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A kernel adaptive algorithm for quaternion-valued inputs.

Thomas K Paul, Tokunbo Ogunfunmi

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    |January 17, 2015
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    Summary

    This study introduces the quaternion kernel least mean square (Quat-KLMS) algorithm for processing 3-D spatial data. This new method enhances machine learning for robotics and image recognition tasks using quaternion representations.

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    Area of Science:

    • Mathematics
    • Computer Science
    • Engineering

    Background:

    • Quaternion data is valuable for 3-D spatial transformations in fields like robotics and image recognition.
    • Existing adaptive filtering methods may not fully leverage the properties of quaternion data.

    Purpose of the Study:

    • To develop a novel kernel adaptive algorithm for quaternion data processing.
    • To enhance the learning of nonlinear transformations using quaternion representations.

    Main Methods:

    • Derivation of the quaternion kernel least mean square (Quat-KLMS) algorithm based on a least mean square (LMS) approach.
    • Introduction of the quaternion reproducing kernel Hilbert space (RKHS) and suitable kernel functions.
    • Application of modified HR calculus for gradient computation on quaternion RKHS.
    • Proposal of widely linear (augmented) filtering to boost performance.

    Main Results:

    • Successful derivation and formulation of the Quat-KLMS algorithm.
    • Demonstration of improved performance through the integration of widely linear filtering.
    • Validation of the algorithm's effectiveness in learning nonlinear transformations of quaternion data via simulations.

    Conclusions:

    • The Quat-KLMS algorithm offers a powerful new tool for processing quaternion data in complex applications.
    • Widely linear filtering further enhances the capabilities of quaternion-based adaptive algorithms.
    • The developed methods show significant promise for advancing robotics, image recognition, and other 3-D data processing fields.