On the convergence of some possibilistic clustering algorithms
Tóm tắt
In this paper, an analysis of the convergence performance is conducted for a class of possibilistic clustering algorithms (PCAs) utilizing the Zangwill convergence theorem. It is shown that under certain conditions the iterative sequence generated by a PCA converges, at least along a subsequence, to either a local minimizer or a saddle point of the objective function of the algorithm. The convergence performance of more general PCAs is also discussed.
Tài liệu tham khảo
Bezdek, J. C. (1980). A Convergence theorem for the fuzzy ISODATA clustering algorithms. IEEE Transactions on Pattern Analysis and Machine Intellegence, PAMI-2(1), 1–8.
Dave, R. N., & Krishnapuram, R. (1997). Robust clustering methods: a unified view. IEEE Transactions on Fuzzy Systems, 5(2), 270–293.
Dey, V., Pratihar, D. K., & Datta, G. L. (2011). Genetic algorithm-tuned entropy-based fuzzy C-means algorithm for obtaining distinct and compact clusters. Fuzzy Optimization and Decision Making, 10(2), 153–166.
Hathaway, R. J., Bezdek, J. C., & Tucker, W. T. (1987). An improved convergence theory for the fuzzy ISODATA clustering algorithms, the analysis of fuzzy information (Vol. 3, pp. 123–132). Boca Raton: CRC Press.
Höppner, F., & Klawonn, F. (2003). A contribution to convergence theory of fuzzy \(c\)-means and derivatives. IEEE Transactions on Fuzzy Systems, 11(5), 682–694.
Krishnapuram, R., & Keller, J. M. (1993). A possibilistic approach to clustering. IEEE Transactions on Fuzzy Systems, 1(2), 98–110.
Krishnapuram, R., & Keller, J. M. (1996). The possibilistic \(c\)-means algorithm: insights and recommendations. IEEE Transactions on Fuzzy Systems, 4(3), 385–393.
Krishnapuram, R., Frigui, H., & Nasraoui, O. (1995). Fuzzy and possibilistic shell clustering algorihm and their application to boundary detection and surface approximation. IEEE Transactions on Fuzzy Systems, 3, 29–60.
Oussalah, M., & Nefti, S. (2008). On the use of divergence distance in fuzzy clustering. Fuzzy Optimization and Decision Making, 7(2), 147–167.
Yang, M.-S., & Wu, K.-L. (2006). Unsupervised possibilistic clustering. Pattern Recognition, 39(1), 5–21.
Zangwill, W. (1969). Nolinear programming: a unified approach. Englewood Cliffs, NJ: Prentice-Hall.
Zhang, Y., & Chi, Z.-X. (2008). A fuzzy support vector classifier based on Bayesian optimization. Fuzzy Optimization and Decision Making, 7(1), 75–86.
Zhou, J., & Hung, C. C. (2007). A generalized approach to possibilistic clustering algorithms. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 15(2), 117–138.