title: Principal Component Analysis With Sparse Fused Loadings.
abstract: In this article, we propose a new method for principal component analysis (PCA), whose main objective is to capture natural "blocking" structures in the variables. Further, the method, beyond selecting different variables for different components, also encourages the loadings of highly correlated variables to have the same magnitude. These two features often help in interpreting the principal components. To achieve these goals, a fusion penalty is introduced and the resulting optimization problem solved by an alternating block optimization algorithm. The method is applied to a number of simulated and real datasets and it is shown that it achieves the stated objectives. The supplemental materials for this article are available online.
authors: Department of Statistics, University of Michigan, 269 West Hall, 1085 South University Avenue, Ann Arbor, MI 48109-1107.
authors: Jian
authors: J
authors: Guo
authors: Marshall School of Business, University of Southern California, Los Angeles, CA 90089-0809.
authors: Gareth
authors: G
authors: James
authors: University of Michigan, 459 West Hall, 1085 South University Avenue, Ann Arbor, MI 48109-1107.
authors: Elizaveta
authors: E
authors: Levina
authors: University of Michigan, 459 West Hall, 1085 South University Avenue, Ann Arbor, MI 48109-1107.
authors: George
authors: G
authors: Michailidis
authors: University of Michigan, 459 West Hall, 1085 South University Avenue, Ann Arbor, MI 48109-1107.
authors: Ji
authors: J
authors: Zhu
keywords: Fusion penalty; Local quadratic approximation; Sparsity; Variable selection