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Subspace Clustering Meets Dense Subgraph Mining: A Synthesis of Two Paradigms

Todays 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.

Subspace search and visualization to make sense of alternative clusterings in high-dimensional data

In explorative data analysis, the data under consideration often resides in a high-dimensional (HD) data space. Currently many methods are available to analyze this type of data. So far, proposed automatic approaches include dimensionality reduction and cluster analysis, whereby visual-interactive methods aim to provide effective visual mappings to show, relate, and navigate HD data. Furthermore, almost all of these methods conduct the analysis from a singular perspective, meaning that they consider the data in either the original HD data space, or a reduced version thereof. Additionally, HD data spaces often consist of combined features that measure different properties, in which case the particular relationships between the various properties may not be clear to the analysts a priori since it can only be revealed if appropriate feature combinations (subspaces) of the data are taken into consideration. Considering just a single subspace is, however, often not sufficient since different subspaces may show complementary, conjointly, or contradicting relations between data items. Useful information may consequently remain embedded in sets of subspaces of a given HD input data space. Relying on the notion of subspaces, we propose a novel method for the visual analysis of HD data in which we employ an interestingness-guided subspace search algorithm to detect a candidate set of subspaces. Based on appropriately defined subspace similarity functions, we visualize the subspaces and provide navigation facilities to interactively explore large sets of subspaces. Our approach allows users to effectively compare and relate subspaces with respect to involved dimensions and clusters of objects. We apply our approach to synthetic and real data sets. We thereby demonstrate its support for understanding HD data from different perspectives, effectively yielding a more complete view on HD data.

External evaluation measures for subspace clustering

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.

Detection of orthogonal concepts in subspaces of high dimensional data

In the knowledge discovery process, clustering is an established technique for grouping objects based on mutual similarity. However, in todays 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. In this work we propose a novel clustering method aiming only at orthogonal concept detection in subspaces of the data. Unlike existing clustering approaches, OSCLU (Orthogonal Subspace CLUstering) detects for each object the orthogonal concepts described by differing attributes while pruning similar concepts. Thus, each detected cluster in an orthogonal subspace provides novel information about the hidden structure of the data. Thorough experiments on real and synthetic data show that OSCLU yields substantial quality improvements over existing clustering approaches.

Spectral Subspace Clustering for Graphs with Feature Vectors

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.

Biometric template protection

ZusammenfassungBiometrische Systeme sind zwar technisch weit ausgereift und bieten heute Erkennungsleistungen, die noch vor 10 Jahren unerreichbar waren. Jedoch ist ein weit verbreiteter Einsatz von biometrischen Authentisierungsverfahren durch Bedenken hinsichtlich des notwendigen Schutzes von Referenzdaten gebremst. Eine sichere und datenschutzfreundliche Verarbeitung von biometrischen Daten wird möglich, wenn Template Protection Verfahren zum Einsatz kommen. Diese Verfahren wurden in einer wissenschaftlichen Studie (BioKeyS-Pilot-DB Teil 2) des Bundesamtes für Sicherheit in der Informationstechnik (BSI) untersucht. Dieser Artikel berichtet über die Ergebnisse im Projekt. Er zeigt auf, wie Mechanismen zum Schutz von biometrischen Daten mit Zusatzinformationen z.B. Passwörtern verknüpft und wie die Verfahren auch in Identifikationssystemen eingesetzt werden können.

Efficient Mining of Combined Subspace and Subgraph Clusters in Graphs with Feature Vectors

Large graphs are ubiquitous in today’s applications. Besides the mere graph structure, data sources usually provide information about single objects by feature vectors. To realize the full potential for knowledge extraction, recent approaches consider both information types simultaneously. Thus, for the task of clustering, combined clustering models determine object groups within one network that are densely connected and show similar characteristics. However, due to the inherent complexity of such a combination, the existing methods are not efficiently executable and are hardly applicable to large graphs.

GAMer: a synthesis of subspace clustering and dense subgraph mining

In this work, we propose a new method to find homogeneous object groups in a single vertex-labeled graph. The basic premise is that many prevalent datasets consist of multiple types of information: graph data to represent the relations between objects and attribute data to characterize the single objects. Analyzing both information types simultaneously can increase the expressiveness of the resulting patterns. Our patterns of interest are sets of objects that are densely connected within the associated graph and as well show high similarity regarding their attributes. As for attribute data it is known that full-space clustering often is futile, we have to analyze the similarity of objects regarding subsets of their attributes. In order to take full advantage of all present information, we combine the paradigms of dense subgraph mining and subspace clustering. For our approach, we face several challenges to achieve a sound combination of the two paradigms. We maximize our twofold clusters according to their density, size, and number of relevant dimensions. The optimization of these three objectives usually is conflicting; thus, we realize a trade-off between these characteristics to obtain meaningful patterns. We develop a redundancy model to confine the clustering to a manageable size by selecting only the most interesting clusters for the result set. We prove the complexity of our clustering model and we particularly focus on the exploration of various pruning strategies to design the efficient algorithm GAMer (Graph & Attribute Miner). In thorough experiments on synthetic and real world data we show that GAMer achieves low runtimes and high clustering qualities. We provide all datasets, measures, executables, and parameter settings on our website http://dme.rwth-aachen.de/gamer.

Multi-view clustering using mixture models in subspace projections

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 models 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.

Subspace correlation clustering: finding locally correlated dimensions 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. In this work, we introduce the novel paradigm of subspace correlation clustering: we analyze subspace projections to find subsets of objects showing linear correlations among this subset of dimensions. In contrast to existing techniques, which determine correlations based on the full-space, our method is able to exclude locally irrelevant dimensions, enabling more precise detection of the correlated features. Since we analyze subspace projections, each object can contribute to several correlations. Our model allows multiple overlapping clusters in general but simultaneously avoids redundant clusters deducible from already known correlations. We introduce the algorithm SSCC that exploits different pruning techniques to efficiently generate a subspace correlation clustering. In thorough experiments we demonstrate the strength of our novel paradigm in comparison to existing methods.