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You searched for subject:( Orthogonality constraint). Showing records 1 – 2 of 2 total matches.

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1. Khatavkar, Rohan. Sparse and orthogonal singular value decomposition.

Degree: MS, Department of Statistics, 2013, Kansas State University

The singular value decomposition (SVD) is a commonly used matrix factorization technique in statistics, and it is very e ective in revealing many low-dimensional structures in a noisy data matrix or a coe cient matrix of a statistical model. In particular, it is often desirable to obtain a sparse SVD, i.e., only a few singular values are nonzero and their corresponding left and right singular vectors are also sparse. However, in several existing methods for sparse SVD estimation, the exact orthogonality among the singular vectors are often sacri ced due to the di culty in incorporating the non-convex orthogonality constraint in sparse estimation. Imposing orthogonality in addition to sparsity, albeit di cult, can be critical in restricting and guiding the search of the sparsity pattern and facilitating model interpretation. Combining the ideas of penalized regression and Bregman iterative methods, we propose two methods that strive to achieve the dual goal of sparse and orthogonal SVD estimation, in the general framework of high dimensional multivariate regression. We set up simulation studies to demonstrate the e cacy of the proposed methods. Advisors/Committee Members: Kun Chen.

Subjects/Keywords: Bregman iteration; Multivariate regression; Orthogonality constraint; Singular value decomposition; Sparsity; Statistics (0463)

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Khatavkar, R. (2013). Sparse and orthogonal singular value decomposition. (Masters Thesis). Kansas State University. Retrieved from http://hdl.handle.net/2097/15992

Chicago Manual of Style (16th Edition):

Khatavkar, Rohan. “Sparse and orthogonal singular value decomposition.” 2013. Masters Thesis, Kansas State University. Accessed July 10, 2020. http://hdl.handle.net/2097/15992.

MLA Handbook (7th Edition):

Khatavkar, Rohan. “Sparse and orthogonal singular value decomposition.” 2013. Web. 10 Jul 2020.

Vancouver:

Khatavkar R. Sparse and orthogonal singular value decomposition. [Internet] [Masters thesis]. Kansas State University; 2013. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2097/15992.

Council of Science Editors:

Khatavkar R. Sparse and orthogonal singular value decomposition. [Masters Thesis]. Kansas State University; 2013. Available from: http://hdl.handle.net/2097/15992


Université Catholique de Louvain

2. Boumal, Nicolas. Optimization and estimation on manifolds.

Degree: 2014, Université Catholique de Louvain

How to make the best decision? This general concern, pervasive in both research and industry, is what optimization is all about. Optimization is a field of applied mathematics concerned with making the best use—according to some quantitative criterion called the cost function—of our degrees of freedom called the variables, possibly under some constraints. Optimization problems come in various forms. We consider continuous variables with differentiable cost functions. Furthermore, and this is central to our investigation, we assume that the variables are constrained to belong to a Riemannian manifold, that is, to a smooth space. Building upon prior theory, we develop Manopt, a toolbox which considerably simplifies the use of Riemannian optimization. We apply this tool to two applications. First, we study low-rank matrix completion, which appears in recommender systems. Such systems aim at predicting which movies, books, etc. different users might appreciate, based on partial knowledge of their preferences. Second, we study synchronization of rotations. This is a central player in the reconstruction of 3D computer models of physical objects based on scans of their surface. In both cases, Riemannian optimization provides competitive, scalable and accurate algorithms. Both applications constitute estimation problems. In estimation, one wishes to determine the value of unknown parameters based on noisy measurements. We address the following fundamental question: given a noise level on the measurements, how accurately can one hope to estimate the parameters? This prompts us to further develop Cramér-Rao bounds when the parameter space is a manifold. Applied to synchronization, these bounds bring about practical implications. First, they suggest that in many nontrivial scenarios, our estimation algorithm could be optimal. Second, they reveal the defining features that make a synchronization task more or less difficult, hinting at which measurements should be acquired.

(FSA - Sciences de l)  – UCL, 2014

Advisors/Committee Members: UCL - SST/ICTM/INMA - Pôle en ingénierie mathématique, UCL - Ecole Polytechnique de Louvain, Absil, Pierre-Antoine, Blondel, Vincent, Verleysen, Michel, Van Dooren, Paul, d'Aspremont, Alexandre, Sepulchre, Rodolphe, Singer, Amit.

Subjects/Keywords: Riemannian optimization; Intrinsic Cramér-Rao bounds; Synchronization of rotations; Low-rank matrix completion; Optimization toolbox; Rank constraint; Orthogonality constraint; Estimation of rotations; Manopt

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APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Boumal, N. (2014). Optimization and estimation on manifolds. (Thesis). Université Catholique de Louvain. Retrieved from http://hdl.handle.net/2078.1/142831

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Boumal, Nicolas. “Optimization and estimation on manifolds.” 2014. Thesis, Université Catholique de Louvain. Accessed July 10, 2020. http://hdl.handle.net/2078.1/142831.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Boumal, Nicolas. “Optimization and estimation on manifolds.” 2014. Web. 10 Jul 2020.

Vancouver:

Boumal N. Optimization and estimation on manifolds. [Internet] [Thesis]. Université Catholique de Louvain; 2014. [cited 2020 Jul 10]. Available from: http://hdl.handle.net/2078.1/142831.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Boumal N. Optimization and estimation on manifolds. [Thesis]. Université Catholique de Louvain; 2014. Available from: http://hdl.handle.net/2078.1/142831

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.