Encyclopedia of GIS

2017 Edition
| Editors: Shashi Shekhar, Hui Xiong, Xun Zhou

3D Crisp Clustering of Geo-Urban Data

  • Suhaibah Azri
  • Alias Abdul Rahman
  • Uznir Ujang
  • François Anton
  • Darka Mioc
Reference work entry
DOI: https://doi.org/10.1007/978-3-319-17885-1_1610

Synonyms

Definition

Crisp clustering is a technique to cluster objects into group without having overlapping partitions. Each data point is either belongs to or not to a group. Most of the clustering algorithms are categorized as crisp clustering. There are several categories of crisp clustering algorithm such as partitional algorithm, hierarchical algorithm, density-based algorithm, and grid-based algorithm. The general definition of each group could be defined as follows (Kovács et al.  2005):
  • Partitional algorithms: divide the data into a set of separate category. This algorithm attempts to define the number of partitions to optimize a certain criterion function. This optimization is an iterative procedure.

  • Hierarchical algorithms: This algorithm creates clusters repeatedly by merging a small cluster into a larger cluster. It also split cluster into several small...

This is a preview of subscription content, log in to check access.

References

  1. Ang CH, Tan TC (1997) New linear node splitting algorithm for R-trees. In: Scholl M, Voisard A (eds) Advances in spatial databases, vol 1262. Lecture notes in computer science. Springer, Berlin/Heidelberg, pp 337–349. doi:10.1007/3-540-63238-7_38CrossRefGoogle Scholar
  2. Arthur D, Vassilvitskii S (2007) k-means++: the advantages of careful seeding. In: Proceedings of the eighteenth annual ACM-SIAM symposium on discrete algorithms, New Orleans. Society for Industrial and Applied Mathematics, pp 1027–1035zbMATHGoogle Scholar
  3. Deren L, Qing Z, Qiang L, Peng X (2004) From 2D and 3D GIS for CyberCity. Geo-Spat Inf Sci 7(1):1–5. doi:10.1007/bf02826668CrossRefGoogle Scholar
  4. Ester M, Kriegel H-P, Sander J, Xu X (1996) A density-based algorithm for discovering clusters in large spatial databases with noise. Paper presented at the proceeding of 2nd international conference on knowledge discovery and data mining, PortlandGoogle Scholar
  5. Figueiredo M, Oliveira J, Araújo B, Pereira J (2010) An efficient collision detection algorithm for point cloud models. In: 20th international conference on computer graphics and vision, Warsaw. Citeseer, p 44Google Scholar
  6. Fu Y, Teng J-C, Subramanya S (2002) Node splitting algorithms in tree-structured high-dimensional indexes for similarity search. In: Proceedings of the 2002 ACM symposium on applied computing, Madrid. ACM, pp 766–770Google Scholar
  7. Gong J, Ke S, Li X, Qi S (2009) A hybrid 3D spatial access method based on quadtrees and R-trees for globe data. 74920R–74920R. doi:10.1117/12.837594Google Scholar
  8. Guha S, Rastogi R, Shim K (1998) CURE: an efficient clustering algorithm for large databases. SIGMOD Rec 27(2):73–84. doi:10.1145/276305.276312CrossRefzbMATHGoogle Scholar
  9. Guttman A (1984) R-trees: a dynamic index structure for spatial searching. SIGMOD Rec 14(2):47–57. doi:10.1145/971697.602266CrossRefGoogle Scholar
  10. Hinneburg A, Keim DA (1998) An efficient approach to clustering in large multimedia databases with noise. Paper presented at the proceedings of the 4th ACM SIGKDD, New YorkGoogle Scholar
  11. Korotkov A (2012) A new double sorting-based node splitting algorithm for R-tree. Programm Comput Softw 38(3):109–118MathSciNetCrossRefGoogle Scholar
  12. Kovács F, Legány C, Babos A (2005) Cluster validity measurement techniques. In: Proceeding of sixth international symposium Hungarian researchers on computational intelligence (CINTI), Barcelona. Citeseer,Google Scholar
  13. Liu Y, Fang J, Han C (2009) A new R-tree node splitting algorithm using MBR partition policy. In: 2009 17th international conference on geoinformatics, Fairfax. IEEE, pp 1–6Google Scholar
  14. MacQueen J (1967) Some methods for classification and analysis of multivariate observations. In: Proceedings of the fifth Berkeley symposium on mathematical statistics and probability, Berkeley, p 14Google Scholar
  15. Ng RT, Han J (1994) Efficient and effective clustering methods for spatial data mining. In: Proceedings of the 20th VLDB conference, SantiagoGoogle Scholar
  16. Sheikholeslami G, Chatterjee S, Zhang A (2000) WaveCluster: a wavelet-based clustering approach for spatial data in very large databases. VLDB J 8(3–4):289–304. doi:10.1007/s007780050009CrossRefGoogle Scholar
  17. Sleit A, Al-Nsour E (2014) Corner-based splitting: an improved node splitting algorithm for R-tree. J Inf Sci. doi:10.1177/0165551513516709Google Scholar
  18. Theodoridis S, Koutroumbas K (2009) Chapter 13 – clustering algorithms II: hierarchical algorithms. In: Theodoridis S, Koutroumbas K (eds) Pattern recognition, 4th edn. Academic, Boston, pp 653–700. doi:http://dx.doi.org/10.1016/B978-1-59749-272-0.50015-3
  19. Wand M, Berner A, Bokeloh M, Fleck A, Hoffmann M, Jenke P, Maier B, Staneker D, Schilling A (2007) Interactive editing of large point clouds. In: SPBG, Prague, pp 37–45Google Scholar
  20. Wang W, Yang J, Muntz RR (1997) STING: a statistical information grid approach to spatial data mining. In: Paper presented at the proceedings of the 23rd international conference on very large data bases, AthensGoogle Scholar
  21. Wang Y, Guo M (2012) An integrated spatial indexing of huge point image model. In: Paper presented at the international archives of the photogrammetry, remote sensing and spatial information Sciences, Melbourne, 25 Aug–01 Sept 2012Google Scholar
  22. Zhang T, Ramakrishnan R, Livny M (1996) BIRCH: an efficient data clustering method for very large databases. SIGMOD Rec 25(2):103–114. doi:10.1145/235968.233324CrossRefGoogle Scholar
  23. Zhu Q, Gong J, Zhang Y (2007) An efficient 3D R-tree spatial index method for virtual geographic environments. ISPRS J Photogramm Remote Sens 62(3):217–224. doi:http://dx.doi.org/10.1016/j.isprsjprs.2007.05.007
  24. Zlatanova S (2000) 3D GIS for urban development. International Institute for Aerospace Survey and Earth Sciences (ITC)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Suhaibah Azri
    • 1
  • Alias Abdul Rahman
    • 1
  • Uznir Ujang
    • 1
  • François Anton
    • 2
  • Darka Mioc
    • 3
  1. 1.Department of Geoinformation 3D GIS Research LabUniversiti Teknologi MalaysiaJohor BahruMalaysia
  2. 2.Department of GeodesyTechnical University of DenmarkLyngbyDenmark
  3. 3.Department of GeodesyTechnical University of DenmarkLyngbyDenmark