基于非负矩阵分解的修正模糊聚类算法  

Modified Fuzzy Clustering Algorithm Based on Non-negative Matrix Factorization

作　　者：李向利[1] 范学珍 逯喜燕 LI Xiangli;FAN Xuezhen;LU Xiyan(School of Mathematics&Computing Science,Guilin University of Electronic Techology,Guilin 541004,Guangxi Zhuang Autonomous Region,China)

机构地区：[1]桂林电子科技大学数学与计算科学学院,广西桂林541004

出　　处：《吉林大学学报（理学版）》2022年第6期1416-1422,共7页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11961010,61967004)。

摘　　要：针对传统模糊C-均值(FCM)算法在处理复杂结构的高维数据集时产生大规模计算量导致聚类效果下降的问题,提出一种基于非负矩阵分解的修正模糊聚类算法.首先,该算法提出了新的目标函数,采用交替迭代的方式求解该目标函数;其次,在迭代过程中利用三角不等式过滤出满足不等式条件的样本,同时采用新的隶属度更新公式,减少计算量,提高聚类性能;最后,在数据集UCI和图像数据集上进行实验,并与其他经典的FCM算法进行对比.实验结果表明,该算法提高了聚类效果.Aiming at the problem that the traditional fuzzy C-means(FCM)algorithm produced a large amount of computation when dealing with high-dimensional data sets with complex structures,which led to the decline of clustering effect,we proposed a modified fuzzy clustering algorithm based on non-negative matrix factorization.Firstly,the algorithm proposed a new objective function,which was solved by alternating iterations.Secondly,in the iterative process,triangular inequalities were used to filter out samples that met the inequality conditions,and at the same time,a new membership updating formula was used to reduce the amount of calculation and improve the clustering performance.Finally,experiments were carried ou on the UCI dataset and image dataset,and compared with other classical FCM algorithms.The experimental results show that the algorithm improves the clustering effect.

关 键 词：模糊C-均值 聚类 非负矩阵分解 交替迭代 三角不等式 

分 类 号：TP391.1[自动化与计算机技术—计算机应用技术]