Complex Variants of GLVQ Based on Wirtinger's Calculus.

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.