The focus of this study is the development and evaluation of a new partially supervised learning framework. This framework belongs to an emerging field in machine learning that augments unsupervised learning processes with some elements of supervision. It is based on proximity fuzzy clustering, where an active learning process is designed to query for the domain knowledge required in the supervision. Furthermore, the framework is extended to the parametric optimization of the kernel function in the proximity fuzzy clustering algorithm, where the goal is to achieve interesting non-spherical cluster structures through a non-linear mapping. It is demonstrated that the performance of kernel-based clustering is sensitive to the selection of these kernel parameters. Proximity hints procured from domain knowledge are exploited in the partially supervised framework. The theoretic developments with proximity fuzzy clustering are evaluated in several interesting and practical applications. One such problem is the clustering of a set of graphs based on their structural and semantic similarity. The segmentation of music is a second problem for proximity fuzzy clustering, where the aim is to determine the points in time, i.e. boundaries, of significant structural changes in the music. Finally, a time series prediction problem using a fuzzy rule-based system is established and evaluated. The antecedents of the rules are constructed by clustering the time series using proximity information in order to localize the behavior of the rule consequents in the architecture. Evaluation of these efforts on both synthetic and real-world data demonstrate that proximity fuzzy clustering is well suited for a variety of problems. / Digital Signals and Image Processing

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