Abstract
We present a fast approximate Minimum spanning tree(MST) framework on the complete graph of a dataset with N points, and any exact MST algorithm can be incorporated into the framework and speeded up. It employs a divide-and-conquer scheme to produce an approximate MST with theoretical time complexity of O(N 1.5), if the incorporated exact MST algorithm has the running time of O(N 2). Experimental results show that the proposed approximate MST algorithm is computational efficient, and the accuracy is close to the true MST.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
An, L., Xiang, Q.S., Chavez, S.: A fast implementation of the minimum spanning tree method for phase unwrapping. IEEE Trans. Medical Imaging 19, 805–808 (2000)
Bezdek, J.C., Pal, N.R.: Some new indexes of cluster validity. IEEE Trans. Systems, Man and Cybernetics, Part B 28, 301–315 (1998)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. The MIT Press (2001)
Juszczak, P., Tax, D.M.J., Pękalska, E., Duin, R.P.W.: Minimum spanning tree based one-class classifier. Neurocomputing 72, 1859–1869 (2009)
Karypis, G., Han, E.H., Kumar, V.: CHAMELEON: A hierarchical clustering algorithm using dynamic modeling. IEEE Trans. Comput. 32, 68–75 (1999)
Lai, C., Rafa, T., Nelson, D.E.: Approximate minimum spanning tree clustering in high-dimensional space. Intelligent Data Analysis 13, 575–597 (2009)
Wang, X., Wang, X., Wilkes, D.M.: A divide-and-conquer approach for minimum spanning tree-based clustering. IEEE Trans., Knowledge and Data Engineering 21, 945–958 (2009)
Yang, L.: Building k edge-disjoint spanning trees of minimum total length for isometric data embedding. IEEE Trans. Pattern Analysis and Machine Intelligence 27, 1680–1683 (2005)
Zhong, C., Miao, D., Wang, R.: A graph-theoretical clustering method based on two rounds of minimum spanning trees. Pattern Recognition 43, 752–766 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Zhong, C., Malinen, M., Miao, D., Fränti, P. (2013). Fast Approximate Minimum Spanning Tree Algorithm Based on K-Means. In: Wilson, R., Hancock, E., Bors, A., Smith, W. (eds) Computer Analysis of Images and Patterns. CAIP 2013. Lecture Notes in Computer Science, vol 8047. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40261-6_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-40261-6_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40260-9
Online ISBN: 978-3-642-40261-6
eBook Packages: Computer ScienceComputer Science (R0)