Abstract
Incorporating geographical constraints is one of the main challenges of spatial clustering. In this paper we propose a new algorithm for clustering of spatial data using a conjugate Bayesian model and weighted MAX-SAT solvers. The fast and flexible Bayesian model is used to score promising partitions of the data. However, the partition space is huge and it cannot be fully searched, so here we propose an algorithm that naturally incorporates the geographical constraints to guide the search over the space of partitions. We illustrate our proposed method on a simulated dataset of social indexes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Crowley, E. M. (1997). Product partition models for normal means. Journal of the American Statistical Association, 92(437), 192–198.
Cussens, J. (2008). Bayesian network learning by compiling to weighted MAX-SAT. In Proceedings of the 24th conference on Uncertainty in Artificial Intelligence (UAI 2008).
Fraley, C., & Raftery, A. E. (1998). How many clusters? Which clustering method? Answers via model-based cluster analysis. The Computer Journal, 41, 578–588.
Gordon, A. D. (1996). A survey of constrained classification. Computational Statistics & Data Analysis, 21(1), 17–29.
Heard, N. A., Holmes, C. C., & Stephens, D. A. (2006). A quantitative study of gene regulation involved in the immune response of anopheline mosquitoes: An application of Bayesian hierarchical clustering of curves. Journal of the American Statistical Association, 101(473), 18–29.
Johnston, R. J. (1976). Classification in Geography: CLADAG 6. Geo Abstracts.
Legendre, P. (1987). Constrained clustering. In P. Legendre & L. Legendre (Eds.), Developments in numerical ecology (pp. 289–307). Springer-Verlag.
Liverani, S., Anderson, P. E., Edwards, K. D., Millar, A. J., & Smith, J. Q. (2009). Efficient utility-based clustering over high dimensional partition spaces. Journal of Bayesian Analysis, 4(3), 539–572.
Liverani, S., Cussens, J., & Smith, J. Q. (2009). Searching a multivariate partition space using weighted MAX-SAT. In Proceedings of 6th International Meeting of Computational Intelligence Methods for Bioinformatics and Biostatistics (CIBB2009).
Ray, S., & Mallick, B. (2006). Functional clustering by Bayesian wavelet methods. Journal of the Royal Statistical Society: Series B, 68(2), 305–332.
Smith, J. Q., Anderson, P. E., & Liverani, S. (2008). Separation measures and the geometry of bayes factor selection for classification. Journal of the Royal Statistical Society: Series B, 70(5), 957–980.
Tompkins, D. A. D., & Hoos, H. H. (2005). UBCSAT: An implementation and experimentation environment for SLS algorithms for SAT and MAX-SAT. In H. H. Hoos & D. G. Mitchell (Eds.), Theory and applications of satisfiability testing: Revised selected papers of the seventh international conference (SAT 2004, Vancouver, BC, Canada, May 10–13, 2004) (pp. 306–320), Volume 3542 of Lecture Notes in Computer Science. Berlin, Germany: Springer Verlag.
Zhou, C., Wakefield, J. C., & Breeden, L. L. (2006). Bayesian analysis of cell-cycle gene expression data. In K. A. Do, P. Müller, & M. Vannucci (Eds.), Bayesian inference for gene expression and proteomics (pp. 177–200). Cambridge University Press.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liverani, S., Petrucci, A. (2011). Spatial Clustering of Multivariate Data Using Weighted MAX-SAT. In: Ingrassia, S., Rocci, R., Vichi, M. (eds) New Perspectives in Statistical Modeling and Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11363-5_27
Download citation
DOI: https://doi.org/10.1007/978-3-642-11363-5_27
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11362-8
Online ISBN: 978-3-642-11363-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)