Efficiently Clustering Very Large Attributed Graphs

Attributed graphs model real networks by enriching their nodes with attributes accounting for properties. Several techniques have been proposed for partitioning these graphs into clusters that are homogeneous with respect to both semantic attributes and to the structure of the graph. However, time and space complexities of state of the art algorithms limit their scalability to medium-sized graphs. We propose SToC (for Semantic-Topological Clustering), a fast and scalable algorithm for partitioning large attributed graphs. The approach is robust, being compatible both with categorical and with quantitative attributes, and it is tailorable, allowing the user to weight the semantic and topological components. Further, the approach does not require the user to guess in advance the number of clusters. SToC relies on well known approximation techniques such as bottom-k sketches, traditional graph-theoretic concepts, and a new perspective on the composition of heterogeneous distance measures. Experimental results demonstrate its ability to efficiently compute high-quality partitions of large scale attributed graphs.Comment: This work has been published in ASONAM 2017. This version includes an appendix with validation of our attribute model and distance function, omitted in the converence version for lack of space. Please refer to the published versio

Mining Dense Subgraphs with Similar Edges

When searching for interesting structures in graphs, it is often important to take into account not only the graph connectivity, but also the metadata available, such as node and edge labels, or temporal information. In this paper we are interested in settings where such metadata is used to define a similarity between edges. We consider the problem of finding subgraphs that are dense and whose edges are similar to each other with respect to a given similarity function. Depending on the application, this function can be, for example, the Jaccard similarity between the edge label sets, or the temporal correlation of the edge occurrences in a temporal graph. We formulate a Lagrangian relaxation-based optimization problem to search for dense subgraphs with high pairwise edge similarity. We design a novel algorithm to solve the problem through parametric MinCut, and provide an efficient search scheme to iterate through the values of the Lagrangian multipliers. Our study is complemented by an evaluation on real-world datasets, which demonstrates the usefulness and efficiency of the proposed approach

Data mining using concepts of independence, unimodality and homophily

With the widespread use of information technologies, more and more complex data is generated and collected every day. Such complex data is various in structure, size, type and format, e.g. time series, texts, images, videos and graphs. Complex data is often high-dimensional and heterogeneous, which makes the separation of the wheat (knowledge) from the chaff (noise) more difficult. Clustering is a main mode of knowledge discovery from complex data, which groups objects in such a way that intra-group objects are more similar than inter-group objects. Traditional clustering methods such as k-means, Expectation-Maximization clustering (EM), DBSCAN and spectral clustering are either deceived by "the curse of dimensionality" or spoiled by heterogenous information. So, how to effectively explore complex data? In some cases, people may only have some partial information about the complex data. For example, in social networks, not every user provides his/her profile information such as the personal interests. Can we leverage the limited user information and friendship network wisely to infer the likely labels of the unlabeled users so that the advertisers can do accurate advertising? This is the problem of learning from labeled and unlabeled data, which is literarily attributed to semi-supervised classification. To gain insights into these problems, this thesis focuses on developing clustering and semi-supervised classification methods that are driven by the concepts of independence, unimodality and homophily. The proposed methods leverage techniques from diverse areas, such as statistics, information theory, graph theory, signal processing, optimization and machine learning. Specifically, this thesis develops four methods, i.e. FUSE, ISAAC, UNCut, and wvGN. FUSE and ISAAC are clustering techniques to discover statistically independent patterns from high-dimensional numerical data. UNCut is a clustering technique to discover unimodal clusters in attributed graphs in which not all the attributes are relevant to the graph structure. wvGN is a semi-supervised classification technique using the theory of homophily to infer the labels of the unlabeled vertices in graphs. We have verified our clustering and semi-supervised classification methods on various synthetic and real-world data sets. The results are superior to those of the state-of-the-art.Täglich werden durch den weit verbreiteten Einsatz von Informationstechnologien mehr und mehr komplexe Daten generiert und gesammelt. Diese komplexen Daten unterscheiden sich in der Struktur, Größe, Art und Format. Häufig anzutreffen sind beispielsweise Zeitreihen, Texte, Bilder, Videos und Graphen. Dabei sind diese Daten meist hochdimensional und heterogen, was die Trennung des Weizens ( Wissen ) von der Spreu ( Rauschen ) erschwert. Die Cluster Analyse ist dabei eine der wichtigsten Methoden um aus komplexen Daten wssen zu extrahieren. Dabei werden die Objekte eines Datensatzes in einer solchen Weise gruppiert, dass intra-gruppierte Objekte ähnlicher sind als Objekte anderer Gruppen. Der Einsatz von traditionellen Clustering-Methoden wie k-Means, Expectation-Maximization (EM), DBSCAN und Spektralclustering wird dabei entweder "durch der Fluch der Dimensionalität" erschwert oder ist angesichts der heterogenen Information nicht möglich. Wie erforscht man also solch komplexe Daten effektiv? Darüber hinaus ist es oft der Fall, dass für Objekte solcher Datensätze nur partiell Informationen vorliegen. So gibt in sozialen Netzwerken nicht jeder Benutzer seine Profil-Informationen wie die persönlichen Interessen frei. Können wir diese eingeschränkten Benutzerinformation trotzdem in Kombination mit dem Freundschaftsnetzwerk nutzen, um von von wenigen, einer Klasse zugeordneten Nutzern auf die anderen zu schließen. Beispielsweise um zielgerichtete Werbung zu schalten? Dieses Problem des Lernens aus klassifizierten und nicht klassifizierten Daten wird dem semi-supversised Learning zugeordnet. Um Einblicke in diese Probleme zu gewinnen, konzentriert sich diese Arbeit auf die Entwicklung von Clustering- und semi-überwachten Klassifikationsmethoden, die von den Konzepten der Unabhängigkeit, Unimodalität und Homophilie angetrieben werden. Die vorgeschlagenen Methoden nutzen Techniken aus verschiedenen Bereichen der Statistik, Informationstheorie, Graphentheorie, Signalverarbeitung, Optimierung und des maschinelles Lernen. Dabei stellt diese Arbeit vier Techniken vor: FUSE, ISAAC, UNCut, sowie wvGN. FUSE und ISAAC sind Clustering-Techniken, um statistisch unabhängige Muster aus hochdimensionalen numerischen Daten zu entdecken. UNCut ist eine Clustering-Technik, um unimodale Cluster in attributierten Graphen zu entdecken, in denen die Kanten und Attribute heterogene Informationen liefern. wvGN ist eine halbüberwachte Klassifikationstechnik, die Homophilie verwendet, um von gelabelten Kanten auf ungelabelte Kanten im Graphen zu schließen. Wir haben diese Clustering und semi-überwachten Klassifizierungsmethoden auf verschiedenen synthetischen und realen Datensätze überprüft. Die Ergebnisse sind denen von bisherigen State-of-the-Art-Methoden überlegen

Context Selection on Attributed Graphs for Outlier and Community Detection

Today\u27s applications store large amounts of complex data that combine information of different types. Attributed graphs are an example for such a complex database where each object is characterized by its relationships to other objects and its individual properties. Specifically, each node in an attributed graph may be characterized by a large number of attributes. In this thesis, we present different approaches for mining such high dimensional attributed graphs

Engineering Graph Clustering Algorithms

Networks in the sense of objects that are related to each other are ubiquitous. In many areas, groups of objects that are particularly densely connected, so called clusters, are semantically interesting. In this thesis, we investigate two different approaches to partition the vertices of a network into clusters. The first quantifies the goodness of a clustering according to the sparsity of the cuts induced by the clusters, whereas the second is based on the recently proposed measure surprise