Research On Robust Weighted Principal Component And Factor Clustering Method

Cluster analysis method is a very classic and effective classification method,but when there are outliers in the data or there is a high degree of correlation,the results of the traditional clustering method will be distorted.And principal components analysis and factor analysis are the methods that can handle the high correlation of the data,so the two methods are often combined with clustering analysis.However,traditional principal components clustering and factor clustering methods ignore the importance of different principal components and factors for clustering.The weighted principal components distance clustering analysis method can not only deal with the correlation of the data,but also consider the differences between different principal components on the cluster.Robust principal components and robust factor analysis can effectively resist outliers,and can deal with high correlation of the data.Therefore,this paper combines robust principal components,robust factor analysis and weighted principal components distance clustering analysis,which can not only deal with the high correlation of the data,and can effectively resist the influence of outliers,and can take into account different principal components,differences in the importance of different factors for clustering.The research content of this paper mainly includes the following two aspects:1.Based on the robust principal components clustering analysis method and the weighted principal components distance clustering analysis method,a feasible robust weighted principal components clustering method is proposed.The method combines the advantages of robust principal components clustering and weighted principal components distance clustering method,which can reduce the influence of outliers and consider the influence of different principal components for clustering.And at different outlier ratios,the robustness of the method is proved,and the performance effect of the proposed method is further proved by numerical simulation and case analysis.2.Based on the robust factor analysis and weighted principal components distance clustering method,a robust weighted factor clustering method is proposed,which takes the FAST-MCD method as the robust estimation method,and considers the differences between different factors themselves.And through numerical simulation,the effectiveness of the proposed method is proved under different outlier ratios.