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Clustering Contextual Neural Gas: A New Approach for Spatial Planning and Analysis Tasks

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Computational Approaches for Urban Environments

Part of the book series: Geotechnologies and the Environment ((GEOTECH,volume 13))

Abstract

Spatial clustering is a method that can reveal structures and identify groupings in large spatial data sets, which is in particular useful for spatial planning and analysis tasks. A recent and powerful clustering algorithm for spatial data is contextual neural gas (CNG). The CNG algorithm is closely related to the basic self-organizing map algorithm but additionally takes spatial dependence into account. However, like most clustering algorithms, CNG requires the analyst to specify the number of clusters beforehand. Even though the chosen number of clusters critically affects the results of the clustering, it is unclear how to determine it. This study introduces a new method which combines CNG, the learning of the CNG’s topology, and graph clustering. It can be used to cluster spatial data without any prior knowledge of present clusters in the data. The proposed method is in particular useful for spatial planning and analysis tasks, because it provides means to find groupings in the data and identify homogeneous regions. To evaluate the method, this study draws from two experiments which are based on a synthetic and a real-world data set. The results of the synthetic data set show that it can correctly identify clusters in a predefined setting. The results of the real-world data set demonstrate that the proposed method outlines meaningful and theoretically sound regions.

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References

  • Amedeo D (1969) An optimization approach to the identification of a system of regions. Pap Reg Sci 23(1):25–44

    Google Scholar 

  • Arribas-Bel D, Schmidt CR (2013) Self-organizing maps and the US urban spatial structure. Environ Plan B Plan Des 40(2):362–371

    Google Scholar 

  • Aupetit M (2005) Learning topology with the generative gaussian graph and the EM algorithm. In: Advances in neural information processing systems, Vancouver, pp 83–90

    Google Scholar 

  • Bação F, Lobo V, Painho M (2005) The self-organizing map, the geo-som, and relevant variants for geosciences. Comput Geosci 31:155–163

    Google Scholar 

  • Bailey T, Gatrell A (1995) Interactive spatial data analysis. Longman Scientific & Technical, Harlow Essex

    Google Scholar 

  • Blondel VD, Guillaume JL, Lambiotte R, Lefebvre E (2008) Fast unfolding of communities in large networks. J Stat Mech Theory Exp 2008(10):P10008

    Google Scholar 

  • Brandes U, Delling D, Gaertler M, Gorke R, Hoefer M, Nikoloski Z, Wagner D (2008) On modularity clustering. IEEE Trans Knowl Data Eng 20(2):172–188

    Google Scholar 

  • Costa J, De Andrade Netto M (1999) Cluster analysis using self-organizing maps and image processing techniques. In: IEEE international conference on systems, man, and cybernetics 1999. IEEE SMC ’99 conference proceedings, Tokyo, vol 5, pp 367–372

    Google Scholar 

  • Costa J, Oliveira R (2007) Cluster analysis using growing neural gas and graph partitioning. In: International joint conference on neural networks, IJCNN 2007, Orlando, pp 3051–3056

    Google Scholar 

  • De Silva V, Carlsson G (2004) Topological estimation using witness complexes. In: Proceedings of the first eurographics conference on point-based graphics. Eurographics Association, Aire-la-Ville, pp 157–166

    Google Scholar 

  • Edelsbrunner H, Shah NR (1997) Triangulating topological spaces. Int J Comput Geom Appl 7(04):365–378

    Google Scholar 

  • Flexer A (2001) On the use of self-organizing maps for clustering and visualization. Intell Data Anal 5(5):373–384

    Google Scholar 

  • Fortunato S (2010) Community detection in graphs. Phys Rep 486(3–5):75–174

    Google Scholar 

  • Fortunato S, Barthelemy M (2006) Resolution limit in community detection. Proc Natl Acad Sci 104(1):36–41

    Google Scholar 

  • Fritzke B (1995) A growing neural gas network learns topologies. Adv Neural Inf Process Syst 7:625–632

    Google Scholar 

  • Goodchild MF (1986) Spatial autocorrelation. Concepts and techniques in modern geography. Geo Books, Norwich

    Google Scholar 

  • Guo D, Peuquet D, Gahegan M (2003) ICEAGE: interactive clustering and exploration of large and high-dimensional geodata. GeoInformatica 7(3):229–253

    Google Scholar 

  • Hagenauer J, Helbich M (2013) Contextual neural gas for spatial clustering and analysis. Int J Geogr Inf Sci 27(2):251–266

    Google Scholar 

  • Hagenauer J, Helbich M, Leitner M (2011) Visualization of crime trajectories with self-organizing maps: a case study on evaluating the impact of hurricanes on spatio-temporal crime hotspots. In: Proceedings of the 25th international cartographic conference, International Cartographic Association, Paris

    Google Scholar 

  • Han J, Kamber M, Tung AKH (2001) Spatial clustering methods in data mining: a survey. In: Miller HJ, Han J (eds) Geographic data mining and knowledge discovery. Taylor and Francis, London, pp 188–217

