINING COMPONENTS
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Input Data
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Statistical Foundations
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Output patterns
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Computational Process
OUTLINE
•
Introduction
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Spatial Data and Models
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Statistical models
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Spatial Pattern Families
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Computational Challenges
SPATIAL DATA TYPES
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Two data representation models
Vector Data (Object Model)
Raster Data (Field Model)
Data representation
Geometric objects
Continuous field with attribute
functions
Examples
Disease reports (point)
GPS traces (lines/curves)
Counties, states (polygons)
Satellite images
Temperature map of the U.S.
Vegetation cover in Africa
Picture source: [2]
SPATIAL RELATIONSHIPS AND OPERATIONS
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Between spatial objects:
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Set-oriented: Union, Intersection, Membership…
Topological: Meet, within, overlap, connected…
Directional: North, East, left, above, below…
Metric: Distance, area, perimeter
Spatial field operations
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Local, Focal, Zonal, Global
Individual location
(elevation > 1000 ft.)
A small neighborhood
(slope, gradient)
Part of a region
(Mountain peak)
Among all the locations
(The Everest)
OUTLINE
•
Introduction
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Spatial Data and Models
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Statistical models
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Spatial Pattern Families
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Computational Challenges
TWO KEY FEATURES
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Spatial Autocorrelation
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The first law of geography[*]: “Everything is related to everything, but near
things are more relevant than distant things”.
Spatial features are usually auto-correlated or clustered rather than
randomly distributed
Spatial heterogeneity
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Spatial patterns are not uniform globally – they vary from place to place.
[*] Tobler W., (1970) "A computer movie simulating urban growth in the Detroit region". Economic
Geography, 46(2): 234-240.
STATISTICAL FOUNDATIONS
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Spatial statistics – a brunch of statistics
Models[4]
Geostatistical
Lattice(Areal)
Point Process
Scenarios
Continuous space
Disjoint and complete
partitions of the space (e.g.,
grids, areas)
Distribution of points
Examples
Temperature in US
Population of counties
Locations of birds
Spatial Autoregressive
Regression (SAR)
Markov Random Field (MRF)
Ripley’s K-function
Cross k-function
Complete Spatial
Randomness (CSR)
Major
Kriging (spatial
techniques interpolation)
* These are statistical models (like normal distribution) and may not lineup with data
representation models.
SPATIAL NEIGHBORHOOD
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A collection of nearby location/spatial object
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Adjacent/connected objects/locations
Within a certain distance
r
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The W-matrix:
A
B
C
D
𝐴
𝐵
𝐶
𝐷
𝐴 𝐵 𝐶
0 1 1
1 0 0
1 0 0
0 1 1
𝐷
0
1
1
0
𝐴
𝐵
𝐶
𝐷
𝐴
𝐵
𝐶
𝐷
0 0.5 0.5 0
0.5 0
0 0.5
0.5 0
0 0.5
0 0.5 0.5 0
OUTLINE
•
Introduction
•
Spatial Data and Models
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Statistical models
•
Spatial Pattern Families
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Computational Challenges
SPATIAL PATTERN FAMILIES
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A comparison with traditional DM tasks
Traditional Data Mining Pattern Families
Spatial Data Mining Pattern Families
Prediction/Classification
Spatial Prediction/Geographic
Classification
Clustering
Spatial Clustering/Hotspot detection
Anomaly Detection
Spatial Anomaly/Outlier Detection
Association Rule Mining
Spatial Co-location Patterns
SPATIAL PREDICTION
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C4.5 results on land cover data [5]
Traditional classifiers based on i.i.d. and global model
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Linear regression, Decision Tree, SVM, CART, etc.
