摘要:对于概率模糊聚类，贝叶斯模糊聚类方法表现出良好的聚类性能，它从先验知识和贝叶斯理论的角度出发，采用最大后验概率理论处理模糊划分，进而获取最终的聚类结果.该方法有效地结合了概率论和模糊论两者的优点，较之传统的模糊聚类算法（如FCM算法），该方法能够获取全局最优解并估计聚类个数.但在大数据时代，该方法较高的时间复杂度限制了它的实用性.针对此问题，首先在贝叶斯模糊聚类中引入加权机制，提出了加权贝叶斯模糊聚类算法；然后将其与单趟聚类框架相结合，提出了面向大规模数据的快速单趟贝叶斯模糊聚类算法，并从理论上对相关性质进行了较为深入的分析.所提出的单趟贝叶斯模糊聚类新算法较之贝叶斯模糊聚类算法在时间复杂度和收敛性上均有着不同程度的性能提升，同时继承了贝叶斯模糊聚类的良好的聚类性能.最后，相关实验结果亦验证了所提方法的有效性.



Abstract:Based on the maximum a posteriori (MAP) principle and Bayesian framework, the Bayesian fuzzy clustering (BFC) method recently proposed exhibits promising characteristics in estimating the number of clusters and finding the globally optimal clustering solution, for the method effectively combines the advantages of both probability theory and fuzzy theory. However, since it suffers from its high computational burden, BFC becomes impractical for large-scale datasets. In this paper, in order to circumvent this drawback of BFC, a weighted Bayesian fuzzy clustering (WBFC) algorithm is first proposed by introducing weighting mechanism in BFC. Then, a fast single pass Bayesian fuzzy clustering (SPBFC) algorithm is developed by combining WBFC with a single pass clustering framework. Theoretical analysis on convergence and time complexity is also discussed. The experimental results show that SPBFC not only inherits the promising characteristics, but also has a fast convergence speed for large-scale datasets.



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