This Matlab code provides implementations of the PSDMF algorithms described in the following papers. The key idea is that each subproblem is updated based on a phase retrieval or affine rank minimization algorithm.

1. D. Lahat, Y. Lang, V. Y. F. Tan, and C. Févotte. Positive Semidefinite Matrix Factorization: A Connection with Phase Retrieval and Affine Rank Minimization. IEEE Transactions on Signal Processing, Vol. 69, 2021, pp. 3059--3074. [preprint] [paper]
2. D. Lahat and C. Févotte. Positive semidefinite matrix factorization based on truncated Wirtinger flow. EUSIPCO, Amsterdam, The Netherlands, January 2021. Virtual format. [paper]
3. D. Lahat and C. Févotte. Positive semidefinite matrix factorization: a link to phase retrieval and a block gradient algorithm. ICASSP, Barcelona, Spain, May 2020. Virtual format. [paper].

Additional PSDMF algorithms and links to related code can be found in:

• Vandaele, Arnaud, François Glineur, and Nicolas Gillis. "Algorithms for positive semidefinite factorization." Computational Optimization and Applications 71, no. 1 (2018): 193-219.
• Vandaele et al.'s paper presents PSDMF algorithms in which each subproblem is updated based on coordinate descent (CD) or projected gradient descent (PGM).
• Glasser, I., Sweke, R., Pancotti, N., Eisert, J. and Cirac, I., 2019. Expressive power of tensor-network factorizations for probabilistic modeling. Advances in Neural Information Processing Systems, 32, pp.1498-1510.
• Stark, Cyril. "Recommender systems inspired by the structure of quantum theory." arXiv preprint arXiv:1601.06035 (2016).