Subspace clustering for complex data

The increasing potential of storage technologies and information systems has opened the possibility to conveniently and affordably gather large amounts of complex data. Going beyond simple descriptions of objects by some few characteristics, such data sources range from high dimensional vector spaces over imperfect data containing errors to network data describing relations between the objects. Data Mining is the task of extracting previously unknown and useful patterns from such data sources by using automatic or semi-automatic algorithms. In this thesis, we focus on the mining task of clustering, which aims at grouping similar objects while separating dissimilar ones. Since in today's applications usually many characteristics for each object are recorded, one cannot expect to find similar objects by considering all attributes together. In contrast, valuable clusters are hidden in subspace projections of the data. As a general solution to this problem, the paradigm of subspace clustering has been introduced, which aims at automatically determining for each group of objects a set of relevant attributes these objects are similar in. In this thesis, we introduce novel methods for effective subspace clustering on various types of complex data. Our methods tackle major open challenges for clustering in subspace projections. We study the problem of redundancy in subspace clustering results and propose models whose solutions contain only non-redundant and, thus, valuable clusters. Since different subspace projections represent different views on the data, often several groupings of the objects are reasonable. Thus, we propose techniques that are not restricted to a single partitioning of the objects but that enable the detection of multiple clustering solutions. Besides tackling these challenges of subspace clustering for the case of vector data, we study the task of subspace clustering on two further data types: imperfect data and network data in combination with vector data. We propose integrated mining techniques directly handling errors in the data and simultaneously mining different information sources. In thorough experiments, we demonstrate the strengths of our novel clustering approaches. Overall, for the first time, meaningful subspace clustering results can be obtained for these types of complex data