Research On New Methods Of Clustering Analysis

Cluster analysis is an unsupervised learning that aims to divide the data set into several disjoint clusters?or"classes"?based on specific criteria,and thus to discover the inherent structural information in the data.The main researches of this paper are:?1?In order to improve the robustness of clustering,an improved fuzzy C-Means algorithm is proposed;?2?A new semi-supervised and avoiding saddle point clustering method is proposed.The proposed two new clustering methods are compared with experimental results to show their effectiveness."A Robust Fuzzy Clustering Method":In Fuzzy C-Means clustering?Fuzzy C-Means,FCM?,the influence of noise and outliers on clustering has not been considered,so FCM is less robust.To enhance the robustness,the smooth distance metric in FCM is changed to a non-smooth distance metric.Therefore,a robust fuzzy clustering method?Robust FCM,RFCM?is proposed.In order to solve the non-smooth optimization problem corresponding to RFCM,the framework of Majorization-Minimization?MM?is used.Through experiments on some datasets,comparing RFCM with traditional FCM algorithms shows that RFCM is more effective than FCM in some cases."A new semi-supervised and avoiding saddle point clustering method":Pairwise constraints are introduced into the spectral clustering model as weak semi-supervised information,and then a new semi-supervised avoiding saddle point clustering method?Semi-Supervised Negative Curvature Clustering,SSNC?.The?accelerated?gradient descent method can be used to solve the optimization problem corresponding to SSNC.However,since the objective function of the model of SSNC is non-convex,it is possible to converge to the saddle point instead of the local minimum point via the gradient-type method.In order to avoid the saddle point problem,this paper resorts to the random perturbed negative-curvature direction method?NEON?proposed by Xu et al.^[44].Experiments on some datasets show that compared with the kernel learning-based spectral clustering method^[46],the SSNC proposed in this paper is more effective in some cases.