Hyperbox-GLVQ Based on Min-Max-Neurons

In this paper we propose the application of min-max-neurons for the use in generalized learning vector quantization (GLVQ) models, which correspond to min-max-prototypes. These prototypes can be identified with hyperboxes in the data space. Keeping the general GLVQ cost function, we redefine the Hebb-responsibilities for min-max-prototypes and derive consistent learning rules for stochastic gradient descent learning. We demonstrate that the resulting hyperbox-based GLVQ is capable to solve two illustrating toy classification tasks in robust manner, which can be dedicated to the use of robust min-max-prototypes. Finally, we give suggestions for future research for GLVQ based on min-max-prototypes.