Since data is often multi-faceted in its very nature, it might not adequately be summarized by just a single clustering. To better capture the data's complexity, methods aiming at the detection of multiple, alternative clusterings have been proposed. Independent of this research area, semi-supervised clustering techniques have shown to substantially improve clustering results for single-view clustering by integrating prior knowledge. In this paper, we join both research areas and present a solution for integrating prior knowledge in the process of detecting multiple clusterings.

Clustering graphs annotated with feature vectors has recently gained much attention. The goal is to detect groups of vertices that are densely connected in the graph as well as similar with respect to their feature values. While early approaches treated all dimensions of the feature space as equally important, more advanced techniques consider the varying relevance of dimensions for different groups. In this work, we propose a novel clustering method for graphs with feature vectors based on the principle of spectral clustering. Following the idea of subspace clustering, our method detects for each cluster an individual set of relevant features. Since spectral clustering is based on the eigendecomposition of the affinity matrix, which strongly depends on the choice of features, our method simultaneously learns the grouping of vertices and the affinity matrix. To tackle the fundamental challenge of comparing the clustering structures for different feature subsets, we define an objective function that is unbiased regarding the number of relevant features. We develop the algorithm SSCG and we show its application for multiple real-world datasets.

Traditional clustering algorithms identify just a single clustering of the data. Today's complex data, however, allow multiple interpretations leading to several valid groupings hidden in different views of the database. Each of these multiple clustering solutions is valuable and interesting as different perspectives on the same data and several meaningful groupings for each object are given. Especially for high dimensional data, where each object is described by multiple attributes, alternative clusters in different attribute subsets are of major interest. In this tutorial, we describe several real world application scenarios for multiple clustering solutions. We abstract from these scenarios and provide the general challenges in this emerging research area. We describe state-of-the-art paradigms, we highlight specific techniques, and we give an overview of this topic by providing a taxonomy of the existing clustering methods. By focusing on open challenges, we try to attract young researchers for participating in this emerging research field.

Detecting multiple clustering solutions is an emerging research field. While data is often multi-faceted in its very nature, traditional clustering methods are restricted to find just a single grouping. To overcome this limitation, methods aiming at the detection of alternative and multiple clustering solutions have been proposed. In this work, we present a Bayesian framework to tackle the problem of multi-view clustering. We provide multiple generalizations of the data by using multiple mixture models. Each mixture describes a specific view on the data by using a mixture of Beta distributions in subspace projections. Since a mixture summarizes the clusters located in similar subspace projections, each view highlights specific aspects of the data. In addition, our model handles overlapping views, where the mixture components compete against each other in the data generation process. For efficiently learning the distributions, we propose the algorithm MVGen that exploits the ICM principle and uses Bayesian model selection to trade-off the cluster model's complexity against its goodness of fit. With experiments on various real-world data sets, we demonstrate the high potential of MVGen to detect multiple, overlapping clustering views in subspace projections of the data.

The necessity to analyze subspace projections of complex data is a well-known fact in the clustering community. While the full space may be obfuscated by overlapping patterns and irrelevant dimensions, only certain subspaces are able to reveal the clustering structure. Subspace clustering discards irrelevant dimensions and allows objects to belong to multiple, overlapping clusters due to individual subspace projections for each set of objects. As we will demonstrate, the observations, which originate the need to consider subspace projections for traditional clustering, also apply for the task of correlation analysis.

Knowledge discovery in databases requires not only development of novel mining techniques but also fair and comparable quality assessment based on objective evaluation measures. Especially in young research areas where no common measures are available, researchers are unable to provide a fair evaluation. Typically, publications glorify the high quality of one approach only justified by an arbitrary evaluation measure. However, such conclusions can only be drawn if the evaluation measures themselves are fully understood. In this paper, we provide the basis for systematic evaluation in the emerging research area of subspace clustering. We formalize general quality criteria for subspace clustering measures not yet addressed in the literature. We compare the existing external evaluation methods based on these criteria and pinpoint limitations. We propose a novel external evaluation measure which meets the requirements in form of quality properties. In thorough experiments we empirically show characteristic properties of evaluation measures. Overall, we provide a set of evaluation measures that fulfill the general quality criteria as recommendation for future evaluations. All measures and datasets are provided on our website and are integrated in our evaluation framework.

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.

Traditional clustering algorithms identify just a single clustering of the data. Today's complex data, however, allow multiple interpretations leading to several valid groupings hidden in different views of the database. Each of these multiple clustering solutions is valuable and interesting as different perspectives on the same data and several meaningful groupings for each object are given. Especially for high dimensional data where each object is described by multiple attributes, alternative clusters in different attribute subsets are of major interest. In this tutorial, we describe several real world application scenarios for multiple clustering solutions. We abstract from these scenarios and provide the general challenges in this emerging research area. We describe state-of-the-art paradigms, we highlight specific techniques, and we give an overview of this topic by providing a taxonomy of the existing methods. By focusing on open challenges, we try to attract young researchers for participating in this emerging research field.

Large data resources are ubiquitous in science and business. For these domains, an intuitive view on the data is essential to fully exploit the hidden knowledge. Often, these data can be semantically structured by concepts. Since the determination of concepts requires a thorough analysis of the data, data mining methods have to be applied. In the field of subspace clustering, some techniques have recently shown to be effective for this task. Although these methods generate concept-based patterns, the user has to provide domain knowledge to gain reasonable concepts out of the data. Our demonstration CoDA (Concept Determination and Analysis) is a tool that supports the user in the final step of concept definition. More concretely, the user is guided through an iterative, interactive process in which concepts are suggested, analyzed, and potentially refined. The core aspect of CoDA is an intuitive, concept-driven presentation of subspace clusters such that concepts can be visually captured.

In the knowledge discovery process, clustering is an established technique for grouping objects based on mutual similarity. However, in today's applications for each object very many attributes are provided. As multiple concepts described by different attributes are mixed in the same data set, clusters do not appear in all dimensions. In these high dimensional data spaces, each object can be clustered in several projections of the data. However, recent clustering techniques do not succeed in detection of these orthogonal concepts hidden in the data. They either miss multiple concepts for each object by partitioning approaches or provide redundant clusters in very similar subspaces.