An Alternating Manifold Proximal Gradient Method for Sparse PCA and Sparse CCA
Sparse principal component analysis (PCA) and sparse canonical correlation analysis (CCA) are two essential techniques from high-dimensional statistics and machine learning for analyzing large-scale data. Both problems can be formulated as an optimization problem with nonsmooth objective and nonconvex constraints. Since non-smoothness and nonconvexity bring numerical difficulties, most algorithms suggested in the literature either solve some relaxations or are heuristic and lack convergence guarantees. In this paper, we propose a new alternating manifold proximal gradient method to solve these two high-dimensional problems and provide a unified convergence analysis. Numerical experiment results are reported to demonstrate the advantages of our algorithm.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Robust Low-rank Matrix Completion via an Alternating Manifold Proximal Gradient Continuation Method
Robust low-rank matrix completion (RMC), or robust principal component analysis with partially observed data, has been studied extensively for computer vision, signal processing and machine learning applications. This pr…
Low-Rank Matrix CompletionMatrix CompletionRiemannian optimizationConverting ADMM to a Proximal Gradient for Efficient Sparse Estimation
In sparse estimation, such as fused lasso and convex clustering, we apply either the proximal gradient method or the alternating direction method of multipliers (ADMM) to solve the problem. It takes time to include matri…
ClusteringA Manifold Proximal Linear Method for Sparse Spectral Clustering with Application to Single-Cell RNA Sequencing Data Analysis
Spectral clustering is one of the fundamental unsupervised learning methods widely used in data analysis. Sparse spectral clustering (SSC) imposes sparsity to the spectral clustering and it improves the interpretability …
ClusteringArray SAR 3D Sparse Imaging Based on Regularization by Denoising Under Few Observed Data
Array synthetic aperture radar (SAR) three-dimensional (3D) imaging can obtain 3D information of the target region, which is widely used in environmental monitoring and scattering information measurement. In recent years…
compressed sensingDenoisingAn Efficient Alternating Algorithm for ReLU-based Symmetric Matrix Decomposition
Symmetric matrix decomposition is an active research area in machine learning. This paper focuses on exploiting the low-rank structure of non-negative and sparse symmetric matrices via the rectified linear unit (ReLU) ac…