Unconstrained representation of orthogonal matrices with application to common principle components (Record no. 717)

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fixed length control field 250101s2019 xx o 000 0 eng d
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Luca Bagnato
245 10 - TITLE STATEMENT
Title Unconstrained representation of orthogonal matrices with application to common principle components
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Name of producer, publisher, distributor, manufacturer arXiv
Date of production, publication, distribution, manufacture, or copyright notice 2019
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Content type term text
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Summary, etc. Many statistical problems involve the estimation of a $\left(d\times d\right)$ orthogonal matrix $\textbf{Q}$. Such an estimation is often challenging due to the orthonormality constraints on $\textbf{Q}$. To cope with this problem, we propose a very simple decomposition for orthogonal matrices which we abbreviate as PLR decomposition. It produces a one-to-one correspondence between $\textbf{Q}$ and a $\left(d\times d\right)$ unit lower triangular matrix $\textbf{L}$ whose $d\left(d-1\right)/2$ entries below the diagonal are unconstrained real values. Once the decomposition is applied, regardless of the objective function under consideration, we can use any classical unconstrained optimization method to find the minimum (or maximum) of the objective function with respect to $\textbf{L}$. For illustrative purposes, we apply the PLR decomposition in common principle components analysis (CP
506 0# - RESTRICTIONS ON ACCESS NOTE
Terms governing access Open access — freely available to read.
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Uniform Resource Identifier <a href="https://arxiv.org/pdf/1906.00587v1">https://arxiv.org/pdf/1906.00587v1</a>
Link text Read the full paper (PDF)
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      Available online General Yegates University Library Yegates University Library Science and Computing 09/01/2026   YGE000978 09/01/2026 https://arxiv.org/pdf/1906.00587v1 09/01/2026 Research paper — read online