Matlab ADMM code to compute some norm-minimizing generalized inverses. Written for the following two-part paper series by Ivan Dokmanić and Rémi Gribonval:
- Beyond Moore-Penrose, Part I: Generalized Inverses that Minimize Matrix Norms
- Beyond Moore-Penrose, Part II: The Sparse Pseudoinverse
| Filename | Description |
|---|---|
| ginvadmm.m | (Linearized) ADMM for generalized inverse computation |
| Filename | Description |
|---|---|
| prox_l1.m | Proximal operator for the l1 entrywise norm |
| prox_l1l1.m | Proximal operator for the l1->l1 induced norm |
| prox_l1l2.m | Proximal operator for the l1->l2 induced norm |
| prox_row21.m | Proximal operator for the (2,1)-rowwise mixed norm |
| proj_col21.m | Projection onto the norm ball of the (2,1)-columnwise mixed norm |
For more details about the relevant definitions see the above two papers. The proximal mapping for the l1->l1 induced norm uses a projection operator proposed in the following paper:
Quattoni, A., Carreras, X., Collins, M., & Darrell, T. (2009). An Efficient Projection for
$\ell_{1,\infty}$ Regularization (pp. 857–864). Presented at ICML 2009. http://doi.org/10.1145/1553374.1553484
The associated C (MEX) implemention (by Quattoni et al.) is in projL1Inf.c. It should be MEX-compiled in Matlab on the target platform.
| Filename | Description |
|---|---|
| Example_FrobeniusSpinv.m | Creates the figures related to the Frobenius norm of the Moore-Penrose and sparse pseudoinverses |