A Robust Sparse Principle Component Analysis Based On DDC Algorithm And Its Empirical Study

Dimensionality reduction is a common step in multivariate statistical analysis.Principal component analysis(PCA),an effective dimensionality reduction method,is widely used in various fields.However,the classical principal component method has two disadvantages: first,the classical PCA tends to obtain a wrong result(that is,wrong loading vectors and score matrix)when there are outliers in samples;second,the loadings of each PC are not equal to zero.In most cases,the(absolute values of)loadings of secondary variables are close to those of primary variables,accounting for the weakened interpretability of PCs.Moreover,traditional robust PCAs achieve robustness by deleting outliers.This is inappropriate for those outliers who have just a few outlying cells.In view of the above points,this paper proposed a robust sparse PCA DDCSPCA with DDC(Detecting Detecting Cell)algorithm as the main robust method.First of all,simulation experiments were conducted to prove the method's robustness against rowwise outliers and its better robustness performance with cellwise outliers in the dataset,compared with traditional robust PCA.The method also maintained its sparsity in all simulations.Secondly,two empirical studies with a group of glass sample data and a group of financial index data of Chinese listed companies accordingly were conducted.The result of the former one proved that DDCSPCA is more robust than the two traditional robust PCAs dealing with cellwise outlying data,while in the latter one three realistic and sparse PC loading vectors were drawn through DDCSPCA,and a comprehensive evaluation based on the robust PC scores and the comprehensive score ended up successful.The results showed that DDCSPCA is robust against outliers in data,thus tends to obtain practical and robust sparse loading vectors,which is essential for a successful comprehensive evaluation.Furthermore,since DDC is a main robustness tool in DDCSPCA,the method is far more robust than previous robust PCAs with cellwise contaminated data.