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Volume 10 Issue 6
Jun.  2023

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2023  >  10(6): 1388-1406
F. H. Bi, X. Luo, B. Shen, H. L. Dong, and  Z. D. Wang,  “Proximal alternating-direction-method-of-multipliers-incorporated nonnegative latent factor analysis,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 6, pp. 1388–1406, Jun. 2023. doi: 10.1109/JAS.2023.123474
Citation: F. H. Bi, X. Luo, B. Shen, H. L. Dong, and  Z. D. Wang,  “Proximal alternating-direction-method-of-multipliers-incorporated nonnegative latent factor analysis,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 6, pp. 1388–1406, Jun. 2023. doi: 10.1109/JAS.2023.123474
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Proximal Alternating-Direction-Method-of- Multipliers-Incorporated Nonnegative Latent Factor Analysis

doi: 10.1109/JAS.2023.123474
Funds:  This work was supported by the National Natural Science Foundation of China (62272078, U21A2019), the Hainan Province Science and Technology Special Fund of China (ZDYF2022SHFZ105), and the CAAI-Huawei MindSpore Open Fund (CAAIXSJLJJ-2021-035A)
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    Abstract

  • High-dimensional and incomplete (HDI) data subject to the nonnegativity constraints are commonly encountered in a big data-related application concerning the interactions among numerous nodes. A nonnegative latent factor analysis (NLFA) model can perform representation learning to HDI data efficiently. However, existing NLFA models suffer from either slow convergence rate or representation accuracy loss. To address this issue, this paper proposes a proximal alternating-direction-method-of-multipliers-based nonnegative latent factor analysis (PAN) model with two-fold ideas: 1) adopting the principle of alternating-direction-method-of-multipliers to implement an efficient learning scheme for fast convergence and high computational efficiency; and 2) incorporating the proximal regularization into the learning scheme to suppress the optimization fluctuation for high representation learning accuracy to HDI data. Theoretical studies verify that PAN converges to a Karush-Kuhn-Tucker (KKT) stationary point of its nonnegativity-constrained learning objective with its learning scheme. Experimental results on eight HDI matrices from real applications demonstrate that the proposed PAN model outperforms several state-of-the-art models in both estimation accuracy for missing data of an HDI matrix and computational efficiency.

     

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    Highlights

    • A proximal ADMM-based nonnegative latent factor analysis (PAN) model is proposed. It adopts the following two-fold ideas: 1) adopting the ADMM principle to implement an efficient learning scheme for fast convergence and high computational efficiency; and 2) incorporating the proximal regularization into the learning scheme to suppress the optimization fluctuation for high representation learning accuracy to an HDI matrix
    • Detailed algorithm design and analysis for a PAN model are presented
    • Theoretical proof of PAN’s convergence is given. The proof indicates that a PAN model converges to a Karush-Kuhn-Tucker (KKT) stationary point of its constrained learning objective with its ADMM-incorporated learning scheme

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