Quaternion Gradient and Hessian

Article, Preprint English OPEN
Xu, D; Xia, Y; Mandic, DP;
(2015)
  • Publisher: Institute of Electrical and Electronics Engineers (IEEE)
  • Identifiers: doi: 10.1109/TNNLS.2015.2440473
  • Subject: quaternion gradient | nonlinear adaptive filtering | OPERATOR | Computer Science - Learning | NEURAL-NETWORK | Engineering, Electrical & Electronic | Computer Science | MATRICES | Mathematics - Numerical Analysis | MULTILAYER PERCEPTRONS | Computer Science, Artificial Intelligence | BACKPROPAGATION ALGORITHM | LMS ALGORITHM | COMPLEX-VARIABLES | real-time recurrent learning | Technology | Engineering | generalized Hamiltonreal (GHR) calculus | CLASSIFICATION | Computer Science, Theory & Methods | Computer Science, Hardware & Architecture | quaternion least mean square (QLMS) | SIGNALS | Science & Technology | Backpropagation | PREDICTION | quaternion optimization
    acm: MathematicsofComputing_NUMERICALANALYSIS | ComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISION | ComputingMethodologies_COMPUTERGRAPHICS

The optimization of real scalar functions of quaternion variables, such as the mean square error or array output power, underpins many practical applications. Solutions typically require the calculation of the gradient and Hessian. However, real functions of quaternion ... View more
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