A Kernel-Based Membrane Clustering Algorithm

  • Jinyu Yang
  • Ru Chen
  • Guozhou Zhang
  • Hong PengEmail author
  • Jun Wang
  • Agustín Riscos-Núñez
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11270)


The existing membrane clustering algorithms may fail to handle the data sets with non-spherical cluster boundaries. To overcome the shortcoming, this paper introduces kernel methods into membrane clustering algorithms and proposes a kernel-based membrane clustering algorithm, KMCA. By using non-linear kernel function, samples in original data space are mapped to data points in a high-dimension feature space, and the data points are clustered by membrane clustering algorithms. Therefore, a data clustering problem is formalized as a kernel clustering problem. In KMCA algorithm, a tissue-like P system is designed to determine the optimal cluster centers for the kernel clustering problem. Due to the use of non-linear kernel function, the proposed KMCA algorithm can well deal with the data sets with non-spherical cluster boundaries. The proposed KMCA algorithm is evaluated on nine benchmark data sets and is compared with four existing clustering algorithms.


4K MCA Optimal Cluster Centers Original Data Space Existing Clustering Algorithms Map Data Sets 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This work was partially supported by the National Natural Science Foundation of China (No. 61472328), Chunhui Project Foundation of the Education Department of China (Nos. Z2016143 and Z2016148), the Innovation Fund of Postgraduate, Xihua University (No. ycjj2018184), and Research Foundation of the Education Department of Sichuan province (No. 17TD0034), China.


