A scaled-MST-based clustering algorithm and application on image segmentation

Abstract

Minimum spanning tree (MST)-based clustering is one of the most important clustering techniques in the field of data mining. Although traditional MST-based clustering algorithm has been researched for decades, it still has some limitations for data sets with different density distribution. After analyzing the advantages and disadvantages of the traditional MST-based clustering algorithm, this paper presents two new methods to improve the traditional clustering algorithm. There are two steps of our first method: compute a scaled-MST with scaled distance to find the longest edges between different density clusters and clustering based on the MST. To improve the performance, our second scaled-MST-clustering works by merging the MST construction and inconsistent edges’ detection into one step. To verify the effectiveness and practicability of the proposed method, we apply our algorithm on image segmentation and integration. The encouraging performance demonstrates the superiority of the proposed method on both small data sets and high dimensional data sets.

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References

  1. An, L., Xiang, Q.S., Chavez, S. (2000). A fast implementation of the minimum spanning tree method for phase unwrapping. IEEE Transactions on Medical Imaging, 19(8), 805–8.

    Article  Google Scholar 

  2. Arya, S., & Mount, D.M. (2016). A fast and simple algorithm for computing approximate euclidean minimum spanning trees. In Twenty-seventh ACM-SIAM symposium on discrete algorithms (pp. 1220–1233).

  3. Beygelzimer, A.M., Kakade, S., Langford, J. (2000). Cover trees for nearest neighbor. In ICML 2006 - Proceedings of the 23rd international conference on machine learning 2006. https://doi.org/10.1145/1143844.1143857.

  4. Borůvka, O. (1926). O jistém problému minimálním. Práce moravská přirodovédecké společnosti, 3(1926), 37–58.

    Google Scholar 

  5. Boser, B., Guyon, I.N., Vapnik, V. (1996). A training algorithm for optimal margin classifier. In Proceedings of the fifth annual ACM workshop on computational learning theory, Vol. 5,https://doi.org/10.1145/130385.130401.

  6. Chang, H., & Yeung, D.Y. (2008). Robust path-based spectral clustering. Pattern Recognition, 41(1), 191–203.

    Article  Google Scholar 

  7. Chong, K.W., & Zaroliagis, C. (2015). An optimal parallel algorithm for minimum spanning trees in planar graphs. Berlin: Springer International Publishing.

    Google Scholar 

  8. Cormen, T.T., Leiserson, C.E., Rivest, R.L. (2009). Introduction to algorithms. Resonance, 1(9), 14–24.

    MATH  Google Scholar 

  9. Dhanachandra, N., Manglem, K., Chanu, Y.J. (2015). Image segmentation using k -means clustering algorithm and subtractive clustering algorithm. Procedia Computer Science, 54, 764–771. 10.1016/j.procs.2015.06.090. http://www.sciencedirect.com/science/article/pii/S1877050915014143.

    Article  Google Scholar 

  10. Dua, D., & Graff, C. (2017). UCI machine learning repository. http://archive.ics.uci.edu/ml.

  11. Economou, G., Pothos, V., Ifantis, A. (2004). Geodesic distance and mst based image segmentation. In 2004 12th European Signal Processing Conference (pp. 941–944).

  12. Gil, D., Girela, J.L., Juan, J.D., Gomez-Torres, M.J., Johnsson, M. (2012). Predicting seminal quality with artificial intelligence methods. Expert Systems with Applications, 39(16), 12564–12573.

    Article  Google Scholar 

  13. Güngör, E, & Özmen, A. (2016). Distance and density based clustering algorithm using gaussian kernel. Expert Systems with Applications, 69, 10–20.

    Article  Google Scholar 

  14. Halkidi, M., Batistakis, Y., Vazirgiannis, M. (2001). On clustering validation techniques. Journal of Intelligent Information Systems, 17(2-3), 107–145.

    Article  Google Scholar 

  15. He, Y., & Chen, L. (2004). Minclue: a mst-based clustering method with auto-threshold-detection. In IEEE conference on cybernetics and intelligent systems, (Vol. 1 pp. 229–233), https://doi.org/10.1109/ICCIS.2004.1460417.

  16. Hubert, L., & Arabie, P. (1985). Comparing partitions. Journal of Classification, 2(1), 193–218.

    Article  Google Scholar 

  17. Jothi, R., Mohanty, S.K., Ojha, A. (2015). Fast minimum spanning tree based clustering algorithms on local neighborhood graph. Berlin: Springer International Publishing.

    Google Scholar 

  18. Jothi, R., Mohanty, S.K., Ojha, A. (2017). Fast approximate minimum spanning tree based clustering algorithm. Neurocomputing 272.

  19. Juszczak, P., Tax, D.M.J., Peķalska, E, Duin, R.P.W. (2009). Minimum spanning tree based one-class classifier. Neurocomputing, 72(7–9), 1859–1869.

    Article  Google Scholar 

  20. Karypis, G., Han, E.H., Kumar, V. (2008). Chameleon a hierarchical clustering algorithm using dynamic modeling. Computer, 32(8), 68–75.

    Article  Google Scholar 

  21. Larsen, B., & Aone, C. (1999). Fast and effective text mining using linear-time document clustering. In ACM SIGKDD international conference on knowledge discovery and data mining (pp. 16–22).

