Prototypes and matrix relevance learning in complex fourier space

In this contribution, we consider the classification of time-series and similar functional data which can be represented in complex Fourier coefficient space. We apply versions of Learning Vector Quantization (LVQ) which are suitable for complex-valued data, based on the so-called Wirtinger calculus. It makes possible the formulation of gradient based update rules in the framework of cost-function based Generalized Matrix Relevance LVQ (GMLVQ). Alternatively, we consider the concatenation of real and imaginary parts of Fourier coefficients in a real-valued feature vector and the classification of time domain representations by means of conventional GMLVQ.