A fast minimum spanning tree algorithm based on K-means

Information Sciences

Volumn 295, Issue , 2015, Pages 1-17

  Zhong, Caiming ^a   Malinen, Mikko ^b   Miao, Duoqian ^c   Fränti, Pasi ^c  

^a NINGBO UNIVERSITY   (China)

^b UNIVERSITY OF EASTERN FINLAND   (Finland)

^c TONGJI UNIVERSITY   (China)

Author keywords

Clustering; Manifold learning K means; Minimum spanning tree

Indexed keywords

ALGORITHMS; APPROXIMATION ALGORITHMS; ARTIFICIAL INTELLIGENCE; COMPUTATIONAL COMPLEXITY; DATA MINING; LEARNING SYSTEMS; PARALLEL ARCHITECTURES; PATTERN RECOGNITION; TELECOMMUNICATION NETWORKS; TREES (MATHEMATICS);

CLUSTERING; COMPLETE GRAPHS; COMPUTATIONALLY EFFICIENT; DIVIDE AND CONQUER; K-MEANS; LARGE DATASET; MINIMUM SPANNING TREES; TIME COMPLEXITY;

CLUSTERING ALGORITHMS;

EID: 84961371771     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2014.10.012     Document Type: Article

References (54)

1. H. Abdel-Wahab, I. Stoica, F. Sultan, and K. Wilson A simple algorithm for computing minimum spanning trees in the internet Inform. Sci. 101 1997 47 69
2. L. An, Q.S. Xiang, and S. Chavez A fast implementation of the minimum spanning tree method for phase unwrapping IEEE Trans. Med. Imag. 19 2000 805 808
3. B. Awerbuch, Optimal distributed algorithms for minimum weight spanning tree, counting, leader election, and related problems, in: Proceedings of the 19th ACM Symposium on Theory of Computing, 1987.
4. D.A. Bader, and G. Cong Fast shared-memory algorithms for computing the minimum spanning forest of sparse graphs J. Paral. Distrib. Comput. 66 2006 1366 1378
5. J.C. Bezdek, and N.R. Pal Some new indexes of cluster validity IEEE Trans. Syst., Man Cybernet., Part B 28 1998 301 315
6. O. Borůvka O jistém problému minimálním (About a Certain Minimal Problem) Práce moravské přírodovědecké společnosti v Brně III 1926 37 58 (in Czech with German summary)
7. P.B. Callahan, S.R. Kosaraju, Faster algorithms for some geometric graph problems in higher dimensions, in: Proceedings of the Fourth Annual ACM-SIAM Symposium on Discrete algorithms, 1993.
8. H. Chang, and D.Y. Yeung Robust path-based spectral clustering Patt. Recog. 41 2008 191 203
9. B. Chazelle A minimum spanning tree algorithm with inverse-Ackermann type complexity J. ACM 47 2000 1028 1047
10. G. Chen The multi-criteria minimum spanning tree problem based genetic algorithm Inform. Sci. 177 2007 5050 5063
11. D. Cheriton, and R.E. Tarjan Finding minimum spanning trees SIAM J. Comput. 5 1976 24 742
12. K.W. Chong, Y. Han, and T.W. Lam Concurrent threads and optimal parallel minimum spanning trees algorithm J. ACM 48 2001 297 323
13. G. Choquet Etude de certains réseaux de routes Comptesrendus de l'Acadmie des Sciences 206 1938 310 (in French)
14. T.H. Cormen, C.E. Leiserson, R.L. Rivest, and C. Stein Introduction to Algorithms second ed. 2001 The MIT Press
15. E.W. Dijkstra A note on two problems in connexion with graphs Numer. Math. 1 1959 269 271
16. Q. Du, V. Faber, and M. Gunzburger Centroidal Voronoi tessellations: applications and algorithms SIAM Rev. 41 1999 637 676
17. B. Fischer, and J.M. Buhmann Path-based clustering for grouping of smooth curves and texture segmentation IEEE Trans. Pattern Anal. Mach. Intell. 25 2003 513 518
18. B. Fischer, and J.M. Buhmann Bagging for path-based clustering IEEE Trans. Pattern Anal. Mach. Intell. 25 2003 1411 1415
19. K. Florek, J. Łkaszewicz, H. Perkal, H. Steinhaus, and S. Zubrzycki Sur la liaison et la division des points d'un ensemble fini Colloq. Mathemat. 2 1951 282 285
20. M.L. Fredman, and R.E. Tarjan Fibonacci heaps and their uses in improved network optimization algorithms J. ACM 34 1987 596 615
21. H.N. Gabow, Z. Galil, T.H. Spencer, and R.E. Tarjan Efficient algorithms for finding minimum spanning trees in undirected and directed graphs Combinatorica 6 1986 109 122
22. H.N. Gabow, Z. Galil, and T.H. Spencer Efficient implementation of graph algorithms using contraction J. ACM 36 1989 540 572
23. R.G. Gallager, P.A. Humblet, and P.M. Spira A distributed algorithm for minimum-weight spanning trees ACM Trans. Program. Lang. Syst. 5 1983 66 77
24. J.C. Gower, and G.J.S. Ross Minimum spanning trees and single linkage cluster analysis J. R. Statist. Soc., Ser. C (Appl. Statist.) 18 1969 54 64
25. C.M. Hsu, and M.S. Chen On the design and applicability of distance functions in high-dimensional data space IEEE Trans. Knowl. Data Eng. 21 2009 523 536
