The Research On Kernel FCM Clustering Algorithm Based On Optimal Regularization Parameters

Fuzzy C-mean(FCM)is a commonly used unsupervised clustering algorithm.The algorithm has the following shortcomings in practical applications:(1)FCM algorithm randomly selects the initial cluster center and noise data.It will lead to unstable clustering result,that is,the algorithm has ill-posed problem.Using regularization method to introduce regularization term into objective function of FCM clustering algorithm is a method to solve this problem,but how to choose the best regularization parameter Value is a difficult point.(2)FCM algorithm uses Euclidean distance to calculate the similarity of data.This method has large deviations for high-dimensional and complex-feature data identification,leading to low clustering accuracy.(3)The value of the fuzzy weight parameter of the FCM algorithm is fixed and cannot be adaptively adjusted according to the data set.The improper value of the fuzzy weight parameter will lead to a decrease in the clustering accuracy of the algorithm.In view of the above deficiencies,this paper proposes a regularization kernel FCM clustering algorithm with fuzzy weight parameter adaptation.The main improvement measures are as follows:(1)On the issue of selecting regularized parameters,we propose to use L-curve method to optimize parameters.Firstly,an iterative update formula for nuclear FCM parameters is deduced.According to the Tikhonov regularization theory,a linear minimization problem for optimizing regularization parameters is constructed.Finally,the minimization problem is solved iteratively using the L-curve method and the optimal regularization parameters are obtained.This improves the computational stability of the FCM algorithm.(2)For the insufficiency of the Euclidean distance similarity calculation method,the Gaussian kernel function with support vector machine(SVM)is introduced to map the data from the low-dimensional Euclidean space to the high-dimensional and nonlinear Hilbert space,which improves the algorithm's nonlinearity and complexity.Identification of data features.(3)Aiming at the problem of the value of fuzzy weight parameter,a dynamic adjustment formula of fuzzy weight parameter is designed.Through the formula's iterative process,the weight parameter value is adaptively and dynamically adjusted.Finally,the proposed algorithm is validated on UCI dataset.The results show that the clustering accuracy and clustering stability of the proposed algorithm are better than those of similar algorithms.The proposed algorithm is feasible.