Spatial auto-correlation and variation are not modeled
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Predicting land cover types, location-based recommendation
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Regression
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Linear regression
SAR
GWR
𝑦 = 𝑋𝛽 + 𝜖
𝑦 = 𝜌𝑊𝑦 + 𝑋𝛽 + 𝜖
𝑦 = 𝑋𝛽 ′ + 𝜖 ′
(𝛽 ′ 𝑎𝑛𝑑 𝜖 ′ 𝑎𝑟𝑒 𝑙𝑜𝑐𝑎𝑡𝑖𝑜𝑛 𝑑𝑒𝑝𝑒𝑛𝑑𝑒𝑛𝑡)
Spatial Decision Tree[5]
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Information gain function: add spatial autocorrelation measure
Spatial
Decision rules: Traditional
Illustration of focal-test-based
f(x) > 1? Left : Right
Flip if neighbors classified differently
spatial decision tree[5]
SPATIAL OUTLIER DETECTION
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Traditional Anomaly Detection
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Data is anomalous w.r.t. global data distribution
Spatial outlier[6]
Data is anomalous w.r.t. its neighbors (discontinuity)
• Finding Suspicious buildings, broken sensors, or other points of interest…
• Methods:
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Variogram clouds
• Moran scatterplot
• Spatial Statistic (S)
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1-D spatial data and distribution [1]
SPATIAL ASSOCIATION
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Spatial Co-location pattern[7]
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Given a number of spatial object types and instances
Find sets of types that are frequently located in proximity
Example: {Fox, Rabbits}, {Nile Crocodiles, Egyptian Plover}
Frequent item set
Co-location
Comment
Transactions
Neighbor set
Space is continuous, no
transactions
Support,
Confidence
Participation
index
PI = min(AB/A, AB/B)
{‘+’, ‘x’}, {‘o’, ‘*’}
Pictures source: [1]
SPATIAL CLUSTERING
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Grouping spatial objects into clusters such that
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Intra-cluster similarity is maximized
Inter-cluster similarity is minimized
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Detecting communities, crowds, building blocks, etc.
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Is there a clustering tendency of data in space (point data)?
1. Hierarchical
2. Partitioning: k-means
3. Density-based: DBSCAN
Picture Courtesy: Prof. Shashi
Shekhar @ UMN
Complete Spatial
Randomness(CSR)
Clustered
Di-clustered
SPATIAL HOTSPOT DETECTION
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Special case of clustering
Identify regions with high density - not a complete partitioning of data
• Ignore noise or sparse clusters
• Crime/disease outbreaks, traffic jam, water pollution…
• Statistical significance – avoid random clusters
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Density-based approaches: DBSCAN[8]
DBSCAN output on clustered dataset: min neighbors=3, radius=7
100
DBSCAN output on CSR dataset: min neighbors=3, radius=7
100
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Statistical tests – spatial scan statistics[9] (public health)
90
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Spatial Scan
Statistics
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Y
Y
80
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10
0
DBSCAN
Spatial Scan
Statistics
10
0
DBSCAN
NEW DIMENSIONS OF SPATIAL PATTERNS
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Patterns on Spatial Networks
Hotspots (Dangerous routes with high risk of accidents)[10]
• Clusters (Crimes along the streets, bus/bike route planning)
• Predictions
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Irregular/complex-shaped Spatial Patterns
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Complex-shaped clusters (terrain constraints)
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Irregular Hotspots (gerrymander …)
Results on pedestrian fatality data from Orlando, FL.[10]
ADDING TIME
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Input data
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Spatial data  Spatio-temporal data
Time series
• Vector: point sequences, polygon series…
• Raster: image sequences, spatial time series (a time series at each grid)
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Relationship: before, after, during, simultaneous, …
Statistical Foundations
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Markov Chain, Hidden Markov Model…
Spatiotemporal Statistics
ADDING TIME - PATTERNS
Spatial Data Mining Pattern Families
Spatiotemporal Patterns
Spatial Prediction/Geographic
Classification
ST prediction (trajectory prediction, climate
projection, market prediction…)
Spatial Anomaly/Outlier Detection
ST Anomaly (abnormal climate events,
traffic sensors…)
Spatial Co-location Patterns
Co-occurrence[11], Cascading pattern[12]
(Crime associations, potential social
connections)
Spatial Clustering/Hotspot detection
Space-time clusters[13] (disease monitoring)
Moving clusters (flocks, fleet, etc)
Emerging Hotspot (New market…)
Spreading hotspot (Strikes, Arabic Spring…)
ADDING TIME – NEW PATTERNS
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New Dimensions of Temporal Information
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Change
Repeating/periodicity
Temporal dimensions
Spatiotemporal Patterns
Change
Change Footprint Pattern Discovery[2]
- Where and When changes occur
- Climate change, Business grow, urban sprawl, etc
Change Prediction
- Where and When will change occur
Repeating/periodic
Finding periodic travel patterns, schedules, habits
0.4
NDVI
0.35
2001
2006
2012
0.3
An annual increase
of 11.5%, 2001-2012
0.25
0.2
2000
2002
Vegetation increase in Saudi Arabia due to irrigation [14]
2004
2006
Year
2008
2010
2012
CHANGE FOOTPRINT PATTERNS
Static
Local
Time
Between
snapshots
Time
Focal
Point in
time series
Time
Zonal
Interval in
time series
Time
OUTLINE
•
Introduction
•
Spatial Data and Models
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Statistical models
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Spatial Pattern Families
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Computational Challenges
COMPUTATIONAL CHALLENGES
Neighborhood graph generation
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Parameter Estimation
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Better Interpretability
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Complex-shapes of pattern
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Filter-n-refine approach
Pattern Completeness
High combinatorics of patterns
• Enumeration and pruning strategies
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Interest measure property
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Conceptual
Modeling
balance
Interest
measure
DP or Greedy may not be used
HPC with Spatial Data Mining
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Pattern
Interpretability
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Parallel/Cloud Computing
GIS on Hadoop (ESRI)
Algorithm
Design
Computational
Scalability
SUMMARY
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What is SDM and why it’s important
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What’s special about spatial
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Pattern families, potential directions and applications
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Computational Challenges
ACKNOWLEDGEMENT
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This presentation is prepared based on materials from Prof. Shashi Shekhar
and the Spatial Database and Spatial Data Mining Group at the University
of Minnesota (http://www.spatial.cs.umn.edu/).
