An iterative coordinate descent algorithm to compute sparse low-rank approximations

Abstract

In this paper, we describe a new algorithm to build a few sparse principal components from a given data matrix. Our approach does not explicitly create the covariance matrix of the data and can be viewed as an extension of the Kogbetliantz algorithm to build an approximate singular value decomposition for a few principal components. We show the performance of the proposed algorithm to recover sparse principal components on various datasets from the literature and perform dimensionality reduction for classification applications.

References in corpus (10)

• Generalized power method for sparse principal component analysis
• On the Computational Intractability of Exact and Approximate Dictionary Learning
• Sparse Generalized Eigenvalue Problem via Smooth Optimization
• Orthogonal Sparse PCA and Covariance Estimation via Procrustes Reformulation
• Learning Fast Sparsifying Transforms
• A Dictionary-Based Generalization of Robust PCA Part II: Applications to Hyperspectral Demixing
• A Dictionary-Based Generalization of Robust PCA with Applications to Target Localization in Hyperspectral Imaging
• Multi-Rank Sparse and Functional PCA: Manifold Optimization and Iterative Deflation Techniques
• Constructing fast approximate eigenspaces with application to the fast graph Fourier transforms
• An iterative Jacobi-like algorithm to compute a few sparse approximate eigenvectors