A Matlab solver for preconditioned Riemannian optimization methods on product manifolds.
This solver is applicable for the following optimization problem
min f(U,V), s. t. (U,V) \in M = St_{M_1}(p,m) \times St_{M_2}(p,n),
where St_{M_1}(p,m) := {U in \mathbb{R}^{m\times p}:\ U^T M_1 U=I_p} is the generalized Stiefel Manifold.
The search space M is endowed with a preconditioned metric
g_(U,V) (xi,eta)=< xi_1 , B11(U,V) eta_1 B12(U,V) > + < xi_2, B21(U,V) eta_2 B22(U,V) > for xi,eta in T_(U,V) M,
where B11(U,V) is an m-by-m matrix, B12(U,V) is an p-by-p matrix, B21(U,V) is an n-by-n matrix, B22(U,V) is an p-by-p matrix.
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Make sure you have installed the package Manopt.
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Run
test_CCA.mfor Canonical correlation analysis -
Run
test_SVD.mfor truncated singular value decomposition
Bin Gao, Renfeng Peng, Ya-xiang Yuan
- Renfeng Peng (AMSS, China)
Copyright (C) 2023, Bin Gao, Renfeng Peng, Ya-xiang Yuan
This solver is based on a third-party package Manopt.
This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.
You should have received a copy of the GNU General Public License along with this program. If not, see http://www.gnu.org/licenses/