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):
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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.
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Hierarchical algorithms: This algorithm creates clusters repeatedly by merging a small cluster into a larger cluster. It also split cluster into several small classes.
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References
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_38
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 1027–1035
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/bf02826668
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, Portland
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 44
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 766–770
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:10.1117/12.837594
Guha S, Rastogi R, Shim K (1998) CURE: an efficient clustering algorithm for large databases. SIGMOD Rec 27(2):73–84. doi:10.1145/276305.276312
Guttman A (1984) R-trees: a dynamic index structure for spatial searching. SIGMOD Rec 14(2):47–57. doi:10.1145/971697.602266
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 York
Korotkov A (2012) A new double sorting-based node splitting algorithm for R-tree. Programm Comput Softw 38(3):109–118
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,
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 1–6
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 14
Ng RT, Han J (1994) Efficient and effective clustering methods for spatial data mining. In: Proceedings of the 20th VLDB conference, Santiago
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/s007780050009
Sleit A, Al-Nsour E (2014) Corner-based splitting: an improved node splitting algorithm for R-tree. J Inf Sci. doi:10.1177/0165551513516709
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
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 37–45
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, Athens
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 2012
Zhang T, Ramakrishnan R, Livny M (1996) BIRCH: an efficient data clustering method for very large databases. SIGMOD Rec 25(2):103–114. doi:10.1145/235968.233324
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
Zlatanova S (2000) 3D GIS for urban development. International Institute for Aerospace Survey and Earth Sciences (ITC)
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Azri, S., Rahman, A.A., Ujang, U., Anton, F., Mioc, D. (2017). 3D Crisp Clustering of Geo-Urban Data. In: Shekhar, S., Xiong, H., Zhou, X. (eds) Encyclopedia of GIS. Springer, Cham. https://doi.org/10.1007/978-3-319-17885-1_1610
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