一种具有最优保证特性的贝叶斯可能性聚类方法

刘解放; 王士同; 王骏; 邓赵红

doi:10.11999/JEIT160908

一种具有最优保证特性的贝叶斯可能性聚类方法

doi: 10.11999/JEIT160908

2.
(江南大学数字媒体学院无锡 214122) ②(湖北交通职业技术学院交通信息学院武汉 430079)

基金项目:

国家自然科学基金(61572236)，江苏省杰出青年基金(BK20140001)，江苏省自然科学基金(BK20151299)

计量
- 文章访问数: 959
- HTML全文浏览量: 121
- PDF下载量: 428
- 被引次数: 0
出版历程
- 收稿日期: 2016-09-09
- 修回日期: 2017-02-10
- 刊出日期: 2017-07-19

Bayesian Possibilistic Clustering Method with Optimality Guarantees

2.
(School of Digital Media, Jiangnan University, Wuxi 214122, China)

Funds:

The National Natural Science Foundation of China (61572236), Jiangsu Province Outstanding Youth Fund (BK20140001), Natural Science Foundation of Jiangsu Province (BK20151299)

摘要

摘要: 该文结合概率理论和可能性理论，提出一种具有最优保证特性的贝叶斯可能性聚类新方法。首先，将未知隶属度和聚类中心作为随机变量，为每个随机变量选择一个合适的概率分布，提出贝叶斯可能性聚类模型；在此基础上，基于贝叶斯推理和和蒙特卡洛采样方法，通过最大后验概率框架求解贝叶斯可能性聚类模型中的未知参数，从而提出一种具有最优保证特性的贝叶斯可能性聚类新方法。并对算法收敛性、算法复杂度等方面作了理论探讨。在合成数据集和真实数据集上的实验表明，所提算法扩展了传统可能性聚类性能，改进了聚类结果。
- 可能性聚类 /
- 贝叶斯推理 /
- 最大后验概率 /
- 蒙特卡洛方法
Abstract: 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.
- Possibilistic clustering /
- Bayesian inference /
- Maximum-A-Posteriori (MAP) /
- Monte Carlo method

HTML全文

参考文献(28)

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.

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.

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): 517530. doi: 10.1109/tfuzz. 2004.840 099.

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.

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.

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.

范九伦, 裴继红. 基于可能性分布的聚类有效性[J]. 电子学报, 1998, 26(4): 113-115.

FAN Jiulun and PEI Jihong. Cluster validity based on possibilistic distribution[J]. Acta Electronica Sinica, 1998, 26(4): 113-115.

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.

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.

夏建明, 杨俊安, 陈功. 参数自适应调整的稀疏贝叶斯重构算法[J]. 电子与信息学报, 2014, 36(6): 1355-1361. doi: 10.3724/SP.J.1146.2013.00629.

XIA Jianming, YANG Junan, and CHEN Gong. Bayesian sparse reconstruction with adaptive parameters adjustment[J]. Journal of Electronics Information Technology, 2014, 36(6): 1355-1361. doi: 10.3724/SP.J.1146. 2013.00629.

王峰, 向新, 易克初, 等. 基于隐变量贝叶斯模型的稀疏信号恢复[J]. 电子与信息学报, 2015, 37(1): 97-102. doi: 10.11999/ JEIT140169.

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.

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.

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.

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.

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.

BEZDEK J C, EHRLICH R, and FULL W. FCM: The fuzzy c-means clustering algorithm[J]. Computers Geosciences, 1984, 10(2-3): 191203.

KRISHNAPURAM R and KELLER J M. A Possibilistic approach to clustering[J]. IEEE Transactions on Fuzzy Systems, 1993, 1(2): 98-110.

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.

CHIB S and GREENBERG E. Understanding the metropolis-hastings algorithm[J]. The American Statistician, 1995, 49(4): 327-335.

PLUMMER M, BEST N, COWLES K, et al. CODA: Convergence diagnosis and output analysis for MCMC[J]. R News, 2006, 6(1): 7-11.

朱崇军. MCMC样本确定的后验密度的收敛性[J]. 数学杂志, 2002, 22(3): 345-348. doi: 10.3969/j.issn.0255-7797.2002. 03.019.

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.

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): 207216.

ZELLNER A and MIN C K. Gibbs sampler convergence criteria[J]. Journal of the American Statistical Association, 1995, 90(431): 921-927.

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.

施引文献

资源附件(0)

访问统计