一种基于神经网络的广义熵模糊聚类算法

以模糊聚类为基础，将广义熵引入到模糊聚类的目标函数中，提出一种基于模糊熵的模糊聚类的统一形式，即广义熵模糊聚类模型；利用增广拉格朗日求解方法，以及Hopfield神经网络和复突触神经网络解决了基于广义熵的目标函数的优化问题，提出了基于神经网络的广义熵模糊聚类算法，表明了使用神经网络求解的收敛性；同时，给出一种用于确定增广拉格朗日乘子的迭代方法.实验中选取人工生成数据集和UCI标准数据集对提出的算法进行了实验研究，并与常用的聚类算法进行了性能比较.

A Fuzzy Clustering Algorithm with Generalized Entropy Based on Neural Network

Based on fuzzy clustering,an unified form is presented for fuzzy clustering algorithm based on fuzzy entro-py by introducing the generalized fuzzy entropy into objective function of fuzzy clustering,namely generalized entropy’s fuzzy clustering model.Optimization problem for generalized entropy’s objective function is solved using Hopfield neural network and multiple synapses based on augmented Lagrange method.After that,the generalized entropy’s fuzzy clustering algorithm based on neural network is presented.And convergence of neural network is shown.At the same time,iterative method is given to determine Lagrange multipliers.In experiments,a synthetic data set and some standard UCI data sets are chosen to conduct some experimental studies.And clustering performance is compared with commonly used clustering algo-rithms.