000			01432nam a2200169 a 4500
005			20260901030417.0
008			250101s2019 xx o 000 0 eng d
100	1		_aLuca Bagnato
245	1	0	_aUnconstrained representation of orthogonal matrices with application to common principle components
264		1	_barXiv _c2019
336			_atext
338			_aonline resource
520			_aMany 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		_aOpen access — freely available to read.
856	4	0	_uhttps://arxiv.org/pdf/1906.00587v1 _yRead the full paper (PDF)
942			_cERES
999			_c717 _d717