Fuzzy Clustering Algorithm Based On Credibility And Sample-features Biweighted Generalized Entropy

As an important part of multivariate statistical analysis and data mining algorithms,many clustering analysis methods based on different theories and methods have been proposed by researchers.Fuzzy clustering has high quality characteristics of soft clustering,so it occupies a pivotal position in the field of clustering analysis.As we all know,entropy can represent the related information between things and can be used to measure weights.Under the framework of credibility theory,further research on fuzzy clustering method by combining generalized entropy,the weights of samples and the weights of features is done in this paper.A fuzzy clustering algorithm based on credibility and sample-features biweighted generalized entropy(CSGEF-WFCM)is put forward.The main research work is as follows:(1)Firstly,a feature weighted generalized entropy method is obtained by weighting the data features and combining it with the maximum entropy theory.Then,through weighting the data features,weighting the data samples and combining them with fuzzy clustering method,a weighted fuzzy clustering method based on samples and generalized entropy feature(SGEF-WFCM)is proposed.Further more,this paper gives the objective function and clustering optimization problem of SGEF-WFCM method.Among them,the implementation of clustering optimization is conditional on probabilistic membership degree and feature weight and solved by Lagrange method.(2)On the basis of SGEF-WFCM algorithm,through introducing the credibility theory we obtain a fuzzy clustering algorithm based on credibility and sample-features biweighted generalized entropy(CSGEF-WFCM).So we can use the credibility measure to describe the membership degree of the sample points relative to each category and solve the membership normalization problem of the SGEF-WFCM algorithm.(3)By selecting artificial datasets and representative UCI datasets,this paper does experimental study on both SGEF-WFCM algorithm and CSGEF-WFCM algorithm.At the same time,the effects of the two parameters in the algorithm on the clustering results are also studied,and then compare it to other fuzzy clustering method.The experiment results not only verify the effectiveness of SGEF-WFCM algorithm and CSGEF-WFCM algorithm,but also have achieved a good clustering result.