REFERENCES AND READINGS
[1]. Shekhar, Shashi, et al. "Identifying patterns in spatial information: A survey of methods." Wiley Interdisciplinary Reviews:
Data Mining and Knowledge Discovery 1.3 (2011): 193-214.
[2]. Xun Zhou, Shashi Shekhar, and Reem Y. Ali. "Spatiotemporal change footprint pattern discovery: an inter‐disciplinary
survey." Wiley Interdisciplinary Reviews: Data Mining and Knowledge Discovery 4.1 (2014): 1-23.
[3]. Shashi Shekhar and Sanjay Chawla. Spatial Database: A Tour. Prentice Hall 2003.
[4]. Banerjee, Sudipto, Alan E. Gelfand, and Bradley P. Carlin. Hierarchical modeling and analysis for spatial data. CRC Press,
2004.
[5]. Jiang, Z., Shekhar, S., Zhou, X., Knight, J., & Corcoran, J. (2013, December). Focal-test-based spatial decision tree
learning: A summary of results. In Data Mining (ICDM), 2013 IEEE 13th International Conference on (pp. 320-329). IEEE.
[6]. Shekhar, Shashi, Chang-Tien Lu, and Pusheng Zhang. "A unified approach to detecting spatial outliers." GeoInformatica
7, no. 2 (2003): 139-166.
[7]. Y Huang, S Shekhar, H Xiong, Discovering colocation patterns from spatial data sets: a general approach. Knowledge
and Data Engineering, IEEE Transactions on 16 (12), 1472-1485
[8]. Ester, Martin; Kriegel, Hans-Peter; Sander, Jörg; Xu, Xiaowei (1996). "A density-based algorithm for discovering clusters in
large spatial databases with noise". In Simoudis, Evangelos; Han, Jiawei; Fayyad, Usama M. Proceedings of the Second
International Conference on Knowledge Discovery and Data Mining (KDD-96)
[9]. Kulldorff, Martin. "A spatial scan statistic." Communications in Statistics-Theory and methods 26.6 (1997): 1481-1496.
[10]. Dev Oliver, Shashi Shekhar, Xun Zhou, Emre Eftelioglu, Michael Evans, Qiaodi Zhuang, James Kang, Renee Laubscher
and Christopher Farah. Significant Route Discovery: A Summary of Results. In GIScience 2014 (to appear).
[11]. Celik, Mete, et al. "Mixed-drove spatiotemporal co-occurrence pattern mining." Knowledge and Data Engineering, IEEE
Transactions on 20.10 (2008): 1322-1335.
[12]. Mohan, Pradeep, Shashi Shekhar, James A. Shine, and James P. Rogers. "Cascading spatio-temporal pattern
discovery." Knowledge and Data Engineering, IEEE Transactions on 24, no. 11 (2012): 1977-1992.
[13]. Daniel B. Neill, Andrew W. Moore, Maheshkumar Sabhnani, and Kenny Daniel. Detection of emerging space-time
clusters. Proceedings of the 11th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, 218-227, 2005
[14]. Xun Zhou, Shashi Shekhar, Dev Oliver. "Discovering Persistent Change Windows in Spatiotemporal Datasets: A Summary
of Results". In 2nd ACM SIGSPATIAL International Workshop on Analytics for Big Geospatial Data (BigSpatial-2013), Nov 5,
2013, Orlando, Florida, USA.