Identifying Patterns In Spatial Data

1. Identifying Patterns InSpatial Data Xun Zhou University of Iowa September 5, 2014

2. Outline • Introduction • Spatial Dataand Models • Statistical models • Spatial Pattern Families • Computational Challenges

3. What is spatial Data mining (SDM) • Identifying interesting, non-trivia, and useful patterns from large spatial datasets • “Spatial” is general – includes spatio-temporal • Examples of spatial/spatio-temporal datasets: • 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

4. Why is SDM important • Location/time information brings rich context • Support decision making • Understanding natural phenomenon • Improve the quality of knowledge • London Cholera 1854 – John Snow • Modern examples • 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

5. What is “special” about “spatial” Picture Source: [1]

6. Spatial Data Mining Components • Input Data • Statistical Foundations • Output patterns • Computational Process

7. Outline • Introduction • Spatial Dataand Models • Statistical models • Spatial Pattern Families • Computational Challenges

8. Spatial Data Types • Two data representation models Picture source: [2]

9. Spatial Relationships and operations • Between spatial objects: • Set-oriented: Union, Intersection, Membership… • Topological: Meet, within, overlap, connected… • Directional: North, East, left, above, below… • Metric: Distance, area, perimeter • Spatial field operations • Local, Focal, Zonal, Global Individual location (elevation > 1000 ft.) Among all the locations (The Everest) Part of a region (Mountain peak) A small neighborhood (slope, gradient)

10. Outline • Introduction • Spatial Dataand Models • Statistical models • Spatial Pattern Families • Computational Challenges

11. Two key features • Spatial Autocorrelation • 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 • 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.

12. Statistical foundations • Spatial statistics – a brunch of statistics * These are statistical models (like normal distribution) and may not lineup with data representation models.

13. Spatial Neighborhood • A collection of nearby location/spatial object • Adjacent/connected objects/locations • Within a certain distance • The W-matrix: A B C D r

14. Outline • Introduction • Spatial Dataand Models • Statistical models • Spatial Pattern Families • Computational Challenges

15. Spatial Pattern families • A comparison with traditional DM tasks

16. Spatial Prediction C4.5 results on land cover data [5] • Traditional classifiers based on i.i.d. and global model • Linear regression, Decision Tree, SVM, CART, etc. • Spatial auto-correlation and variation are not modeled • Predicting land cover types, location-based recommendation • Regression • Spatial Decision Tree[5] • Information gain function: add spatial autocorrelation measure • Decision rules: Illustration of focal-test-based spatial decision tree[5]

17. Spatial Outlier detection • Traditional Anomaly Detection • 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: • Variogram clouds • Moran scatterplot • Spatial Statistic (S) 1 1 1 2 1 5 1 2 1 1 1 2 2 2 2 2 4 5 4 5 4 5 4 5 4 5 5 5 5 4 4 5 4 5 5 4 1-D spatial data and distribution [1]

18. Spatial Association • Spatial Co-location pattern[7] • 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} Pictures source: [1] {‘+’, ‘x’}, {‘o’, ‘*’}

19. Spatial Clustering • Grouping spatial objects into clusters such that • Intra-cluster similarity is maximized • Inter-cluster similarity is minimized • Detecting communities, crowds, building blocks, etc. • 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

20. Spatial hotspot detection • 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 • Density-based approaches: DBSCAN[8] • Statistical tests – spatial scan statistics[9](public health) Spatial Scan Statistics Spatial Scan Statistics DBSCAN DBSCAN

21. New dimensions of spatial patterns • Patterns on Spatial Networks • Hotspots (Dangerous routes with high risk of accidents)[10] • Clusters (Crimes along the streets, bus/bike route planning) • Predictions • Irregular/complex-shaped Spatial Patterns • Complex-shaped clusters (terrain constraints) • Irregular Hotspots (gerrymander …) Results on pedestrian fatality data from Orlando, FL.[10]

22. Adding Time • Input data • Spatial data  Spatio-temporal data • Time series • Vector: point sequences, polygon series… • Raster: image sequences, spatial time series (a time series at each grid) • Relationship: before, after, during, simultaneous, … • Statistical Foundations • Markov Chain, Hidden Markov Model… • Spatiotemporal Statistics

23. Adding Time - PATTERNS

24. Adding Time – New PATTERNS • New Dimensions of Temporal Information • Change • Repeating/periodicity 2006 2001 2012 Vegetation increase in Saudi Arabia due to irrigation [14] An annual increase of 11.5%, 2001-2012

25. Change Footprint PATTERNS Static Local Time Between snapshots Time Focal Point in time series Time Interval in time series Zonal Time

26. Outline • Introduction • Spatial Dataand Models • Statistical models • Spatial Pattern Families • Computational Challenges

27. Computational Challenges • Neighborhood graph generation • Parameter Estimation • Better Interpretability • Complex-shapes of pattern • Filter-n-refine approach • Pattern Completeness • High combinatorics of patterns • Enumeration and pruning strategies • Interest measure property • DP or Greedy may not be used • HPC with Spatial Data Mining • Parallel/Cloud Computing • GIS on Hadoop (ESRI) Pattern Interpretability Conceptual Modeling balance Interest measure Algorithm Design Computational Scalability

28. Summary • What is SDM and why it’s important • What’s special about spatial • Pattern families, potential directions and applications • Computational Challenges

29. Acknowledgement • 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/).

30. 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, EmreEftelioglu, 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, MaheshkumarSabhnani, 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.