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An Unbalanced Optimal Transport-Based Approach for Robust Dictionary Learning.

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    This study introduces a robust dictionary learning (DL) model using unbalanced optimal transport (UOT) to overcome outlier sensitivity. The novel approach enhances data structure analysis and outlier resilience in machine learning applications.

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    Area of Science:

    • Machine Learning
    • Signal Processing
    • Data Science

    Background:

    • Dictionary learning (DL) is crucial for feature extraction but sensitive to outliers.
    • Existing robust DL methods using Wasserstein distance have limitations.

    Purpose of the Study:

    • Introduce a novel robust DL model based on unbalanced optimal transport (UOT).
    • Develop a computationally tractable hybrid block coordinate descent (BCD) algorithm.
    • Demonstrate strong resilience to outliers and leverage data structure.

    Main Methods:

    • Developed a new DL model utilizing unbalanced optimal transport (UOT).
    • Designed a hybrid block coordinate descent (BCD) algorithm tailored for the UOT-DL model.
    • Established algorithm convergence without requiring Lipschitz smooth conditions.

    Main Results:

    • The proposed UOT-based DL model shows superior outlier resilience compared to existing methods.
    • The hybrid BCD algorithm is computationally tractable and effective.
    • Theoretical convergence is proven without the Lipschitz smooth condition.

    Conclusions:

    • The novel UOT-based DL model offers robust feature extraction.
    • The developed BCD algorithm provides an efficient solution for robust DL.
    • The method is validated on diverse datasets, including hyperspectral images (HSIs).