A constrained singular value decomposition method that integrates sparsity and orthogonality

• DOI: 10.1371/journal.pone.0211463
• Publication Date: 2019-03-13T17:37:57Z
• Authors: Vincent Guillemot; Derek Beaton; Arnaud Gloaguen; Tommy Löfstedt; Brian Levine; Nicolas Raymond; Arthur Tenenhaus; Hervé Abdi
• Keywords: Orthogonality; Singular value

We propose a new sparsification method for the singular value decomposition—called constrained decomposition (CSVD)—that can incorporate multiple constraints such as and orthogonality left right vectors. The CSVD combine different because it implements each constraint projection onto convex set, integrates these projections intersection of sets. show that, with appropriate constants, algorithm is guaranteed to converge stable point. also analyze convergence an efficient specific case balls defined by norms L1 L2. illustrate compare standard non-orthogonal related with: 1) simulated example, 2) small set face images (corresponding configuration number variables much larger than observations), 3) psychometric application large observations variables. companion R-package, csvd, that algorithms described in this paper, along reproducible examples, are available download from https://github.com/vguillemot/csvd.