中文摘要：

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。

英文摘要：

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.