  1. 1.
    Păun, Gh.: Computing with membranes. J. Comput. Syst. Sci. 61(1), 108–143 (2000)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Pǎun, Gh.: Membrane Computing: An Introduction. Springer, Berlin (2002). Scholar
  3. 3.
    Cavaliere, M.: Evolution–communication P systems. In: Păun, Gh., Rozenberg, G., Salomaa, A., Zandron, C. (eds.) WMC 2002. LNCS, vol. 2597, pp. 134–145. Springer, Heidelberg (2003). Scholar
  4. 4.
    Freund, R., Pǎun, Gh., Pérez-Jiménez, M.J.: Tissue-like P systems with channel-states. Theor. Comput. Sci. 330(1), 101–116 (2005)Google Scholar
  5. 5.
    Bernardini, F., Gheorghe, M.: Population P systems. J. Univ. Comput. Sci. 10(5), 509–539 (2004)MathSciNetGoogle Scholar
  6. 6.
    Pǎun, Gh., Pǎun, R.: Membrane computing and economics: numerical P systems. Fundam. Inform. 73(1–2), 213–227 (2006)Google Scholar
  7. 7.
    Ciencialová, L., Csuhaj-Varjú, E., Kelemenová, A., Vaszil, G.: Variants of P colonies with very simple cell structure. Int. J. Comput. Commun. Control IV(3), 224–233 (2009)CrossRefGoogle Scholar
  8. 8.
    Ionescu, M., Păun, Gh., Yokomori, T.: Spiking neural P systems. Fundam. Inform. 71, 279–308 (2006)Google Scholar
  9. 9.
    Song, T., Pan, L., Păun, Gh.: Spiking neural P systems with rules on synapses. Theor. Comput. Sci. 529, 82–95 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Peng, H., et al.: Competitive spiking neural P systems with rules on synapses. IEEE Trans. NanoBiosci. 16(8), 888–895 (2018)CrossRefGoogle Scholar
  11. 11.
    Peng, H., et al.: Spiking neural P systems with multiple channels. Neural Netw. 95, 66–71 (2017)CrossRefGoogle Scholar
  12. 12.
    Buiu, C., Vasile, C., Arsene, O.: Development of membrane controllers for mobile robots. Inf. Sci. 187, 33–51 (2012)CrossRefGoogle Scholar
  13. 13.
    Wang, X., et al.: Design and implementation of membrane controllers for trajectory tracking of nonholonomic wheeled mobile robots. Integr. Comput.-Aided Eng. 23(1), 15–30 (2016)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Zhang, G., Gheorghe, M., Li, Y.: A membrane algorithm with quantum-inspired subalgorithms and its application to image processing. Natural Comput. 11(4), 701–717 (2012)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Díaz-Pernil, D., Berciano, A., Peña-Cantillana, F., Gutiérrez-Naranjo, M.A.: Segmenting images with gradient-based edge detection using membrane computing. Pattern Recogn. Lett. 34(8), 846–855 (2013)CrossRefGoogle Scholar
  16. 16.
    Peng, H., Wang, J., Pérez-Jiménez, M.J.: Optimal multi-level thresholding with membrane computing. Digit. Sig. Process. 37, 53–64 (2015)CrossRefGoogle Scholar
  17. 17.
    Alsalibi, B., Venkat, I., Al-Betar, M.A.: A membrane-inspired bat algorithm to recognize faces in unconstrained scenarios. Eng. Appl. Artif. Intell. 64, 242–260 (2017)CrossRefGoogle Scholar
  18. 18.
    Zhang, G., Liu, C., Rong, H.: Analyzing radar emitter signals with membrane algorithms. Math. Comput. Model. 52(11–12), 1997–2010 (2010)CrossRefGoogle Scholar
  19. 19.
    Peng, H., Wang, J., Pérez-Jiménez, M.J., Riscos-Núñez, A.: The framework of P systems applied to solve optimal watermarking problem. Sig. Process. 101, 256–265 (2014)CrossRefGoogle Scholar
  20. 20.
    Wang, J., Shi, P., Peng, H.: Membrane computing model for IIR filter design. Inf. Sci. 329, 164–176 (2016)CrossRefGoogle Scholar
  21. 21.
    Xiong, G., Shi, D., Zhu, L., Duan, X.: A new approach to fault diagnosis of power systems using fuzzy reasoning spiking neural P systems. Math. Problems Eng. 2013(1), 211–244 (2013)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Wang, J., Shi, P., Peng, H., Pérez-Jiménez, M.J., Wang, T.: Weighted fuzzy spiking neural P system. IEEE Trans. Fuzzy Syst. 21(2), 209–220 (2013)CrossRefGoogle Scholar
  23. 23.
    Wang, T., et al.: Fault diagnosis of electric power systems based on fuzzy reasoning spiking neural P systems. IEEE Trans. Power Syst. 30(3), 1182–1194 (2015)CrossRefGoogle Scholar
  24. 24.
    Peng, H., Wang, J., Shi, P., Pérez-Jiménez, M.J., Riscos-Núñez, A.: Fault diagnosis of power systems using fuzzy tissue-like P systems. Integr. Comput.-Aided Eng. 24, 401–411 (2017)CrossRefGoogle Scholar
  25. 25.
    Peng, H.: Fault diagnosis of power systems using intuitionistic fuzzy spiking neural P systems. IEEE Trans. Smart Grid 9(5), 4777–4784 (2018)CrossRefGoogle Scholar
  26. 26.
    Gheorghe, M., Manca, V., Romero-Campero, F.J.: Deterministic and stochastic P systems for modelling cellular processes. Natural Comput. 9(2), 457–473 (2010)MathSciNetCrossRefGoogle Scholar
  27. 27.
    García-Quismondo, M., Levin, M., Lobo-Fernández, D.: Modeling regenerative processes with membrane computing. Inf. Sci. 381, 229–249 (2017)CrossRefGoogle Scholar
  28. 28.
    García-Quismondo, M., Nisbet, I.C.T., Mostello, C.S., Reed, M.J.: Modeling population dynamics of roseate terns (sterna dougallii) in the Northwest Atlantic Ocean. Ecol. Model. 68, 298–311 (2018)CrossRefGoogle Scholar
  29. 29.
    Zhao, Y., Liu, X., Qu, J.: The K-medoids clustering algorithm by a class of P system. J. Inf. Comput. Sci. 9(18), 5777–5790 (2012)Google Scholar
  30. 30.
    Peng, H., Wang, J., Pérez-Jiménez, M.J., Riscos-Núñez, A.: An unsupervised learning algorithm for membrane computing. Inf. Sci. 304, 80–91 (2015)CrossRefGoogle Scholar
  31. 31.
    Peng, H., Wang, J., Shi, P., Riscos-Núñez, A., Pérez-Jiménez, M.J.: An automatic clustering algorithm inspired by membrane computing. Pattern Recogn. Lett. 68, 34–40 (2015)CrossRefGoogle Scholar
  32. 32.
    Peng, H., Wang, J., Shi, P., Pérez-Jiménez, M.J., Riscos-Núñez, A.: An extended membrane system with active membrane to solve automatic fuzzy clustering problems. Int. J. Neural Syst. 26(2), 1–17 (2016)Google Scholar
  33. 33.
    Peng, H., Shi, P., Wang, J., Riscos-Núñez, A., Pérez-Jiménez, M.J.: Multiobjective fuzzy clustering approach based on tissue-like membrane systems. Knowl.-Based Syst. 125, 74–82 (2017)CrossRefGoogle Scholar
  34. 34.
    Shawe-Taylor, J., Cristianini, N.: Kernel Methods for Pattern Analysis. Cambridge University Press, Cambridge (2004)CrossRefGoogle Scholar
  35. 35.
  36. 36.
  37. 37.
    Merwe, D.W., Engelbrecht, A.P.: Data clustering using particle swarm optimization. In: 2003 Congress on Evolutionary Computation (CEC 2003), pp. 215–220 (2003)Google Scholar
  38. 38.
    Zhang, R., Rudnicky, A.I.: A large scale clustering scheme for kernel k-means. In: Proceedings of 16th International Conference on Pattern Recognition, vol. 4, pp. 289–292 (2002)Google Scholar
  39. 39.
    Wei, X.H., Zhang, K.: An improved PSO-means clustering algorithm based on kernel methods. J. Henan Univ. Sci. Technol.: Nat. Sci. 32(2), 41–43 (2011)Google Scholar
  40. 40.
    Rousseeuw, P.J.: Silhouettes: a graphical aid to the interpretation and validation of cluster analysis. J. Comput. Appl. Math. 20(20), 53–65 (1987)CrossRefGoogle Scholar
  41. 41.
    Chou, C.H., Su, M.C., Lai, E.: A new cluster validity measure and its application to image compression. Pattern Anal. Appl. 7(2), 205–220 (2004)MathSciNetCrossRefGoogle Scholar
  42. 42.
    Congalton, R.G., Green, K.: Assessing the Accuracy of Remotely Sensed Data: Principles and Practices. CRC Press, Boca Raton (2009)Google Scholar
  43. 43.
    Hubert, L., Arabie, P.: Comparing partitions. J. Classif. 2(1), 193–218 (1985)CrossRefGoogle Scholar
  44. 44.
    Zhang, J., Niu, Y., He, W.: Using genetic algorithm to improve fuzzy k-NN. In: International Conference on Computational Intelligence and Security, pp. 475–479 (2008)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Jinyu Yang
    • 1
  • Ru Chen
    • 1
  • Guozhou Zhang
    • 1
  • Hong Peng
    • 1
    Email author
  • Jun Wang
    • 2
  • Agustín Riscos-Núñez
    • 3
  1. 1.School of Computer and Software EngineeringXihua UniversityChengduChina
  2. 2.School of Electrical and Information EngineeringXihua UniversityChengduChina
  3. 3.Research Group of Natural Computing, Department of Computer Science and Artificial IntelligenceUniversity of SevilleSevillaSpain

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