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Deep Neural Networks for Image-Based Dietary Assessment
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Dynamic Moore-Penrose Inversion With Unknown Derivatives: Gradient Neural Network Approach.

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    Summary

    A new gradient-based neural network (GNN) method efficiently computes dynamic Moore-Penrose inverses (DMPIs) without needing matrix derivatives. This approach offers superior real-time performance compared to existing methods.

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    Area of Science:

    • Numerical Analysis
    • Computational Mathematics
    • Neural Networks

    Background:

    • Calculating dynamic Moore-Penrose inverses (DMPIs) in real-time is difficult due to matrix time-variation.
    • Existing methods like zeroing neural networks (ZNNs) require continuous matrix derivative availability, which is often impractical or noisy.
    • Traditional numerical techniques are inefficient for dynamic inverse computations.

    Purpose of the Study:

    • To introduce a novel gradient-based neural network (GNN) method for computing DMPIs.
    • To develop a method that does not require the time derivative of the dynamic matrix.
    • To achieve finite-time convergence for DMPI calculation.

    Main Methods:

    • A gradient-based neural network (GNN) model is proposed for DMPI computation.
    • The GNN avoids the need for real-time matrix time derivatives.
    • A large parameter setting is used to maintain finite-time convergence in the presence of noise.

    Main Results:

    • The proposed GNN method successfully computes DMPIs.
    • The neural state matrix of the GNN converges to the theoretical DMPI in finite time.
    • The GNN method demonstrates robustness against additive noise.

    Conclusions:

    • The novel GNN method provides an effective and superior alternative for real-time DMPI computation.
    • The GNN method overcomes the limitations of ZNNs by not requiring matrix derivatives.
    • The proposed approach is efficient and robust, particularly in noisy environments.