    Google Scholar 

  • Helbich M, Brunauer W, Hagenauer J, Leitner M (2013) Data-driven regionalization of housing markets. Ann Assoc Am Geogr 103(4):871–889

    Google Scholar 

  • Jain AK, Murty MN, Flynn PJ (1999) Data clustering: a review. ACM Comput Surv 31(3):264–323

    Google Scholar 

  • Kohonen T (1982) Self-organized formation of topologically correct feature maps. Biol Cybern 43:59–69. doi:10.1007/BF00337288

    Google Scholar 

  • Kohonen T (2001) Self-organizing maps, 3rd edn. Springer, New York/Secaucus

    Google Scholar 

  • Lancichinetti A, Fortunato S (2009) Community detection algorithms: a comparative analysis. Phys Rev E 80:056117

    Google Scholar 

  • Logan JR (2011) Separate and unequal: the neighborhood gap for Blacks, Hispanics and Asians in metropolitan America. http://www.s4.brown.edu/us2010/Data/Report/report0727.pdf. Accessed on 28 Mar 2013

  • Martinetz T (1993) Competitive Hebbian learning rule forms perfectly topology preserving maps. In: Gielen S, Kappen B (eds) ICANN 93, Amsterdam. Springer, London, pp 427–434

    Google Scholar 

  • Martinetz T, Schulten K (1991) A “neural-gas” network learns topologies. Artif Neural Netw 1:397–402

    Google Scholar 

  • Martinetz T, Berkovich S, Schulten K (1993) “Neural-gas” network for vector quantization and its application to time-series prediction. IEEE Trans Neural Netw 4(4):558–569

    Google Scholar 

  • Miller HJ (2004) Tobler’s first law and spatial analysis. Ann Assoc Am Geogr 94(2):284–289

    Google Scholar 

  • Murtagh F (1995) Interpreting the kohonen self-organizing feature map using contiguity-constrained clustering. Pattern Recognit Lett 16(4):399–408

    Google Scholar 

  • Newman MEJ, Girvan M (2004) Finding and evaluating community structure in networks. Phys Rev E 69:026113

    Google Scholar 

  • Openshaw S (1984) The modifiable areal problem. Concepts and techniques in modern geography. Geo Books, Norwich

    Google Scholar 

  • Pearsall H, Christman Z (2012) Tree-lined lanes or vacant lots? Evaluating non-stationarity between urban greenness and socio-economic conditions in Philadelphia, Pennsylvania, USA at multiple scales. Appl Geogr 35(1):257–264

    Google Scholar 

  • Philadelphia City Planning Commission (2004) The political and community service boundaries of Philadelphia. http://www.phila.gov/CityPlanning/resources/Publications/Political_boundaries.pdf. Accessed on 26 Mar 2013

  • Schaeffer SE (2007) Graph clustering. Comput Sci Rev 1(1):27–64

    Google Scholar 

  • Skupin A, Esperbé A (2011) An alternative map of the United States based on an n-dimensional model of geographic space. J Vis Lang Comput 22(4):290–304

    Google Scholar 

  • The Philadelphia Research Initiative (2011) A city transformed – the racial and ethnic changes in Philadelphia over the last 20 years. http://www.pewtrusts.org/uploadedFiles/wwwpewtrustsorg/Reports/Philadelphia_Research_Initiative/Philadelphia-Population-Ethnic-Changes.pdf. Accessed on 26 Mar 2013

  • Ultsch A, Siemon HP (1990) Kohonen’s self organizing feature maps for exploratory data analysis. In: Proceedings of international neural networks conference, Paris. Kluwer Academic, pp 305–308

    Google Scholar 

  • Van Der Laan L, Schalke R (2001) Reality versus policy: the delineation and testing of local labour market and spatial policy areas. Eur Plan Stud 9(2):201–221

    Google Scholar 

  • Wolfgang ME, Figlio R, Sellin T (1987) Delinquency in a birth cohort. Studies in crime and justice. University of Chicago Press, Chicago

    Google Scholar 

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Author information

Authors and Affiliations

  1. Institute of Geography, Heidelberg University, Berliner Straße 48, D-69120, Heidelberg, Germany

    Julian Hagenauer

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  1. Julian Hagenauer
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Correspondence to Julian Hagenauer .

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Editors and Affiliations

  1. Department of Human Geography and Spatial Planning, Utrecht University, Utrecht, The Netherlands

    Marco Helbich

  2. Institute of Geography, Heidelberg University, Heidelberg, Germany

    Jamal Jokar Arsanjani

  3. Dept. of Geography and Anthropology, Louisiana State University, Baton Rouge, Louisiana, USA

    Michael Leitner

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Hagenauer, J. (2015). Clustering Contextual Neural Gas: A New Approach for Spatial Planning and Analysis Tasks. In: Helbich, M., Jokar Arsanjani, J., Leitner, M. (eds) Computational Approaches for Urban Environments. Geotechnologies and the Environment, vol 13. Springer, Cham. https://doi.org/10.1007/978-3-319-11469-9_4

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