Abstract
We present a general framework of hierarchical methods for point cluster analysis on networks, and then consider individual clustering procedures and their time complexities defined by typical variants of distances between clusters. The distances considered here are the closest-pair distance, the farthest-pair distance, the average distance, the median-pair distance and the radius distance. This paper will offer a menu for users to choose hierarchical clustering algorithms on networks from a time complexity point of view.
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References
Aho AV, Hopcroft JE, Ullman JD (1974) The design and analysis of computer algorithms. Addison-Wesley, Reading
Anderberg MR (1973) Cluster analysis for applications. Academic, New York
Clauset A, Moore C, Newman MEJ (2008) Hierarchical structure and the prediction of missing links in networks. Nature 453:98–101
Cormen TH, Leisersen CE, Rivert RL, Stein C (2001) Introduction to algorithms, 2nd edn. MIT, Cambridge
Dasgupta S, Long PM (2005) Performance guarantees for hierarchical clustering. J Comput Syst Sci 70:555–569
Gower JC (1967) A comparison of some methods of cluster analysis. Biometrics 23:623–637
Gower JC, Ross GJS (1969) Minimum spanning trees and single linkage cluster analysis. Appl Stat 18:54–64
Jain AK, Dubes RC (1988) Algorithms for clustering data. Prentice Hall, Englewood Cliffs
Jin W, Jian Y, Qian W, Tung AKH (2006) Mining outliers in spatial networks. Proceedings of the 11th international conference on database systems for advanced applications, Singapore, April 2006. Lecture Notes in Computer Science 3882. Springer, New York, pp 156–170
Johnson SC (1967) Hierarchical clustering schemes. Psychometrika 32:241–254
Lance GN, Williams WT (1967) A general theory of classificatory sorting strategies. 1. Hierarchical systems. Comput J 8:246–249
Manning CD, Raghavan P, Schuẗze H (2009) An introduction to information retrieval. On line edition, Cambridge University Press, Cambridge
Okabe A, Okunuki K-I, Shiode S (2006) SANET: a tool box for spatial analysis on a network. Geogr Anal 38:57–66
Sokal RR, Sneath PH (1963) Principles of numerical taxonomy. Freeman, San Francisco, pp 183–185
Ward Jr, JH (1963) Hierarchical grouping to optimize an objective function. J Am Stat Assoc 58:236–244
Ward Jr, JH, Hook ME (1963) Application of an hierarchical grouping procedure to a problem of grouping profiles. Educ Psychol Meas 23:69–82
Whishart D (1969) An algorithm for hierarchical classifications. Biometrics 22:165–170
Yiu ML, Mamoulis N (2004) Clustering objects on a spatial network. In: Proceedings of the ACM conference on management of data (SIGMOD), Paris, June 2004, pp 443–454
Zahn CT (1971) Graph-theoretical methods for detecting and describing gestalt clusters. IEEE Trans Comput C-20:68–86
Acknowledgements
This study was partly supported by the Grant-in-Aid for Scientific Research (B) No. 20300098 and (B) No. 20360044 of the Japanese Society for Promotion of Science.
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Sugihara, K., Okabe, A. & Satoh, T. Computational method for the point cluster analysis on networks. Geoinformatica 15, 167–189 (2011). https://doi.org/10.1007/s10707-009-0092-5
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DOI: https://doi.org/10.1007/s10707-009-0092-5