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    This study introduces a novel geodesic basis function neural network with subclass extension learning (GBFNN-ScE) to overcome error back-propagation challenges in radial basis function networks. Experiments show GBFNN-ScE achieves superior recognition performance and data separability.

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    Area of Science:

    • Artificial Intelligence
    • Machine Learning
    • Neural Networks

    Background:

    • Existing radial basis function neural networks (RBFNNs) face difficulties with error back-propagation, causing inconsistencies between learning and recognition.
    • This limitation hinders the effective training and performance of RBFNNs in complex classification tasks.

    Purpose of the Study:

    • To propose a novel neural network architecture, the geodesic basis function neural network with subclass extension learning (GBFNN-ScE), designed to address error back-propagation issues.
    • To introduce a new measure, the geodesic basis function (GBF), utilizing geodetic distance on manifolds for improved sample response and error propagation.
    • To enhance classification robustness and data separability through a subclass extension (ScE) learning strategy.

    Main Methods:

    • Introduction of the geodesic basis function (GBF) defined by geodetic distance on manifolds, specifically using a pruned gamma encoding cosine function for hyperspherical manifolds.
    • Development of a lossless information preprocessing technique, nonnegative unit hyperspherical crown (NUHC) mapping, to project samples onto the GBF support set.
    • Implementation of the subclass extension (ScE) learning strategy to improve the differential expression of data labels within classes and network robustness.

    Main Results:

    • The proposed GBFNN-ScE architecture successfully enables error back-propagation through its specialized GBF construction.
    • NUHC mapping effectively prepares samples for processing by the GBF hidden layer.
    • Theoretical analysis confirms that ScE learning enhances data separability, and experimental results demonstrate superior recognition performance compared to existing methods.
    • Ablation studies validate the significant contribution of GBFNN-ScE's core components to its overall performance.

    Conclusions:

    • The GBFNN-ScE offers a significant advancement over traditional RBFNNs by resolving error back-propagation limitations.
    • The novel GBF and ScE learning strategy contribute to improved classification accuracy, robustness, and data separability.
    • The proposed method shows strong potential for enhancing recognition tasks in various machine learning applications.