The Community for Technology Leaders
RSS Icon
Subscribe
Issue No.07 - July (2009 vol.21)
pp: 945-958
Xiaochun Wang , Vanderbilt University, Nashville
Xiali Wang , Changan University, Xi'an
D. Mitchell Wilkes , Vanderbilt University, Nashville
ABSTRACT
Due to their ability to detect clusters with irregular boundaries, minimum spanning tree-based clustering algorithms have been widely used in practice. However, in such clustering algorithms, the search for nearest neighbor in the construction of minimum spanning trees is the main source of computation and the standard solutions take O(N^{2}) time. In this paper, we present a fast minimum spanning tree-inspired clustering algorithm, which, by using an efficient implementation of the cut and the cycle property of the minimum spanning trees, can have much better performance than O(N^{2}).
INDEX TERMS
Clustering, graph algorithms, minimum spanning tree, divisive hierarchical clustering algorithm.
CITATION
Xiaochun Wang, Xiali Wang, D. Mitchell Wilkes, "A Divide-and-Conquer Approach for Minimum Spanning Tree-Based Clustering", IEEE Transactions on Knowledge & Data Engineering, vol.21, no. 7, pp. 945-958, July 2009, doi:10.1109/TKDE.2009.37
REFERENCES
[1] I. Katriel, P. Sanders, and J.L. Traff, “A Practical Minimum Spanning Tree Algorithm Using the Cycle Property,” Proc. 11th European Symp. Algorithms (ESA '03), vol. 2832, pp.679-690, 2003.
[2] C.T. Zahn, “Graph-Theoretical Methods for Detecting and Describing Gestalt Clusters,” IEEE Trans. Computers, vol. 20, no. 1, pp.68-86, Jan. 1971.
[3] R.O. Duda and P.E. Hart, Pattern Classification and Scene Analysis. Wiley-Interscience, 1973.
[4] N. Chowdhury and C.A. Murthy, “Minimum Spanning Tree-Based Clustering Technique: Relationship with Bayes Classifier,” Pattern Recognition, vol. 30, no. 11, pp.1919-1929, 1997.
[5] A. Vathy-Fogarassy, A. Kiss, and J. Abonyi, “Hybrid Minimal Spanning Tree and Mixture of Gaussians Based Clustering Algorithm,” Foundations of Information and Knowledge Systems, pp.313-330, Springer, 2006.
[6] O. Grygorash, Y. Zhou, and Z. Jorgensen, “Minimum Spanning Tree-Based Clustering Algorithms,” Proc. IEEE Int’l Conf. Tools with Artificial Intelligence, pp.73-81, 2006.
[7] R.C. Gonzalez and P. Wintz, Digital Image Processing, second ed. Addison-Wesley, 1987.
[8] Y. Xu, V. Olman, and E.C. Uberbacher, “A Segmentation Algorithm for Noisy Images: Design and Evaluation,” Pattern Recognition Letters, vol. 19, pp.1213-1224, 1998.
[9] Y. Xu and E.C. Uberbacher, “2D Image Segmentation Using Minimum Spanning Trees,” Image and Vision Computing, vol. 15, pp.47-57, 1997.
[10] D.J. States, N.L. Harris, and L. Hunter, “Computationally Efficient Cluster Representation in Molecular Sequence Megaclassification,” ISMB, vol. 1, pp.387-394, 1993.
[11] Y. Xu, V. Olman, and D. Xu, “Clustering Gene Expression Data Using a Graph-Theoretic Approach: An Application of Minimum Spanning Trees,” Bioinformatics, vol. 18, no. 4, pp.536-545, 2002.
[12] M. Laszlo and S. Mukherjee, “Minimum Spanning Tree Partitioning Algorithm for Microaggregation,” IEEE Trans. Knowledge and Data Eng., vol. 17, no. 7, pp.902-911, July 2005.
[13] M. Forina, M.C.C. Oliveros, C. Casolino, and M. Casale, “Minimum Spanning Tree: Ordering Edges to Identify Clustering Structure,” Analytical Chimica Acta, vol. 515, pp.43-53, 2004.
