Projection Algorithms for Non-Convex Minimization with Application to Sparse Principal Component Analysis

2014/04/16 by William W. Hager, Hager, William W., Dzung T. Phan +3 · 2 citations
Computer Science · Engineering · #FOS: Mathematics #Medical Image Segmentation Techniques #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.1404.4132

openalex publication_date 2014/04/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider concave minimization problems over non-convex sets.Optimization problems with this structure arise in sparse principal component analysis. We analyze both a gradient projection algorithm and an approximate Newton algorithm where the Hessian approximation is a multiple of the identity. Convergence results are established. In numerical experiments arising in sparse principal component analysis, it is seen that the performance of the gradient projection algorithm is very similar to that of the truncated power method and the generalized power method. In some cases, the approximate Newton algorithm with a Barzilai-Borwein (BB) Hessian approximation can be substantially faster than the other algorithms, and can converge to a better solution.

Citations

• Structured Sparse Principal Component Analysis
• Sparse Principal Component Analysis
• Atomic Decomposition by Basis Pursuit
• Least angle regression
• Generalized power method for sparse principal component analysis
• Truncated Power Method for Sparse Eigenvalue Problems

Cited by

• A Scalable and Exact Relaxation for Densest k-Subgraph via Error Bounds
• The Vertex-Attribute-Constrained Densest k-Subgraph Problem

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