2,523 research outputs found

    Algorithms for Graph-Constrained Coalition Formation in the Real World

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    Coalition formation typically involves the coming together of multiple, heterogeneous, agents to achieve both their individual and collective goals. In this paper, we focus on a special case of coalition formation known as Graph-Constrained Coalition Formation (GCCF) whereby a network connecting the agents constrains the formation of coalitions. We focus on this type of problem given that in many real-world applications, agents may be connected by a communication network or only trust certain peers in their social network. We propose a novel representation of this problem based on the concept of edge contraction, which allows us to model the search space induced by the GCCF problem as a rooted tree. Then, we propose an anytime solution algorithm (CFSS), which is particularly efficient when applied to a general class of characteristic functions called m+am+a functions. Moreover, we show how CFSS can be efficiently parallelised to solve GCCF using a non-redundant partition of the search space. We benchmark CFSS on both synthetic and realistic scenarios, using a real-world dataset consisting of the energy consumption of a large number of households in the UK. Our results show that, in the best case, the serial version of CFSS is 4 orders of magnitude faster than the state of the art, while the parallel version is 9.44 times faster than the serial version on a 12-core machine. Moreover, CFSS is the first approach to provide anytime approximate solutions with quality guarantees for very large systems of agents (i.e., with more than 2700 agents).Comment: Accepted for publication, cite as "in press

    Online Spectral Clustering on Network Streams

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    Graph is an extremely useful representation of a wide variety of practical systems in data analysis. Recently, with the fast accumulation of stream data from various type of networks, significant research interests have arisen on spectral clustering for network streams (or evolving networks). Compared with the general spectral clustering problem, the data analysis of this new type of problems may have additional requirements, such as short processing time, scalability in distributed computing environments, and temporal variation tracking. However, to design a spectral clustering method to satisfy these requirements certainly presents non-trivial efforts. There are three major challenges for the new algorithm design. The first challenge is online clustering computation. Most of the existing spectral methods on evolving networks are off-line methods, using standard eigensystem solvers such as the Lanczos method. It needs to recompute solutions from scratch at each time point. The second challenge is the parallelization of algorithms. To parallelize such algorithms is non-trivial since standard eigen solvers are iterative algorithms and the number of iterations can not be predetermined. The third challenge is the very limited existing work. In addition, there exists multiple limitations in the existing method, such as computational inefficiency on large similarity changes, the lack of sound theoretical basis, and the lack of effective way to handle accumulated approximate errors and large data variations over time. In this thesis, we proposed a new online spectral graph clustering approach with a family of three novel spectrum approximation algorithms. Our algorithms incrementally update the eigenpairs in an online manner to improve the computational performance. Our approaches outperformed the existing method in computational efficiency and scalability while retaining competitive or even better clustering accuracy. We derived our spectrum approximation techniques GEPT and EEPT through formal theoretical analysis. The well established matrix perturbation theory forms a solid theoretic foundation for our online clustering method. We facilitated our clustering method with a new metric to track accumulated approximation errors and measure the short-term temporal variation. The metric not only provides a balance between computational efficiency and clustering accuracy, but also offers a useful tool to adapt the online algorithm to the condition of unexpected drastic noise. In addition, we discussed our preliminary work on approximate graph mining with evolutionary process, non-stationary Bayesian Network structure learning from non-stationary time series data, and Bayesian Network structure learning with text priors imposed by non-parametric hierarchical topic modeling

    Anytime coalition structure generation on synergy graphs

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    We consider the coalition structure generation (CSG) problem on synergy graphs, which arises in many practical applications where communication constraints, social or trust relationships must be taken into account when forming coalitions. We propose a novel representation of this problem based on the concept of edge contraction, and an innovative branch and bound approach (CFSS), which is particularly efficient when applied to a general class of characteristic functions. This new model provides a non-redundant partition of the search space, hence allowing an effective parallelisation. We evaluate CFSS on two benchmark functions, the edge sum with coordination cost and the collective energy purchasing functions, comparing its performance with the best algorithm for CSG on synergy graphs: DyCE. The latter approach is centralised and cannot be efficiently parallelised due to the exponential memory requirements in the number of agents, which limits its scalability (while CFSS memory requirements are only polynomial). Our results show that, when the graphs are very sparse, CFSS is 4 orders of magnitude faster than DyCE. Moreover, CFSS is the first approach to provide anytime approximate solutions with quality guarantees for very large systems (i.e., with more than 2700 agents