[14] M.F. Jiang, S.S. Tseng, and C.M. Su, “Two-Phase Clustering Process for Outliers Detection,” Pattern Recognition Letters, vol. 22, pp.691-700, 2001.
[15] J. Lin, D. Ye, C. Chen, and M. Gao, “Minimum Spanning Tree-Based Spatial Outlier Mining and Its Applications,” Lecture Notes in Computer Science, vol. 5009/2008, pp.508-515, Springer-Verlag, 2008.
[16] R. Prim, “Shortest Connection Networks and Some Generalization,” Bell Systems Technical J., vol. 36, pp.1389-1401, 1957.
[17] J. Kruskal, “On the Shortest Spanning Subtree and the Traveling Salesman Problem,” Proc. Am. Math. Soc., pp.48-50, 1956.
[18] L. Caccetta and S.P. Hill, “A Branch and Cut Method for the Degree-Constrained Minimum Spanning Tree Problem,” Networks, vol. 37, no. 2, pp.74-83, 2001.
[19] N. Paivinen, “Clustering with a Minimum Spanning Tree of Scale-Free-Like Structure,” Pattern Recognition Letters, vol. 26, no. 7, pp.921-930, Elsevier, 2005.
[20] J.L. Bentley and J.H. Friedman, “Fast Algorithms for Constructing Minimal Spanning Trees in Coordinate Spaces,” IEEE Trans. Computers, vol. 27, no. 2, pp.97-105, Feb. 1978.
[21] S.D. Bay and M. Schwabacher, “Mining Distance-Based Outliers in Near Linear Time with Randomization and a Simple Pruning Rule,” Proc. Ninth ACM SIGKDD Int'l Conf. Knowledge Discovery and Data Mining, pp.29-38, 2003.
[22] H.V. Jagadish, B.C. Ooi, K.L. Tan, C. Yu, and R. Zhang, “iDistance: An Adaptive B+-Tree Based Indexing Method for Nearest Neighbor Search,” ACM Trans. Database System (TODS), vol. 30, no. 2, pp.364-397, 2005.
[23] A.K. Jain and R.C. Dubes, Algorithms for Clustering Data. Prentice Hall, 1988.
[24] J. Kleinberg and E. Tardos, Algorithm Design, pp.142-149. Pearson-Addison Wesley, 2005.
[25] J. Nesetril, E. Milkov'a, and H. Nesetrilov'a, “Otakar Boruvka on Minimum Spanning Tree Problem: Translation of Both the 1926 Papers, Comments, History,” DMATH: Discrete Math., vol. 233, no. 1, pp.3-36, 2001.
[26] M. Fredman and D. Willard, “Trans-Dichotomous Algorithms for Minimum Spanning Trees and Shortest Paths,” Proc. 31st Ann. IEEE Symp. Foundations of Computer Science, pp.719-725, 1990.
[27] H. Gabow, T. Spencer, and R. Tarjan, “Efficient Algorithms for Finding Minimum Spanning Trees in Undirected and Directed Graphs,” Combinatorica, vol. 6, no. 2, pp.109-122, 1986.
[28] D. Karger, P. Klein, and R. Tarjan, “A Randomized Lineartime Algorithm to Find Minimum Spanning Trees,” J. ACM, vol. 42, no. 2, pp.321-328, 1995.
[29] P. Fränti, O. Virmajoki, and V. Hautamäki, “Fast PNN-Based Clustering Using K-Nearest Neighbor Graph,” Proc. Third IEEE Int’l Conf. Data Mining, 2003.
[30] A. Ghoting, S. Parthasarathy, and M.E. Otey, “Fast Mining of Distance-Based Outliers in High Dimensional Data Sets,” Proc. SIAM Int’l Conf. Data Mining (SDM), vol. 16, no. 3, pp.349-364, 2006.
[31] S. Hettich and S.D. Bay,, The UCI KDD Archive, Dept. of Information and Computer Science, Univ. of California, Irvine, http:/kdd.ics.uci.edu/, 1999.
20 ms
(Ver 2.0)

Marketing Automation Platform Marketing Automation Tool