Title: Comparing Grassmann manifold optimization and sequential candidate set algorithm in a principal fitted component model
Authors: Chaeyoung Lee - Ewha Womans University (Korea, South) [presenting]
Jae Keun Yoo - Ewha Womans University (Korea, South)
Abstract: The parameter estimation by Grassmann manifold optimization and the sequential candidate set algorithm are compared in a structured principal-fitted component model. The PFC model is a model-based dimension reduction method which can be divided into three distinct variations according to the forms of the covariance matrix of a random error. The structured PFC model, which is our main focus, has an extended form of the simplest covariance matrix. The extension relieves the limit that occurs due to the simple form of the covariance matrix of a random error. However, the structured PFC model does not have a closed form for parameter estimation in dimension reduction. Therefore, the estimation needs to be done numerically. The computation can be done through Grassmann manifold optimization and sequential candidate set algorithm. We conducted several numerical simulations for comparison. First, we compared the determined dimension obtained from the sequential dimension. In addition, we calculated trace correlation values to compare the accuracy of the estimated basis to conduct dimension reduction. From the simulation results, we could conclude that while Grassmann manifold optimization outperforms the sequential candidate set algorithm in dimension determination, the sequential candidate set algorithm is better in basis estimation for dimension reduction. In other words, there is no optimal method that shows great performance in both aspects.