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

Theoretically-Efficient and Practical Parallel DBSCAN

The DBSCAN method for spatial clustering has received significant attention due to its applicability in a variety of data analysis tasks. There are fast sequential algorithms for DBSCAN in Euclidean space that take $O(n\log n)$ work for two dimensions, sub-quadratic work for three or more dimensions, and can be computed approximately in linear work for any constant number of dimensions. However, existing parallel DBSCAN algorithms require quadratic work in the worst case, making them inefficient for large datasets. This paper bridges the gap between theory and practice of parallel DBSCAN by presenting new parallel algorithms for Euclidean exact DBSCAN and approximate DBSCAN that match the work bounds of their sequential counterparts, and are highly parallel (polylogarithmic depth). We present implementations of our algorithms along with optimizations that improve their practical performance. We perform a comprehensive experimental evaluation of our algorithms on a variety of datasets and parameter settings. Our experiments on a 36-core machine with hyper-threading show that we outperform existing parallel DBSCAN implementations by up to several orders of magnitude, and achieve speedups by up to 33x over the best sequential algorithms

Challenges and Trends in Information Management

From a customer perspective, three main dimensions are relevant when evaluating and procuring database systems: functionality, performance, and total cost of ownership. Traditionally, database research has focused a lot on performance improvements of database systems, but less on new functionality and reducing the total cost of ownership. In this paper, we give our perspective on these three dimensions based on our experience in an industrial research laboratory. The paper is not intended to give a comprehensive overview of all activities, nor is it intended to provide an in-depth discussion of the research work we illustrate. Instead it highlights a set of activities at IBM’s Almaden Research Center and outlines open research challenges that could be tackled by universities in Germany and elsewhere. With respect to the performance dimension, systems are being designed to be more scalable, by utilizing hardware support to evaluate queries close to the storage subsystem (Netezza), and by massively parallel systems like Google’s map/reduce, which go beyond classical shared-nothing or shared-disk parallelism. That said performance seems to play a less important role in modern database systems as users are willing to trad

Computing Clusters of Correlation Connected Objects

The detection of correlations between different features in a set of feature vectors is a very important data mining task because correlation indicates a dependency between the features or some association of cause and effect between them. This association can be arbitrarily complex, i.e. one or more features might be dependent from a combination of several other features. Well-known methods like the principal components analysis (PCA) can perfectly find correlations which are global, linear, not hidden in a set of noise vectors, and uniform, i.e. the same type of correlation is exhibited in all feature vectors. In many applications such as medical diagnosis, molecular biology, time sequences, or electronic commerce, however, correlations are not global since the dependency between features can be different in different subgroups of the set. In this paper, we propose a method called 4C (Computing Correlation Connected Clusters) to identify local subgroups of the data objects sharing a uniform but arbitrarily complex correlation. Our algorithm is based on a combination of PCA and density-based clustering (DBSCAN). Our method has a determinate result and is robust against noise. A broad comparative evaluation demonstrates the superior performance of 4C over competing methods such as DBSCAN, CLIQUE and ORCLUS

Efficient Similarity Search in Large Databases of Tree Structured Objects

Introduction Structured and semi-structured data are getting more and more important for modern database applications. Examples of such data include chemical compounds, CAD drawings, XML documents, web sites or image data. In addition to a variety of content-based attributes, complex objects mostly carry some kind of internal structure which often forms a hierarchy. Whereas for content information the concept of feature vectors has proven to be very successful, for the internal structure of the objects several similarity measures for trees have been proposed [4, 5]. However, the computational complexity of those measures limits their applicability to large databases. New efficient and effective lower-bounding filters for tree structured data in combination with a filter-refinement architecture [1, 3] can be used to overcome this problem. 2. Structural and Content-Based Filters Filtering based on height of nodes. A successful way to filter unordered trees based on their structure i

Ranking Interesting Subspaces for Clustering High Dimensional Data

Application domains such as life sciences, e.g. molecular biology produce a tremendous amount of data which can no longer be managed without the help of e#cient and e#ective data mining methods. One of the primary data mining tasks is clustering. However, traditional clustering algorithms often fail to detect meaningful clusters because of the high dimensional, inherently sparse feature space of most real-world data sets. Nevertheless, the data sets often contain clusters hidden in various subspaces of the original feature space. We present a pre-processing step for traditional clustering algorithms, which detects all interesting subspaces of high-dimensional data containing clusters. For this purpose, we define a quality criterion for the interestingness of a subspace and propose an e#cient algorithm called RIS (Ranking I nteresting Subspaces) to examine all such subspaces. A broad evaluation based on synthetic and real-world data sets empirically shows that RIS is suitable to find all relevant subspaces in large, high dimensional, sparse data and to rank them accordingly