A novel Bayesian possibilistic clustering method with optimality guarantees based on probability theory and possibilistic theory is proposed. First, the unknown membership degree and cluster center are represented as random variables. Given the specific constraints and uncertainty associated with each random variable, an appropriate probability distribution for each random variable is selected and the Bayesian possibilistic clustering model is proposed. On this basis, a novel Bayesian possibilistic clustering method with the optimal guarantee properties is propsed based on Bayesian theory and Monte Carlo sampling method using a Maximum-A-Posteriori (MAP) framework. Then, the convergence of the algorithm and the complexity of the algorithm are discussed. Experimental results on synthetic and real data sets show that the proposed method extends the traditional possibilistic clustering performance, and improves the clustering results.
刘解放,王士同,王骏,邓赵红. 一种具有最优保证特性的贝叶斯可能性聚类方法[J]. 电子与信息学报, 2017, 39(7): 1554-1562.
LIU Jiefang, WANG Shitong, WANG Jun, DENG Zhaohong. Bayesian Possibilistic Clustering Method with Optimality Guarantees. JEIT, 2017, 39(7): 1554-1562.
BARNI M, CAPPELLINI V, and MECOCCI A. Comments on "a possibilistic approach to clustering"[J]. IEEE Transactions on Fuzzy Systems, 1996, 4(3): 393-396.
[2]
PAL N R, PAL K, and BEZDEK J C. A mixed c-means clustering model[C]. Proceedings of the Sixth IEEE International Conference on Fuzzy Systems, Barcelona, Spain, 1997: 11-21.
[3]
PAL N R, PAL K, KELLER J M, et al. A possibilistic fuzzy c-means clustering algorithm[J]. IEEE Transactions on Fuzzy Systems, 2005, 13(4): 517-530. doi: 10.1109/tfuzz. 2004.840 099.
[4]
KRISHNAPURAM R and KELLER J M. The possibilistic c-means algorithm: Insights and recommendations[J]. IEEE Transactions on Fuzzy Systems, 1996, 4(3): 385-393.
[5]
ZHANG J S and LEUNG Y W. Improved possibilistic c-means clustering algorithms[J]. IEEE Transactions on Fuzzy Systems, 2004, 12(2): 209-217. doi: 10.1109/tfuzz. 2004.825079.
[6]
YANG M S and LAI C Y. A robust automatic merging possibilistic clustering method[J]. IEEE Transactions on Fuzzy Systems, 2011, 19(1): 26-41. doi: 10.1109/tfuzz.2010. 2077640.
FAN Jiulun and PEI Jihong. Cluster validity based on possibilistic distribution[J]. Acta Electronica Sinica, 1998, 26(4): 113-115.
[8]
ZARANDI M H F, AVAZBEIGI M, and ANSSARI M H. New possibilistic noise rejection clustering algorithm with simulated annealing[C]. 2011 Annual Meeting of the North American Fuzzy Information Processing Society, Canada, 2011: 1-5. doi: 10.1109/nafips.2011.5752004.
[9]
DENG Z H, CAO L B, JIANG Y Z, et al. Minimax probability TSK fuzzy system classifier: A more transparent and highly interpretable classification model[J]. IEEE Transactions on Fuzzy Systems, 2015, 23(4): 813-826. doi: 10.1109/tfuzz.2014.2328014.
WANG Feng, XIANG Xin, YI Kechu, et al. Sparse signals recovery based on latent variable Bayesian models[J]. Journal of Electronics & Information Technology, 2015, 37(1): 97-102. doi: 10.11999/JEIT140169.
[12]
WANG S T, CHUNG K F, SHEN H B, et al. Note on the relationship between probabilistic and fuzzy clustering[J]. Soft Computing, 2004, 8(5): 366-369. doi: 10.1007/s00500- 003-0309-8.
[13]
YU L, WEI C, and ZHENG G. Adaptive Bayesian estimation with cluster structured sparsity[J]. IEEE Signal Processing Letters, 2015, 22(12): 2309-2313. doi: 10.1109 /lsp.2015. 2477440.
[14]
GLENN T C, ZARE A, and GADER P D. Bayesian fuzzy clustering[J]. IEEE Transactions on Fuzzy Systems, 2015, 23(5): 1545-1561. doi: 10.1109/tfuzz.2014.2370676.
[15]
ZARINBAL M, ZARANDI M H F, and TURKSEN I B. Relative entropy fuzzy c-means clustering[J]. Information Sciences, 2014, 260: 74-97. doi: 10.1016/j.ins.2013.11.004.
[16]
BEZDEK J C, EHRLICH R, and FULL W. FCM: The fuzzy c-means clustering algorithm[J]. Computers & Geosciences, 1984, 10(2-3): 191-203.
[17]
KRISHNAPURAM R and KELLER J M. A Possibilistic approach to clustering[J]. IEEE Transactions on Fuzzy Systems, 1993, 1(2): 98-110.
[18]
ANDRIEU C, DE FREITAS N, DOUCET A, et al. An introduction to MCMC for machine learning[J]. Machine Learning, 2003, 50(1): 5-43. doi: 10.1023/A:1020281327116.
[19]
CHIB S and GREENBERG E. Understanding the metropolis-hastings algorithm[J]. The American Statistician, 1995, 49(4): 327-335.
[20]
PLUMMER M, BEST N, COWLES K, et al. CODA: Convergence diagnosis and output analysis for MCMC[J]. R News, 2006, 6(1): 7-11.
ZHU Chongjun. On the convergences of a posteriori density determined by MCMC samplers[J]. Journal of Math ematics, 2002, 22(3): 345-348. doi: 10.3969/j.issn.0255-7797.2002. 03.019.
[22]
ROBERTS G O and SMITH A F M. Simple conditions for the convergence of the Gibbs sampler and Metropolis- Hastings algorithms[J]. Stochastic Processes and Their Applications, 1994, 49(2): 207-216.
[23]
ZELLNER A and MIN C K. Gibbs sampler convergence criteria[J]. Journal of the American Statistical Association, 1995, 90(431): 921-927.
[24]
ASUNCION A and NEWMAN D J. UC irvine machine learning repository[OL]. http://archive.ics.uci.edu/ml/ machine-learning-databases/iris/iris.names, 2015.
[25]
LIU T, YUAN Z, SUN J, et al. Learning to detect a salient object[J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2011, 33(2): 353-367. doi: 10.1109/ tpami.2010.70.
