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Prof. Dr. N. NavabTo my familyAcknowledgements I am deeply grateful that I had the opportunity to write this thesis while working at the Chair for Pattern Recognition within the project B6 of the Sonderforschungsbereich 603 (funded by Deutsche Forschungsgemeinschaft). Many people contributed to this work and I want to express my gratitude to all of them

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New Techniques for Clustering Complex Objects

The tremendous amount of data produced nowadays in various application domains such as molecular biology or geography can only be fully exploited by efficient and effective data mining tools. One of the primary data mining tasks is clustering, which is the task of partitioning points of a data set into distinct groups (clusters) such that two points from one cluster are similar to each other whereas two points from distinct clusters are not. Due to modern database technology, e.g.object relational databases, a huge amount of complex objects from scientific, engineering or multimedia applications is stored in database systems. Modelling such complex data often results in very high-dimensional vector data ("feature vectors"). In the context of clustering, this causes a lot of fundamental problems, commonly subsumed under the term "Curse of Dimensionality". As a result, traditional clustering algorithms often fail to generate meaningful results, because in such high-dimensional feature spaces data does not cluster anymore. But usually, there are clusters embedded in lower dimensional subspaces, i.e. meaningful clusters can be found if only a certain subset of features is regarded for clustering. The subset of features may even be different for varying clusters. In this thesis, we present original extensions and enhancements of the density-based clustering notion to cope with high-dimensional data. In particular, we propose an algorithm called SUBCLU (density-connected Subspace Clustering) that extends DBSCAN (Density-Based Spatial Clustering of Applications with Noise) to the problem of subspace clustering. SUBCLU efficiently computes all clusters of arbitrary shape and size that would have been found if DBSCAN were applied to all possible subspaces of the feature space. Two subspace selection techniques called RIS (Ranking Interesting Subspaces) and SURFING (SUbspaces Relevant For clusterING) are proposed. They do not compute the subspace clusters directly, but generate a list of subspaces ranked by their clustering characteristics. A hierarchical clustering algorithm can be applied to these interesting subspaces in order to compute a hierarchical (subspace) clustering. In addition, we propose the algorithm 4C (Computing Correlation Connected Clusters) that extends the concepts of DBSCAN to compute density-based correlation clusters. 4C searches for groups of objects which exhibit an arbitrary but uniform correlation. Often, the traditional approach of modelling data as high-dimensional feature vectors is no longer able to capture the intuitive notion of similarity between complex objects. Thus, objects like chemical compounds, CAD drawings, XML data or color images are often modelled by using more complex representations like graphs or trees. If a metric distance function like the edit distance for graphs and trees is used as similarity measure, traditional clustering approaches like density-based clustering are applicable to those data. However, we face the problem that a single distance calculation can be very expensive. As clustering performs a lot of distance calculations, approaches like filter and refinement and metric indices get important. The second part of this thesis deals with special approaches for clustering in application domains with complex similarity models. We show, how appropriate filters can be used to enhance the performance of query processing and, thus, clustering of hierarchical objects. Furthermore, we describe how the two paradigms of filtering and metric indexing can be combined. As complex objects can often be represented by using different similarity models, a new clustering approach is presented that is able to cluster objects that provide several different complex representations

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Stuttgart …to my dearest parentsAcknowledgements I am most grateful to Prof. Dr. Rainer Winter for his guidance through all this years starting from my Diplomarbeit, continued with my dissertational work in Stuttgart, as well as in this past year when the group moved to Regensburg. I am also thankful for opportunity to work on various research topics where I learned a lot both synthetic preparations and different measurement techniques. I sincerely appreciate his patience and great ability for communicating the knowledge. It was always pleasant to work in a such atmosphere. I would like to acknowlegde: Dr. Falk Lissner and Dr. Ingo Hartenbach for performing single crystal structure analysis and structure determinations, Dr. Reiner Ruf for additional calculations, providing me with necessary data very quickly especially in the final phase of my work. Prof. Dr. Dietrich Gudat for professional recording of 1D and 2D NMR spectra, making possible assignment of to us important compounds. Ms. Katarina Török for recording routine NMR and teaching me how to operate NMR spectrometer

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Statistical relational learning analyzes the probabilistic constraints between the entities, their attributes and relationships. It represents an area of growing interest in modern data mining. Many leading researches are proposed with promising results. However, there is no easily applicable recipe of how to turn a relational domain (e.g. a database) into a probabilistic model. There are mainly two reasons. First, structural learning in relational models is even more complex than structural learning in (non-relational) Bayesian networks due to the exponentially many attributes an attribute might depend on. Second, it might be difficult and expensive to obtain reliable prior knowledge for the domains of interest. To remove these constraints, this thesis applies nonparametric Bayesian analysis to relational learning and proposes two compelling models: Dirichlet enhanced relational learning and infinite hidden relational learning. Dirichlet enhanced relational learning (DERL) extends nonparametric hierarchical Bayesian modeling to relational data. In existing relational models, the model parameters are global, which means the conditional probability distributions are the same for eac