Robust Principal Component Analysis based on Purity

Robust principal component analysis has attracted widespread attention in recent years due to its good dimensionality reduction performance. However, most of the current researches identify and process noise by the statistical characteristics of the reconstruction error, while not considering the relationship between the reconstruction error and the projection variance of a data in a principal component space, moreover, they don't consider the overall distribution characteristics of the data. To solve these problems, in this paper, we proposed the robust principal component analysis based on Purity(PRPCA). First, we construct the Cauchy weighted minimization model by reconstruction error and consider the prior probability of the original data based on reconstruction error. Then, the relationship between the reconstruction error of each sample point and the sample projection variance is analyzed based on Purity. Purity describes the membership degree of sample points in principal component space and error reconstruction space so that outliers and sample points can be correctly separated based on Purity. Experimental results illustrate that the PRPCA is more effective than the other robust PCA algorithm.