A MATLAB software for solving optimization problems with orthogonal nonnegative constraints.
The package contains codes for optimization problems with orthogonal nonnegative constraints:
where
Applications have been solved by the solver:
- Projections onto
$\mathcal{S}^{n,k}_+$ : $\min,|X-C|F^2,,s.t.,,X\in\mathcal{S}^{n,k}+$
- Trace minimization with nonnegative orthogonality constraints:
$\min,\mathrm{Tr}(X^\top MX),,s.t.,,X\in\mathcal{S}^{n,k}_+$ - Orthogonal nonnegative matrix factorization (ONMF): $\min ,|A-XY^\top|F^2, s.t.,,X\in\mathcal{S}^{n,k}+,,,Y\in \mathbb R^{n,k}_+$
- K-indicators model: $ \min,|UY-X|F^2,, s.t.,,X\in\mathcal{S}^{n,k}+,,,|X_{i,:}|=1,,,Y^\top Y=I_k$
- Discriminative nonnegative spectral clustering
- Nonnegative principal component analysis (NPCA)
- Bo Jiang, Xiang Meng, Zaiwen Wen, Xiaochun Chen. An exact penalty approach for optimization with nonnegative orthogonality constraints
- Jiang Hu, Bo Jiang, Lin Lin, Zaiwen Wen, Yaxiang Yuan. Structured Quasi-Newton Methods for Optimization with Orthogonality Constraints. SIAM Journal on Scientific Computing, Vol. 41, No. 4, pp. A2239-A2269
- J. Hu, A. Milzarek, Z. Wen, and Y. Yuan, Adaptive quadratically regularized Newton method for Riemannian optimization, SIAM J. Matrix Anal. Appl., 39 (2018), pp. 1181-1207.
- X. Xiao, Y. Li, Z. Wen, and L. Zhang, A regularized semi-smooth Newton method with projection steps for composite convex programs, J. Sci. Comput., 76 (2016), pp. 364-389.
- J. Bolte, S. Sabach, and M. Teboulle, Proximal alternating linearized minimization for nonconvex and nonsmooth problems, Math. Program., 146 (2014), pp. 459-494.
- F. Pompili, N. Gillis, P.-A. Absil, and F. Glineur, Two algorithms for orthogonal non-negative matrix factorization with application to clustering, Neurocomputing, 141 (2014), pp. 15-25.
We hope that the package is useful for your application. If you have any bug reports or comments, please feel free to email one of the toolbox authors:
- Xiang Meng, 1700010614 at pku.edu.cn
- Bo Jiang, jiangbo at njnu.edu.cn
- Zaiwen Wen, wenzw at pku.edu.cn
>> startup
>> cd Examples
>> test_onmf