Impact of Class Assignment on Multinomial Classification Using Multi-Valued Neurons

Multilayer neural networks based on multi-valued neurons (MLMVNs) have been proposed to combine the advantages of complex-valued neural networks with a plain derivative-free learning algorithm. In addition, multi-valued neurons (MVNs) offer a multi-valued threshold logic resulting in the ability to replace multiple conventional output neurons in classification tasks. Therefore, several classes can be assigned to one output neuron. This thesis introduces a novel approach to assign multiple classes on numerous MVNs in the output layer. It was found that classes that possess similarity should be allocated to the same neuron and arranged adjacent to each other on the unit circle. Since MLMVNs require input data located on the unit circle, two employed transformations are reevaluated. The min-max scaler utilizing the exponential function obtains decent results for numerical data. The 2D discrete Fourier transform restricting to the phase information was found to be unsuitable for image recognition. Even if this transformation approach could be improved, it loses key properties such as translational invariance by discarding the magnitude information. The evaluation was performed on the SDD and the Fashion MNIST dataset.