    Multicut Algorithms for Neurite Segmentation

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    Correlation clustering, or multicut partitioning is widely used for image segmentation and graph partitioning. Given an undirected edge weighted graph with positive and negative weights, correlation clustering partitions the graph such that the sum of cut edge weights is minimized. Since the optimal number of clusters is automatically chosen, multicut partitioning is well suited for clustering neural structures in EM connectomics datasets where the optimal number of clusters is unknown a-priori. Due to the NP-hardness of optimizing the multicut objective, exact solvers do not scale and approximative solvers often give unsatisfactory results. In chapter 2 we investigate scalable methods for correlation clustering. To this end we define fusion moves for the multicut objective function which iteratively fuses the current and a proposed partitioning and monotonously improves the partitioning. Fusion moves scale to larger datasets, give near optimal solutions and at the same time show state of the art anytime performance. In chapter 3 we generalize the fusion moves frameworks for the lifted multicut ob- jective, a generalization of the multicut objective which can penalize or reward all decompositions of a graph for which any given pair of nodes are in distinct compo- nents. The proposed framework scales well to large datasets and has a cutting edge anytime performance. In chapter 4 we propose a framework for automatic segmentation of neural structures in 3D EM connectomics data where a membrane probability is predicted for each pixel with a neural network and superpixels are computed based on this probability map. Finally the superpixels are merged to neurites using the techniques described in chapter 3. The proposed pipeline is validated with an extensive set of experiments and a detailed lesion study. This work substantially narrows the accuracy gap between humans and computers for neurite segmentation. In chapter 5 we summarize the software written for this thesis. The provided imple- mentations for algorithms and techniques described in chapters 2 to 4 and many other algorithms resulted in a software library for graph partitioning, image segmentation and discrete optimization

