Clustering Components of PySAL Sergio Rey 1,2 Juan Carlos Duque 1 Luc Anselin 2,3 1 Regional Analysis Laboratory (REGAL) Department of Geography San Diego State University 2 Regional Economics Application Laboratory (REAL) University of Illinois Urbana Champaign 3 Department of Geography University of Illinois Urbana Champaign Regional Science Association International Las Vegas, Nevada November 10-12, 2005 ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 1 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 2 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 2 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 2 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 2 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 3 / 36
PySAL Origins Collaborative Project OpenSpace (UIUC) STARS (SDSU) ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 4 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 5 / 36
Objectives Collaborative Project OpenSpace (UIUC) STARS (SDSU) ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 6 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 7 / 36
Contiguity Constrained Clustering Aggregation of N areas to M regions (M < N), such that: 1 Each area belong to only one region. 2 The areas assigned to a region must be geographically connected. N = 47 M = 6 ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 8 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 9 / 36
Methods ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 10 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 11 / 36
Spatial Aggregation Module Sergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 12 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 13 / 36
Methods ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 14 / 36
Menu Sergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 15 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 16 / 36
ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 17 / 36
K-means two stages ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 18 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 19 / 36
Including Centroids Coordinates ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 20 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 21 / 36
Sergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 22 / 36
AZP-tabu ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 23 / 36
Comparison K-means two stages = 59.346 ARISeL = 45.599 AZP-Tabu = 48.088 Sergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 24 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 25 / 36
ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 26 / 36
Continue... ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 27 / 36
ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 28 / 36
ARISeL ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 29 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 30 / 36
Sergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 31 / 36
ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 32 / 36
Sergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 33 / 36
Outline 1 PySAL Origins Objectives 2 Clustering Components Definition Methods 3 Aggregation Models in PySAL Forward Planning Up to date... K-means two stages Including Centroids Coordinates AZP-tabu Automatic Regionalization with Initial Seeds Location: ARISeL Minimum Spanning Tree Integrating Local Indicators of Spatial Association (LISA) 4 Future Directions ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 34 / 36
Integrating Local Indicators of Spatial Association (LISA) LISA yl i = f (w i., y) (1) Integrating into regionalization algorithms Kmeans Select k significant LISAs to serve as initial seeds. Kmeans Extend attribute set to include local statistics Kmeans Combine: LISA seeds and LISA attributes ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 35 / 36
Future Directions Regionalization Extensions to what we have done here. PySAL Clustering Other aspects of Clustering in PySAL ergio Rey, Juan Carlos Duque, Luc Anselin (San Diego State Clustering University) in PySAL RSAI 2005 36 / 36