Abstract: Principal component analysis (PCA) is widely used in many areas of scientific discoveries due to its dimension reduction and orthogonality of each principal component. However, The principal components are often the linear combinations of all the predictors and it is hard to achieve good model interpretability. In this paper, sparse approximation of the loadings of the principal components is induced by elastic net methods, and we established the sparse approximation principal component analysis (sPCA) algorithm. The sPCA not only keeps the advantages of original PCA, but also can greatly improve the model interpretability due to the sparsity of the loadings.

Key words: Principal component analysis, Sparse principal component analysis, Elastic net, Model interpretability