    Density-based algorithms for active and anytime clustering

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    Data intensive applications like biology, medicine, and neuroscience require effective and efficient data mining technologies. Advanced data acquisition methods produce a constantly increasing volume and complexity. As a consequence, the need of new data mining technologies to deal with complex data has emerged during the last decades. In this thesis, we focus on the data mining task of clustering in which objects are separated in different groups (clusters) such that objects inside a cluster are more similar than objects in different clusters. Particularly, we consider density-based clustering algorithms and their applications in biomedicine. The core idea of the density-based clustering algorithm DBSCAN is that each object within a cluster must have a certain number of other objects inside its neighborhood. Compared with other clustering algorithms, DBSCAN has many attractive benefits, e.g., it can detect clusters with arbitrary shape and is robust to outliers, etc. Thus, DBSCAN has attracted a lot of research interest during the last decades with many extensions and applications. In the first part of this thesis, we aim at developing new algorithms based on the DBSCAN paradigm to deal with the new challenges of complex data, particularly expensive distance measures and incomplete availability of the distance matrix. Like many other clustering algorithms, DBSCAN suffers from poor performance when facing expensive distance measures for complex data. To tackle this problem, we propose a new algorithm based on the DBSCAN paradigm, called Anytime Density-based Clustering (A-DBSCAN), that works in an anytime scheme: in contrast to the original batch scheme of DBSCAN, the algorithm A-DBSCAN first produces a quick approximation of the clustering result and then continuously refines the result during the further run. Experts can interrupt the algorithm, examine the results, and choose between (1) stopping the algorithm at any time whenever they are satisfied with the result to save runtime and (2) continuing the algorithm to achieve better results. Such kind of anytime scheme has been proven in the literature as a very useful technique when dealing with time consuming problems. We also introduced an extended version of A-DBSCAN called A-DBSCAN-XS which is more efficient and effective than A-DBSCAN when dealing with expensive distance measures. Since DBSCAN relies on the cardinality of the neighborhood of objects, it requires the full distance matrix to perform. For complex data, these distances are usually expensive, time consuming or even impossible to acquire due to high cost, high time complexity, noisy and missing data, etc. Motivated by these potential difficulties of acquiring the distances among objects, we propose another approach for DBSCAN, called Active Density-based Clustering (Act-DBSCAN). Given a budget limitation B, Act-DBSCAN is only allowed to use up to B pairwise distances ideally to produce the same result as if it has the entire distance matrix at hand. The general idea of Act-DBSCAN is that it actively selects the most promising pairs of objects to calculate the distances between them and tries to approximate as much as possible the desired clustering result with each distance calculation. This scheme provides an efficient way to reduce the total cost needed to perform the clustering. Thus it limits the potential weakness of DBSCAN when dealing with the distance sparseness problem of complex data. As a fundamental data clustering algorithm, density-based clustering has many applications in diverse fields. In the second part of this thesis, we focus on an application of density-based clustering in neuroscience: the segmentation of the white matter fiber tracts in human brain acquired from Diffusion Tensor Imaging (DTI). We propose a model to evaluate the similarity between two fibers as a combination of structural similarity and connectivity-related similarity of fiber tracts. Various distance measure techniques from fields like time-sequence mining are adapted to calculate the structural similarity of fibers. Density-based clustering is used as the segmentation algorithm. We show how A-DBSCAN and A-DBSCAN-XS are used as novel solutions for the segmentation of massive fiber datasets and provide unique features to assist experts during the fiber segmentation process.Datenintensive Anwendungen wie Biologie, Medizin und Neurowissenschaften erfordern effektive und effiziente Data-Mining-Technologien. Erweiterte Methoden der Datenerfassung erzeugen stetig wachsende Datenmengen und Komplexit\"at. In den letzten Jahrzehnten hat sich daher