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    Area of Science:

    • Machine Learning
    • Computer Vision
    • Signal Processing
    • Data Mining
    • Pattern Recognition

    Background:

    • Incomplete tensor data recovery is crucial in various fields.
    • Low-rank tensor factorization is a common approach.
    • Traditional methods require pre-defined tensor ranks, limiting practical use.

    Purpose of the Study:

    • To develop an adaptive algorithm for accurate and efficient tensor completion.
    • To overcome the limitations of pre-defined tensor ranks in existing methods.

    Main Methods:

    • An adaptive algorithm based on sequentially truncated higher order singular value decomposition (ST-HOSVD) for low-rank approximation.
    • Utilizing adaptive ST-HOSVD and an average operator for tensors with missing data.
    • Convergence analysis of the proposed algorithm.

    Main Results:

    • The proposed method achieves higher accuracy in recovering missing tensor data.
    • Experimental results demonstrate improved running time compared to state-of-the-art methods.
    • Validation on 14 image and three video datasets.

    Conclusions:

    • The adaptive ST-HOSVD-based algorithm effectively addresses the challenge of incomplete tensor data.
    • The method offers a more practical and efficient solution for real-world applications.
    • Outperforms existing techniques in both speed and accuracy.