Median Variants of Prototype Based Learning Vector Quantization: Methods for Classification of General Proximity Data

The amount of digital data increases every year dramatically. The processing of these data requires improved strategies, methods and algorithms for data compression, data visualization and general data processing. Machine Learning is one particular field, which covers parts of these topics and helps to increase the usability of the big amount of data.
An important aspect is to compare data, which requires respective concepts of similarities for example to grouping data. In this thesis, we consider mathematical concepts of those similarities in context of machine learning algorithms. Particularly we provide a taxonomy of such comparison measure based on their mathematical properties.
Another topic of the thesis are machine learning algorithms which working under the assumption that only similarities between data objects are given whereas the objects themselves are not available for inspection. Thereby we focus on classification problems and develop respective approaches keeping the requirement of interpretability of the model for better user acceptance compared to black box approaches in Artificial Intelligence. For this purpose, we generalize the prototype principle known from vector quantization approaches.