Fuzzy variants of prototype based clustering and classification algorithms

PhD ceremony: Ms. T. Geweniger, 14.30 uur, Academiegebouw, Broerstraat 5, Groningen

Dissertation: Fuzzy variants of prototype based clustering and classification algorithms

Promotor(s): prof. M. Biehl, prof. T. Villmann

Faculty: Mathematics and Natural Sciences

Prototype based clustering and classification is a specific topic in the field of machine learning and artificial neural networks. Unsupervised clustering refers to grouping of data into sets of similar objects represented by prototypes and is among others applicable for explorative data mining, statistical data analysis, pattern recognition, and information retrieval. Supervised classification determines prototypes representing respective classes by taking a priori known class information into account. After successful prototype positioning new data samples can be classified accordingly. In practical applications data, which in fact belongs to different groups, i. e. clusters or classes, might be overlapping and therefore cannot be separated clearly. This overlapping of data is called fuzziness and refers to probabilistic or possibilistic assignments of data points to clusters or classes and has to be distinguished from fuzzy sets or fuzzy logic. Rather, it is learning with uncertainties. In this thesis some supervised and unsupervised methods -- in particular c- Means, Learning Vector Quantization, Self Organizing Maps, Neural Gas, and Affinity Propagation -- are modified or extended to incorporate this kind of fuzziness. Although some of the mentioned methods already have variants dealing with fuzzy data, the now proposed modifications concern different further aspects like clustering median data, using divergences as dissimilarity measure, or learning relevances. Further, to evaluate a fuzzy classification or cluster solution different measures are used. One of them, the Fleiss‘ Kappa Index is modified to be also applicable to fuzzy solutions.