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Volume 12 Issue 12
Dec.  2025

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2025  >  12(12): 2399-2426
Q. Hu, H. Wu, and X. Luo, “A comprehensive review of parallel optimization algorithms for high-dimensional and incomplete matrix factorization,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 12, pp. 2399–2426, Dec. 2025. doi: 10.1109/JAS.2025.125774
Citation: Q. Hu, H. Wu, and X. Luo, “A comprehensive review of parallel optimization algorithms for high-dimensional and incomplete matrix factorization,” IEEE/CAA J. Autom. Sinica, vol. 12, no. 12, pp. 2399–2426, Dec. 2025. doi: 10.1109/JAS.2025.125774
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A Comprehensive Review of Parallel Optimization Algorithms for High-Dimensional and Incomplete Matrix Factorization

doi: 10.1109/JAS.2025.125774
Funds:  This work is supported in part by the National Key Research and Development Program of China (2024YFF0908200), the National Natural Science Foundation of China (62302402, 62272078), the Chongqing Natural Science Foundation (CSTB2024TIAD-KPX0018, CSTB2023NSCO-LZX006), and the Southwest University Graduate Research Innovation Project (SWUB24050)
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    Abstract
  • High-dimensional and incomplete (HDI) matrices are commonly encountered in various big data-related applications for illustrating the complex interactions among numerous entities, like the user-item interactions in a commercial recommender system or the user-user interactions in a social network services system. The factorization of such an HDI matrix can embed the involved entities into the low-dimensional feature space for acquiring their principal representation, which is a vital task in various application scenes and is often established through the Latent Factor Analysis (LFA). Nevertheless, an HDI matrix can be huge when the corresponding application explodes to involve millions of users, items, or other interactive nodes. In this case, a parallel optimization algorithm is desired for raising the scalability and time efficiency of an LFA model. This paper provides a comprehensive review of the existing parallel optimization algorithms for the LFA model. Specifically, it performs: 1) discussion and summary of these algorithms based on computing architecture and mode, 2) empirical studies of representative models, and 3) summary of the current challenges and future directions in this domain. This survey aims to offer an exhaustive review of Parallel Optimization Algorithms for High-Dimensional and Incomplete Matrix Factorization, thereby fostering further research in this field.

     

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