  22. Li, Z., & Tang, J. (2017). Weakly supervised deep matrix factorization for social image understanding. IEEE Transactions on Image Processing, 26(1), 276–288. https://doi.org/10.1109/TIP.2016.2624140.

    MathSciNet  Article  MATH  Google Scholar 

  23. Luo, T., & Zhong, C. (2010). A neighborhood density estimation clustering algorithm based on minimum spanning tree. In International conference on rough set and knowledge technology.

  24. Lv, X., Ma, Y., He, X., Huang, H., Yang, J. (2018). CciMST: a clustering algorithm based on minimum spanning tree and cluster centers. Mathematical Problems in Engineering 2018. https://doi.org/10.1155/2018/8451796.

  25. Peng, B., Zhang, L., Zhang, D. (2013). A survey of graph theoretical approaches to image segmentation. Pattern Recognition, 46(3), 1020–1038. https://doi.org/10.1016/j.patcog.2012.09.015. http://www.sciencedirect.com/science/article/pii/S0031320312004219.

    Article  Google Scholar 

  26. Rand, W.M. (1971). Objective criteria for the evaluation of clustering methods. Publications of the American Statistical Association, 66(336), 846–850.

    Article  Google Scholar 

  27. Saglam, A., & Baykan, N.A. (2017). Sequential image segmentation based on minimum spanning tree representation. http://www.sciencedirect.com/science/article/pii/S0167865516301192, advances in Graph-based Pattern Recognition, (Vol. 87 pp. 155–162), https://doi.org/10.1016/j.patrec.2016.06.001.

  28. Tsanas, A., & Xifara, A. (2012). Accurate quantitative estimation of energy performance of residential buildings using statistical machine learning tools. Energy and Buildings, 49(49), 560–567.

    Article  Google Scholar 

  29. Vella, F., Infantino, I., Gaglio, S., Vetrano, G. (2012). Image segmentation through a hierarchy of minimum spanning trees. In 2012 Eighth international conference on signal image technology and internet based systems. https://doi.org/10.1109/SITIS.2012.62 (pp. 381–388).

  30. Wang, X.L., & Wang, X. (2018). An efficient approximate emst algorithm for color image segmentation. In Perner, P. (Ed.) Machine learning and data mining in pattern recognition (pp. 147–159). Cham: Springer International Publishing.

  31. Wang, X., Wang, X.L., Wilkes, D.M. (2012). A minimum spanning tree-inspired clustering-based outlier detection technique. In Industrial conference on advances in data mining: applications and theoretical aspects (pp. 209–223).

  32. Wang, X., Wang, X.L., Chen, C., Wilkes, D.M. (2013). Enhancing minimum spanning tree-based clustering by removing density-based outliers. Digital Signal Processing, 23(5), 1523–1538.

    MathSciNet  Article  Google Scholar 

  33. Wang, X.L., Wang, X., Li, X. Perner, P. (Ed.). (2018). A fast two-level approximate euclidean minimum spanning tree algorithm for high-dimensional data. Cham: Springer International Publishing.

  34. Xu, Y., & Uberbacher, E.C. (1997). 2d image segmentation using minimum spanning trees. Image and Vision Computing, 15(1), 47–57.

    Article  Google Scholar 

  35. Xu, Y., Olman, V., Xu, D. (2002). Clustering gene expression data using a graph-theoretic approach: an application of minimum spanning trees. Bioinformatics, 18(4), 536–545.

    Article  Google Scholar 

  36. Zahn, C.T. (1971). Graph-theoretical methods for detecting and describing gestalt clusters. In IEEE Trans. on Computers (pp. 68–86).

  37. Zhang, H., Fritts, J.E., Goldman, S.A. (2008). Image segmentation evaluation: a survey of unsupervised methods. Computer Vision and Image Understanding, 110 (2), 260–280. https://doi.org/10.1016/j.cviu.2007.08.003. http://www.sciencedirect.com/science/article/pii/S1077314207001294.

    Article  Google Scholar 

  38. Zhong, C., Miao, D., Wang, R. (2010). A graph-theoretical clustering method based on two rounds of minimum spanning trees. Pattern Recognition, 43(3), 752–766.

    Article  Google Scholar 

  39. Zhong, C., Miao, D., Nti, P. (2011). Minimum spanning tree based split-and-merge: a hierarchical clustering method. Information Sciences, 181(16), 3397–3410.

    Article  Google Scholar 

  40. Zhong, C., Malinen, M., Miao, D., Fränti, P. (2015). A fast minimum spanning tree algorithm based on k-means. Information Sciences.

    Google Scholar 

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Acknowledgments

The authors would like to thank the Chinese National Science Foundation for its valuable support of this work under award 61473220 and all the anonymous reviewers and editors for their valuable comments.

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Correspondence to Jia Li.

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Li, J., Wang, X. & Wang, X. A scaled-MST-based clustering algorithm and application on image segmentation. J Intell Inf Syst 54, 501–525 (2020). https://doi.org/10.1007/s10844-019-00572-x

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Keywords

  • Minimum spanning tree
  • Clustering
  • Minimum spanning tree-based clustering
  • Image segmentation
  • Image integration