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.

Clustering graph data has gained much attention in recent years, as data represented as graphs is ubiquitous in today's applications. For many applications, besides the mere graph data also further information about the vertices of a graph is available, which can be represented as attribute vectors. Recently, combined clustering approaches were introduced, which consider graph information and attribute vectors simultaneously for clustering. The visualization of clustering results can help users to get a better understanding of the results. In this paper, we introduce the GC-Viz system, which is implemented as a plugin for the Gephi platform. GC-Viz allows the user to test the combined clustering methods GAMer and DB-CSC on their data and to visualize and explore the clustering results. Furthermore, GC-Viz enables the user to visually compare the results of different clustering algorithms on the same dataset.

Detecting dense subgraphs in a large graph is an important graph mining problem and various approaches have been proposed for its solution. While most existing methods only consider unlabeled and one-dimensional graph data, many real-world applications provide far richer information. Thus, in our work, we consider graphs that contain different types of edges -- represented as different layers/dimensions of a graph -- as well as edge labels that further characterize the relations between two vertices. We argue that exploiting this additional information supports the detection of more interesting clusters. In general, we aim at detecting clusters of vertices that are densely connected by edges with similar labels in subsets of the graph layers.

Data sources representing social networks with additional attribute information about the nodes are widely available in today's applications. Recently, combined clustering methods were introduced that consider graph information and attribute information simultaneously to detect meaningful clusters in such networks. In many cases, such attributed graphs also evolve over time. Therefore, there is a need for clustering methods that are able to trace clusters over different time steps and analyze their evolution over time. In this paper, we extend our combined clustering method DB-CSC to the analysis of evolving combined clusters.

Mining dense subgraphs such as cliques or quasi-cliques is an important graph mining problem and closely related to the notion of graph clustering. In various applications, graphs are enriched by additional information. For example, we can observe graphs representing different types of relations between the vertices. These multiple edge types can also be viewed as different "layers" of the same graph, which is denoted as a "multi-layer graph" in this work. Additionally, each edge might be annotated by a label characterizing the given relation in more detail. By exploiting all these different kinds of information, the detection of more interesting clusters in the graph can be supported.

Today's applications deal with multiple types of information: graph data to represent the relations between objects and attribute data to characterize single objects. Analyzing both data sources simultaneously can increase the quality of mining methods. Recently, combined clustering approaches were introduced, which detect densely connected node sets within one large graph that also show high similarity according to all of their attribute values. However, for attribute data it is known that this full-space clustering often leads to poor clustering results. Thus, subspace clustering was introduced to identify locally relevant subsets of attributes for each cluster. In this work, we propose a method for finding homogeneous groups by joining the paradigms of subspace clustering and dense sub graph mining, i.e. we determine sets of nodes that show high similarity in subsets of their dimensions and that are as well densely connected within the given graph. Our twofold clusters are optimized according to their density, size, and number of relevant dimensions. Our developed redundancy model confines the clustering to a manageable size of only the most interesting clusters. We introduce the algorithm Gamer for the efficient calculation of our clustering. In thorough experiments on synthetic and real world data we show that Gamer achieves low runtimes and high clustering qualities.