Abstract
This paper addresses the application of gradient descent based machine learning methods to complex-valued data. In particular, the focus is on classification using Learning Vector Quantization and extensions thereof. In order to apply gradient-based methods to complex-valued data we use the mathematical formalism of Wirtinger’s calculus to describe the derivatives of the involved dissimilarity measures, which are functions of complex-valued variables. We present a number of examples for those dissimilarity measures, including several complex-valued kernels, together with the derivatives required for the learning procedure. The resulting algorithms are tested on a data set for image recognition using Zernike moments as complex-valued shape descriptors.
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Acknowledgments
M.B. thanks the Aspen Center for Physics and the NSF Grant No. PHYS-1066293 for hospitality while the writing of this paper was finalized.
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Gay, M., Kaden, M., Biehl, M., Lampe, A., Villmann, T. (2016). Complex Variants of GLVQ Based on Wirtinger’s Calculus. In: Merényi, E., Mendenhall, M., O'Driscoll, P. (eds) Advances in Self-Organizing Maps and Learning Vector Quantization. Advances in Intelligent Systems and Computing, vol 428. Springer, Cham. https://doi.org/10.1007/978-3-319-28518-4_26
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DOI: https://doi.org/10.1007/978-3-319-28518-4_26
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