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A function's graph can be modified by changing its position or size without altering its overall shape. These transformations allow the graph to be moved across the coordinate plane while preserving its pattern and structure. One of the most common transformations is shifting, which repositions the graph without distorting it.When the output of a function is adjusted by adding or subtracting a constant, the graph shifts vertically. A positive value moves the graph upward, while a negative value...
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Extreme Learning Machine With Affine Transformation Inputs in an Activation Function.

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    A new Affine Transformation-Extreme Learning Machine (AT-ELM) improves generalization by ensuring uniform hidden layer outputs. This enhanced ELM algorithm shows superior performance in various regression and recognition tasks.

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    Area of Science:

    • Machine Learning
    • Artificial Intelligence
    • Neural Networks

    Background:

    • Extreme Learning Machine (ELM) offers fast learning and good generalization.
    • A key limitation of ELM is the non-uniform distribution of hidden node outputs due to random parameter generation, impacting performance.
    • This non-uniformity can lead to suboptimal generalization capabilities.

    Purpose of the Study:

    • To introduce a novel activation function with affine transformation (AT) to address ELM's generalization issues.
    • To develop an improved ELM algorithm, termed AT-ELM, that enhances hidden layer output distribution.
    • To evaluate the performance and robustness of the proposed AT-ELM algorithm.

    Main Methods:

    • Incorporated a novel activation function with an affine transformation (AT) into the ELM architecture.
    • Calculated AT scaling and translation parameters using the maximum entropy principle for uniform hidden layer outputs.
    • Applied the AT-ELM to nonlinear function regression, real-world data classification, and benchmark image recognition tasks.

    Main Results:

    • The AT-ELM algorithm demonstrated robustness to input range scaling in nonlinear function regression.
    • Experiments showed AT-ELM outperformed original ELM, regularized ELM, and kernel ELM in regression, classification, and image recognition.
    • AT-ELM achieved superior performance compared to several state-of-the-art algorithms on benchmark image datasets.

    Conclusions:

    • The proposed AT-ELM effectively addresses the non-uniform hidden node output issue in ELM.
    • AT-ELM offers improved generalization performance and robustness across diverse machine learning applications.
    • The AT-ELM represents a significant advancement over existing ELM variants and other contemporary algorithms.