This repository contains a MATLAB implementation of the BM-Global algorithm for nuclear-norm regularized matrix optimization problems.
Details of the algorithm can be found in the following paper:
Ching-pei Lee, Ling Liang, Tianyun Tang, and Kim-Chuan Toh, Accelerating Nuclear-Norm Regularized Low-Rank Matrix Optimization Through Burer-Monteiro Decomposition. Journal of Machine Learning Research, 2024.
This repository includes implementations for the nuclear-norm-regularized matrix completion problem and the reformulated nuclear-norm-regularized QSDP problem discussed and evaluated in the above paper.
The subproblem solver for the matrix completion problem is the PolyMF-SS algorithm, as presented in the following paper (implementation provided by its first author):
Po-Wei Wang, Chun-Liang Li, and J. Kolter, Polynomial Optimization Methods for Matrix Factorization. Proceedings of the AAAI Conference on Artificial Intelligence, 2017.
The subproblem solver for the QSDP problem is the trust-region algorithm available in the Manopt package.
To compile the code, you will need MATLAB and GCC (or another C++ compiler compatible with MATLAB).
The implementation for the matrix completion problem is located in the MF folder.
To compile the code, navigate to this folder in MATLAB and run install.m.
The implementation for the QSDP problem is located in the EDME folder.
To run the code, download the Manopt package and extract it into the EDME/manopt folder.
If the precompiled files are not compatible with your system, navigate to EDME/solvers/mexfun/ and run make.m to recompile the necessary C++ code.
To use the matrix completion implementation, run MF/startup.m first.
A script for testing the package on the ml100k dataset is provided in MF/test_ml100k.m.
For the QSDP implementation, a script for testing the package on a small RKE dataset is provided in EDME/test_rke.m.
If you are using a C++ compiler other than g++, you can modify the compilation scripts in MF/cppcode/make.m and EDME/solvers/mexfun/make.m to specify the compiler. After modifying the scripts, run them to recompile the code.