26. V. Jarník O jistém problému minimálním (About a certain minimal problem) Práce moravské přírodovědecké společnosti v Brně VI 1930 57 63 (in Czech)
27. P. Juszczak, D.M.J. Tax, E. Pękalska, and R.P.W. Duin Minimum spanning tree based one-class classifier Neurocomputing 72 2009 1859 1869
28. G. Karypis, E.H. Han, and V. Kumar CHAMELEON: a hierarchical clustering algorithm using dynamic modeling IEEE Trans. Comput. 32 1999 68 75
29. M. Khan, and G. Pandurangan A fast distributed approximation algorithm for minimum spanning trees Distrib. Comput. 20 2008 391 402
30. K. Li, S. Kwong, J. Cao, M. Li, J. Zheng, and R. Shen Achieving balance between proximity and diversity in multi-objective evolutionary algorithm Inform. Sci. 182 2012 220 242
31. K.H. Kim, S. Choi, Neighbor search with global geometry: a minimax message passing algorithm, in: Proceedings of the 24th International Conference on Machine Learning, 2007, pp. 401-408.
32. J.B. Kruskal On the shortest spanning subtree of a graph and the traveling salesman problem Proc. Am. Math. Soc. 7 1956 48 50
33. B. Lacevic, and E. Amaldi Ectropy of diversity measures for populations in Euclidean space Inform. Sci. 181 2011 2316 2339
34. C. Lai, T. Rafa, and D.E. Nelson Approximate minimum spanning tree clustering in high-dimensional space Intell. Data Anal. 13 2009 575 597
35. W.B. March, P. Ram, and A.G. Gray Fast euclidean minimum spanning tree: algorithm, analysis, and applications Proceedings of the 16th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 2010 ACM
36. T. Öncan Design of capacitated minimum spanning tree with uncertain cost and demand parameters Inform. Sci. 177 2007 4354 4367
37. D. Peleg, and V. Rubinovich A near tight lower bound on the time complexity of distributed minimum spanning tree construction SIAM J. Comput. 30 2000 1427 1442
38. S. Pettie, and V. Ramachandran A randomized time-work optimal parallel algorithm for finding a minimum spanning forest SIAM J. Comput. 31 2000 1879 1895
39. R.C. Prim Shortest connection networks and some generalizations Bell Syst. Tech. J. 36 1957 567 574
40. M. Radovanovic, A. Nanopoulos, and M. Ivanovic Hubs in space: popular nearest neighbors in high-dimensional data J. Mach. Learn. Res. 11 2010 2487 2531
41. M.R. Rezaee, B.P.F. Lelieveldt, and J.H.C. Reiber A new cluster validity index for the fuzzy c-mean Patt. Recog. Lett. 19 1998 237 246
42. M. Sollin Le trace de canalisation C. Berge, A. Ghouilla-Houri, Programming, Games, and Transportation Networks 1965 Wiley New York (in French)
43. S. Sundar, and A. Singh A swarm intelligence approach to the quadratic minimum spanning tree problem Inform. Sci. 180 2010 3182 3191
44. P.M. Vaidya Minimum spanning trees in k-dimensional space SIAM J. Comput. 17 1988 572 582
45. X. Wang, X. Wang, and D.M. Wilkes A divide-and-conquer approach for minimum spanning tree-based clustering IEEE Trans. Knowl. Data Eng. 21 2009 945 958
46. Y. Xu, V. Olman, and D. Xu Clustering gene expression data using a graph-theoretic approach: an application of minimum spanning trees Bioinformatics 18 2002 536 545
47. Y. Xu, and E.C. Uberbacher 2D image segmentation using minimum spanning trees Image Vis. Comput. 15 1997 47 57
48. L. Yang, k-Edge Connected neighborhood graph for geodesic distance estimation and nonlinear data projection, in: Proceedings of the 17th International Conference on Pattern Recognition, ICPR'04, 2004.
49. L. Yang Building k edge-disjoint spanning trees of minimum total length for isometric data embedding IEEE Trans. Patt. Anal. Mach. Intell. 27 2005 1680 1683
50. A.C. Yao An O (| E | loglog | V |) algorithm for finding minimum spanning trees Inform. Process. Lett. 4 1975 21 23
51. C.T. Zahn Graph-theoretical methods for detecting and describing gestalt clusters IEEE Trans. Comp. C20 1971 68 86
52. C. Zhong, D. Miao, and R. Wang A graph-theoretical clustering method based on two rounds of minimum spanning trees Patt. Recog. 43 2010 752 766
53. C. Zhong, D. Miao, and P. Fränti Minimum spanning tree based split-and-merge: a hierarchical clustering method Inform. Sci. 181 2011 3397 3410
54. C. Zhong, M. Malinen, D. Miao, P. Fränti, Fast approximate minimum spanning tree algorithm based on K-means, in: 15th International Conference on Computer Analysis of Images and Patterns, York, UK, 2013.