Learning matrix quantization and relevance learning based on Schatten-p-norms

In this paper, we propose an extension of the learning vector quantization approach to classify matrix data. Examples for those data are functional data depending on time and frequency. The resulting learning matrix quantization algorithm is similar to the vectorial approach but now based on matrix norms. We favor Schatten-p-norms as the generalization of lp-norms for vectors. Furthermore, relevance learning for those matrix data allows a greater structural flexibility compared to the vectorial counterpart. We identify different kinds of algebraic relevance weighting and discuss the respective mathematical properties according to the relevance learning paradigm. Exemplary applications accompany the theoretical investigations to demonstrate basic properties.