Comparative Study On Sparse Principal Component Analysis

Principal Component Analysis is a commonly used data feature extraction method based on variable covariance matrix to process,compress and extract sample information.It has been widely used in many fields such as biology,medicine,machine learning and informatics.However,practical applications often face the following challenges: First,each principal component is a linear combination of the original variables and the loading coefficients are mostly non-zero,which makes it difficult to explain the meaning of the principal components;produces “wrong”results.The introduction of sparse PCA improves the application of PCA methods to the above challenges.Sparse Principal Component Analysis combines the LASSO sparsity penalty idea with the principal component analysis method to make the load coefficients sparse,so as to achieve the effect of dimensionality reduction and interpretation.At the same time,different sparsity penalties can also produce sparse principal components of different properties.According to the characteristics of each sparse principal component method,this paper summarizes them into three categories,namely the conventional sparse principal component analysis method,the sparse principal component analysis method that obtains the maximum explained variance,and the sparse principal component analysis method with orthogonal or irrelevant principal component analysis method.In particular,we selected one of the most representative methods from each category,followed by the sparse principal component analysis(SPCA)method of Zou et al.(2006),sparse PCA via regularized SVD(SPCA-r SVD)of Shen and Huang(2008)and Qi et al.'s(2013)norm selection-based sparse principal component analysis(CN-SPCA)method.The basic models and algorithms of each method are described in detail,and the aim is to compare different types of sparse PCA methods.The results of simulation study and case analysis show that the three different sparse PCA methods can extract the principal components with sparse features and improve the interpretability of the principal components.However,compared with the conventional principal component analysis method,the proportion of explained variance extracted by the three different sparse principal component analysis methods has decreased.Among them,the proportion of explained variance extracted by the SPCA-r SVD method among the three methods is always the highest,while the CN-SPCA method extracts uncorrelated sparse principal components but has a lower proportion of explained variance.The results of this study provide a certain reference for selecting a suitable sparse principal component analysis method.