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    Area of Science:

    • Machine Learning
    • Computational Geometry
    • Data Mining

    Background:

    • Traditional large margin classifiers stem from optimization.
    • Support vectors (SVs) can also be derived geometrically.
    • Gabriel graphs (GGs) offer a geometric approach to classification.

    Purpose of the Study:

    • To present advances in using Gabriel graphs (GGs) for binary and multiclass classification.
    • To improve the performance and efficiency of GG-based classifiers.
    • To introduce novel components for enhanced graph regularization and computation.

    Main Methods:

    • Introduced Chipclass, a hyperparameterless and optimization-less GG-based binary classifier.
    • Proposed smoother activation functions and structural SV (SSV)-centered neurons for improved classification contours.
    • Developed a new subgraph-/distance-based membership function for graph regularization.
    • Implemented a more computationally efficient GG recomputation algorithm.
    • Extended neural network architecture trainable via backpropagation or linear equations.

    Main Results:

    • Proposed methods achieved margins with low probabilities and smoother classification contours.
    • The new GG recomputation algorithm is less computationally expensive.
    • Experimental results demonstrated superior performance compared to previous GG-based classifiers.
    • The proposed method showed statistical equivalence to tree-based models.

    Conclusions:

    • The novel GG-based approach enhances binary and multiclass classification.
    • The improvements offer greater efficiency and accuracy.
    • This geometric method provides a competitive alternative to optimization-based and tree-based models.