Relational Extensions of Learning Vector Quantization

Prototype-based models offer an intuitive interface to given data sets by means of an inspection of the model prototypes. Supervised classification can be achieved by popular techniques such as learning vector quantization (LVQ) and extensions derived from cost functions such as generalized LVQ (GLVQ) and robust soft LVQ (RSLVQ). These methods, however, are restricted to Euclidean vectors and they cannot be used if data are characterized by a general dissimilarity matrix. In this approach, we propose relational extensions of GLVQ and RSLVQ which can directly be applied to general possibly non-Euclidean data sets characterized by a symmetric dissimilarity matrix.