• Journal of the Korean Data and Information Science Society
• /
• v.28 no.4
• /
• pp.721-731
• /
• 2017

In this study, principal component analysis methods using Lasso penalty are introduced. There are two popular methods that apply Lasso penalty to principal component analysis. The first method is to find an optimal vector of linear combination as the regression coefficient vector of regressing for each principal component on the original data matrix with Lasso penalty (elastic net penalty in general). The second method is to find an optimal vector of linear combination by minimizing the residual matrix obtained from approximating the original matrix by the singular value decomposition with Lasso penalty. In this study, we have reviewed two methods of principal components using Lasso penalty in detail, and shown that these methods have an advantage especially in applying to data sets that have more variables than cases. Also, these methods are compared in an application to a real data set using R program. More specifically, these methods are applied to the crime data in Ahamad (1967), which has more variables than cases.