The Research On Fuzzy Clustering Algorithm Based On Mahalanobis Distance

In today's information age,the amount of data generated in various fields has increased dramatically,which requires effective data analysis.Cluster analysis can be used as classification preprocessing and data mining.It is also one of the areas in machine learning where the latest algorithms are emerging quickly,and new algorithms can always be designed from a certain perspective.The classification of many things in the real world is not clear,this ambiguous classification exists in the process of understanding and identification universally.Fuzzy clustering analysis has become an important means to solve the problem of indistinct boundary division by mathematical method.Fuzzy clustering expands the membership range of samples and gives the fuzziness of clustering division,making the results of clustering analysis more consistent with the practical significance.Therefore it has become a hotspot in the field of clustering research.Fuzzy clustering algorithm based on Mahalanobis uses Mahalanobis instead of Euclidean distance in FCM.Mahalanobis is not affected by attribute dimension,which solves the problem that using Euclidean distance to cluster data related to attributes will increase the error rate.Because the fuzzy clustering algorithm based on Mahalanobis distance is widely used,its optimization problem is worth further study.This paper proposes a new initialization method for fuzzy clustering algorithm based on Mahalanobis distance,which is sensitive to the initial clustering center and converges slowly.First,in a certain range of categories,the clustering center is searched by heuristic method,and then the kmeans algorithm is used to obtain the initial clustering center.Through the test of artificial data and standard data,the result shows that the new initialization method can search the reasonable initial clustering center quickly.In order to improve the clustering accuracy of Mahalanobis distance fuzzy clustering algorithm,avoid falling into the local optimal solution,and achieve the self-adaptive clustering number,this paper constructs a measure of validity index,combining the compactness in the class with the degree of separation between classes and the clarity between classes.The new validity index contains the covariance factor of Mahalanobis distance,which can effectively guide clustering by combining fuzzy partition of data set with geometric structure.On this basis,a new initialization method combining with the new validity index into the fuzzy clustering algorithm based on Mahalanobis distance.It cooperates to use combined clustering center method,which realizes the cluster number of adaptive and makes the algorithm does not need to give the number of clusters.After through the artificial data and standard data test,the results showed that clustering accuracy of theoptimized fuzzy clustering algorithm based on Mahalanobis distance HDM-FCM is better than M-FCM which without optimization.HDM-FCM has the global optimization.Finally,the paper studies the influence of the weighted parameter values of the fuzzy clustering algorithm on the clustering results,and obtains the weighted parameter values suitable for the new algorithm HDM-FCM by means of theoretical analysis and decision selection.In addition,from the perspective of intelligent algorithm optimization,combined with particle swarm optimization algorithm(PSO),this paper makes the fuzzy clustering algorithm based on Mahalanobis distance get global optimization,which is verified by UCI data set experiment.This algorithm solves the defect that Mahalanobis distance fuzzy clustering is sensitive to initial value and easy to fall into local optimal solution.