ein Bedarf an neuen Data-Mining-Technologien f\"ur komplexe Daten ergeben. In dieser Arbeit konzentrieren wir uns auf die Data-Mining-Aufgabe des Clusterings, in der Objekte in verschiedenen Gruppen (Cluster) getrennt werden, so dass Objekte in einem Cluster untereinander viel \"ahnlicher sind als Objekte in verschiedenen Clustern. Insbesondere betrachten wir dichtebasierte Clustering-Algorithmen und ihre Anwendungen in der Biomedizin. Der Kerngedanke des dichtebasierten Clustering-Algorithmus DBSCAN ist, dass jedes Objekt in einem Cluster eine bestimmte Anzahl von anderen Objekten in seiner Nachbarschaft haben muss. Im Vergleich mit anderen Clustering-Algorithmen hat DBSCAN viele attraktive Vorteile, zum Beispiel kann es Cluster mit beliebiger Form erkennen und ist robust gegen\"uber Ausrei{\ss}ern. So hat DBSCAN in den letzten Jahrzehnten gro{\ss}es Forschungsinteresse mit vielen Erweiterungen und Anwendungen auf sich gezogen. Im ersten Teil dieser Arbeit wollen wir auf die Entwicklung neuer Algorithmen eingehen, die auf dem DBSCAN Paradigma basieren, um mit den neuen Herausforderungen der komplexen Daten, insbesondere teurer Abstandsma{\ss}e und unvollst\"andiger Verf\"ugbarkeit der Distanzmatrix umzugehen. Wie viele andere Clustering-Algorithmen leidet DBSCAN an schlechter Per- formanz, wenn es teuren Abstandsma{\ss}en f\"ur komplexe Daten gegen\"uber steht. Um dieses Problem zu l\"osen, schlagen wir einen neuen Algorithmus vor, der auf dem DBSCAN Paradigma basiert, genannt Anytime Density-based Clustering (A-DBSCAN), der mit einem Anytime Schema funktioniert. Im Gegensatz zu dem urspr\"unglichen Schema DBSCAN, erzeugt der Algorithmus A-DBSCAN zuerst eine schnelle Ann\"aherung des Clusterings-Ergebnisses und verfeinert dann kontinuierlich das Ergebnis im weiteren Verlauf. Experten k\"onnen den Algorithmus unterbrechen, die Ergebnisse pr\"ufen und w\"ahlen zwischen (1) Anhalten des Algorithmus zu jeder Zeit, wann immer sie mit dem Ergebnis zufrieden sind, um Laufzeit sparen und (2) Fortsetzen des Algorithmus, um bessere Ergebnisse zu erzielen. Eine solche Art eines "Anytime Schemas" ist in der Literatur als eine sehr n\"utzliche Technik erprobt, wenn zeitaufwendige Problemen anfallen. Wir stellen auch eine erweiterte Version von A-DBSCAN als A-DBSCAN-XS vor, die effizienter und effektiver als A-DBSCAN beim Umgang mit teuren Abstandsma{\ss}en ist. Da DBSCAN auf der Kardinalit\"at der Nachbarschaftsobjekte beruht, ist es notwendig, die volle Distanzmatrix auszurechen. F\"ur komplexe Daten sind diese Distanzen in der Regel teuer, zeitaufwendig oder sogar unm\"oglich zu errechnen, aufgrund der hohen Kosten, einer hohen Zeitkomplexit\"at oder verrauschten und fehlende Daten. Motiviert durch diese m\"oglichen Schwierigkeiten der Berechnung von Entfernungen zwischen Objekten, schlagen wir einen anderen Ansatz f\"ur DBSCAN vor, namentlich Active Density-based Clustering (Act-DBSCAN). Bei einer Budgetbegrenzung B, darf Act-DBSCAN nur bis zu B ideale paarweise Distanzen verwenden, um das gleiche Ergebnis zu produzieren, wie wenn es die gesamte Distanzmatrix zur Hand h\"atte. Die allgemeine Idee von Act-DBSCAN ist, dass es aktiv die erfolgversprechendsten Paare von Objekten w\"ahlt, um die Abst\"ande zwischen ihnen zu berechnen, und versucht, sich so viel wie m\"oglich dem gew\"unschten Clustering mit jeder Abstandsberechnung zu n\"ahern. Dieses Schema bietet eine effiziente M\"oglichkeit, die Gesamtkosten der Durchf\"uhrung des Clusterings zu reduzieren. So schr\"ankt sie die potenzielle Schw\"ache des DBSCAN beim Umgang mit dem Distance Sparseness Problem von komplexen Daten ein. Als fundamentaler Clustering-Algorithmus, hat dichte-basiertes Clustering viele Anwendungen in den unterschiedlichen Bereichen. Im zweiten Teil dieser Arbeit konzentrieren wir uns auf eine Anwendung des dichte-basierten Clusterings in den Neurowissenschaften: Die Segmentierung der wei{\ss}en Substanz bei Faserbahnen im menschlichen Gehirn, die vom Diffusion Tensor Imaging (DTI) erfasst werden. Wir schlagen ein Modell vor, um die \"Ahnlichkeit zwischen zwei Fasern als einer Kombination von struktureller und konnektivit\"atsbezogener \"Ahnlichkeit von Faserbahnen zu beurteilen. Verschiedene Abstandsma{\ss}e aus Bereichen wie dem Time-Sequence Mining werden angepasst, um die strukturelle \"Ahnlichkeit von Fasern zu berechnen. Dichte-basiertes Clustering wird als Segmentierungsalgorithmus verwendet. Wir zeigen, wie A-DBSCAN und A-DBSCAN-XS als neuartige L\"osungen f\"ur die Segmentierung von sehr gro{\ss}en Faserdatens\"atzen verwendet werden, und bieten innovative Funktionen, um Experten w\"ahrend des Fasersegmentierungsprozesses zu unterst\"utzen
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