Fast growing data sets with a very high number of attributes become a common situation in social, industry and scientific areas. A meaningful analysis of these data sets requires sophisticated data mining techniques as projected clustering that are able to deal with such complex data. In this work, we investigate solutions for extending the state-of-theart projected clustering algorithm P3C for large data sets in highdimensional spaces. We show that the original model of the P3C algorithm is not suitable to deal with huge data sets. Therefore, we propose the necessary changes of the underlying clustering model and then present an efficient MapReduce-based implementation our novel P3C + -MR algorithm. The effectiveness of the proposed changes on large data sets and the efficiency of the P3C + -MR algorithm are comprehensively evaluated on synthetic and real-world data sets. Additionally, we propose the P3C + -MR-Light algorithm, a simplified version of P3C + -MR that shows extraordinary good results in terms of runtime and result quality on large data sets. In the end, we compare our solutions to existing approaches.

Join processing on large-scale vector data is an important problem in many applications, as vectors are a common representation for various data types. Especially, several data analysis tasks like near duplicate detection, density-based clustering or data cleaning are based on similarity self-joins, which are a special type of join. For huge data sets, MapReduce proved to be a suitable, error-tolerant framework for parallel join algorithms. Recent approaches exploit the vector-space properties for low-dimensional vector data for an efficient join computation. However, so far no parallel similarity self-join approaches aiming at high-dimensional vector data were proposed. In this work we propose the novel similarity self-join algorithm PHiDJ (Parallel High-Dimensional Join) for the MapReduce framework. PHiDJ is well suited for medium to high-dimensional data and exploits multiple filter techniques for reducing communication and computational costs. We provide a solution for efficient join computation for skewed distributed data. Our experimental evaluation on medium- to high-dimensional data shows that our approach outperforms existing techniques.