In my research project (prior to my Master's Thesis) I studied Robust Soft Learning Vector Quantization (RSLVQ), which is a method of online learning, used for multiclass classification proposed by Seo and Obermayer (2003) and analyzed its performance within a controlled environment in comparison with other LVQ algorithms.
The general idea of RSLVQ is to place a chosen number of prototypes, representing different classes of data, within the same space as the data and update these prototypes at each time step during the learning process, using a new training sample at each step. When the label of the data sample and a prototype coincide, the prototype is attracted, otherwise repelled. A softness parameter controls to what extend the closest prototypes (closest with matching and mismatching labels) are updated.
During my master thesis project, I did a mathematical analysis of RSLVQ. The goals of this research were to support the findings in the research project, to get a mathematical description of the learning process of RSLVQ, to investigate the role of the softness parameter and possibly to serve the search for an optimal LVQ algorithm.