Code for Positive Semidefinite Matrix Factorization (PSDMF)
Matlab code is available here (click this link)
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.
- 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]
- D. Lahat and C. Févotte. Positive semidefinite matrix factorization based on truncated Wirtinger flow. EUSIPCO, Amsterdam, The Netherlands, January 2021. Virtual format. [paper]
- 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).
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