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In a three-phase circuit, line loss is an indicator of energy dissipated as heat due to the resistance of transmission lines. To address this, incorporating transformers into the system—a step-up transformer at the source and a step-down transformer at the load—is a strategic solution. Two three-phase transformers are introduced to improve this.
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The vertical distance between the actual value of y and the estimated value of y. In other words, it measures the vertical distance between the actual data point and the predicted point on the line
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Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
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Sparse Additive Machine With the Correntropy-Induced Loss.

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    We introduce a robust classification method, Sparse Additive Machines with correntropy-induced loss (CSAM), to improve high-dimensional data analysis. CSAM effectively handles outliers, enhancing variable selection and classification accuracy.

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    Area of Science:

    • Machine Learning
    • Statistical Learning Theory

    Background:

    • Sparse Additive Machines (SAMs) offer flexibility and interpretability for high-dimensional data.
    • Existing SAM methods struggle with outliers due to unbounded or nonsmooth loss functions.

    Purpose of the Study:

    • To develop a robust classification method for high-dimensional data that is resilient to outliers.
    • To enhance the performance of Sparse Additive Machines in the presence of noisy data.

    Main Methods:

    • Integrating correntropy-induced loss (C-loss) into additive machines.
    • Utilizing a data-dependent hypothesis space and a weighted -norm regularizer.
    • Employing novel error decomposition and concentration estimation for theoretical analysis.

    Main Results:

    • Theoretical generalization error bounds and convergence rates are established under specific parameter conditions.
    • Variable selection consistency is theoretically guaranteed.
    • Experimental results demonstrate superior effectiveness and robustness compared to existing methods.

    Conclusions:

    • The proposed CSAM method offers a robust and effective solution for classification and variable selection in high-dimensional, outlier-prone datasets.
    • CSAM advances the application of additive machines in challenging real-world scenarios.