The Community for Technology Leaders
RSS Icon
Issue No.11 - Nov. (2012 vol.24)
pp: 2065-2079
Deepti Joshi , University of Nebraska-Lincoln, Lincoln
Leen-Kiat Soh , University of Nebraska-Lincoln, Lincoln
Ashok Samal , University of Nebraska-Lincoln, Lincoln
Redistricting is the process of dividing a geographic area consisting of spatial units—often represented as spatial polygons—into smaller districts that satisfy some properties. It can therefore be formulated as a set partitioning problem where the objective is to cluster the set of spatial polygons into groups such that a value function is maximized [1]. Widely used algorithms developed for point-based data sets are not readily applicable because polygons introduce the concepts of spatial contiguity and other topological properties that cannot be captured by representing polygons as points. Furthermore, when clustering polygons, constraints such as spatial contiguity and unit distributedness should be strategically addressed. Toward this, we have developed the Constrained Polygonal Spatial Clustering (CPSC) algorithm based on the {\rm A}^\ast search algorithm that integrates cluster-level and instance-level constraints as heuristic functions. Using these heuristics, CPSC identifies the initial seeds, determines the best cluster to grow, and selects the best polygon to be added to the best cluster. We have devised two extensions of CPSC—CPSC* and CPSC*-PS—for problems where constraints can be soft or relaxed. Finally, we compare our algorithm with graph partitioning, simulated annealing, and genetic algorithm-based approaches in two applications—congressional redistricting and school districting.
Clustering algorithms, Algorithm design and analysis, Simulated annealing, Partitioning algorithms, Heuristic algorithms, Genetic algorithms, Spatial databases, spatial databases and GIS, Spatial clustering, polygonal clustering, constraint-based processing, data mining
Deepti Joshi, Leen-Kiat Soh, Ashok Samal, "Redistricting Using Constrained Polygonal Clustering", IEEE Transactions on Knowledge & Data Engineering, vol.24, no. 11, pp. 2065-2079, Nov. 2012, doi:10.1109/TKDE.2011.140
[1] M. Altman, "Is Automation the Answer? The Computational Complexity of Automated Redistricting," Rutgers Computer and Technology Law J., vol. 23, pp. 81-142, 2001.
[2] F. Baçao, V. Lobo, and M. Painho, "Applying Genetic Algorithms to Zone Design," Soft Computing, vol. 9, pp. 341-348, 2005.
[3] S. Basu, A. Banerjee, and R.J. Mooney, "Semisupervised Clustering by Seeding," Proc. 19th Int'l Conf. Machine Learning (ICML '02), pp. 19-26, 2002.
[4] L.D. Bodin, "A Districting Experiment with a Clustering Algorithm," Democratic Representation and Apportionment: Quantitative Methods, Measures and Criteria, Annals of New York Academy of Sciences, 1973.
[5] D.M. Clayton, African Americans and the Politics of Congressional Redistricting, pp. 138-140. New York Garland Publishing Co., 2000.
[6] I. Davidson and S.S. Ravi, "Clustering with Constraints: Feasibility Issues and the K-Means Algorithm," Proc. SIAM Int'l Conf. Data Mining, 2005.
[7] I. Davidson and S.S. Ravi, "Towards Efficient and Improved Hierarchical Clustering with Instance and Cluster Level Constraints," technical report, Dept. of Computer Science, Univ. at Albany, 2005.
[8] A. Demiriz, K. Bennett, and M. Embrechts, "Semi-Supervised Clustering Using Genetic Algorithms" Intelligent Engineering Systems through Artificial Neural Networks 9, C.H. Dagli et al., eds., pp. 809-814, ASME Press, 1999.
[9] N. Grira, M. Crucianu, and N. Boujemaa, "Unsupervised and Semi-Supervised Clustering: A Brief Survey," A Rev. of Machine Learning Techniques for Processing Multimedia Content, Report of the MUSCLE European Network of Excellence (6th Framework Programme), 2005.
[10] J. Han, M. Kamber, and A. Tung, "Spatial Clustering Methods in Data Mining: A Survey," Geographic Data Mining and Knowledge Discovery, H. Miller and J. Han, eds., vol. 21, Taylor and Francis, 2001.
[11] B. Hayes, "Machine Politics," Am. Scientist, vol. 84, pp. 522-526, 1996.
[12] M. Halkidi and M. Vazirgiannis, "NPClu: An Approach for Clustering Spatially Extended Objects," Intelligent Data Analysis vol. 12, no. 6, pp. 587-606, 2008.
[13] D. Joshi, A.K. Samal, and L.-K. Soh, "Density-Based Clustering of Polygons," Proc. IEEE Symp. Series on Computational Intelligence and Data Mining, pp. 171-178, 2009.
[14] D. Joshi, L.-K. Soh, and A.K. Samal, "Redistricting Using Heuristic-Based Polygonal Clustering," Proc. IEEE Int'l Conf. Data Mining, pp. 830-836, 2009.
[15] D. Joshi, A.K. Samal, and L.-K. Soh, "A Dissimilarity Function for Clustering Geospatial Polygons," Proc. 17th ACM SIGSPATIAL Int'l Conf. Advances in Geographic Information Systems (GIS '09), pp. 384-387, 2009.
[16] M.H.C. Law, A. Topchy, and A.K. Jain, "Clustering with Soft and Group Constraints," Proc. Joint IAPR Int'l Workshop Syntactical and Structural Pattern Recognition and Statistical Pattern Recognition, 2004.
[17] W. Macmillan, "Redistricting in a GIS Environment: An Optimization Algorithm Using Switching Points," J. Geographical Systems, vol. 3, pp. 167-180, 2001.
[18] H. Mann and W.B. Fowle, The Common School Journal, pp. 1838-1851. Marsh, Capen, Lyon, and Webb, 1841.
[19] C. Ruiz, M. Spiliopoulou, and E.M. Ruiz, "C-DBSCAN: Density-Based Clustering with Constraints," Proc. 11th Int'l Conf. Rough Sets, Fuzzy Sets, Data Mining and Granular Computing, pp. 216-223, 2007.
[20] S.J. Russell and P. Norvig, Artificial Intelligence: A Modern Approach, pp. 96-101. Prentice Hall, 2003.
[21] C.-A. Saita and F. Llirbat, "Clustering Multidimensional Extended Objects to Speed Up Execution of Spatial Queries," Proc. Ninth Int'l Conf. Extending Database Technology (EDBT '04), pp. 403-421, 2004.
[22] J. Schwartzberg, "Reapportionment, Gerrymanders, and the Notion of Compactness," Minnesota Law Rev., vol. 50, pp. 443-452, 1996.
[23] K. Wagstaff, C. Cardie, S. Rogers, and S. Schroedl, "Constrained K-Means Clustering with Background Knowledge," Proc. 18th Int'l Conf. Machine Learning (ICML), pp. 577-584, 2001.
[24] K. Wagstaff and C. Cardie, "Clustering with Instance-Level Constraints," Proc. 17th Int'l Conf. Machine Learning, pp. 1103-1110, 2000.
32 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool