Orthonormally Constrained Optimization with Application to Regularized PCA

• Activity Number: 136
• Type: Contributed
• Date/Time: Monday, August 2, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Trevor Park*+
• Companies: University of Florida
• Keywords: maximum likelihood ; penalized likelihood ; manifold geometry ; Stiefel manifold ; Newton's method ; conjugate gradient

Abstract

Statistical models for principal component analysis and some related methods involve a matrix parameter constrained to have orthonormal columns. Regularization by optimizing a criterion function can therefore be difficult unless specialized algorithms are used. When the criterion function is continuously differentiable, efficient algorithms, based on manifold geometry, are available that remain practical for problems of moderately high dimension. The challenge of using regularization to promote sparsity is discussed.