Results 1  10
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30
Robust lowrank subspace segmentation with semidefinite guarantees
 In ICDM Workshop
, 2010
"... Abstract—Recently there is a line of research work proposing to employ Spectral Clustering (SC) to segment (group)1 highdimensional structural data such as those (approximately) lying on subspaces2 or lowdimensional manifolds. By learning the affinity matrix in the form of sparse reconstruction, t ..."
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Abstract—Recently there is a line of research work proposing to employ Spectral Clustering (SC) to segment (group)1 highdimensional structural data such as those (approximately) lying on subspaces2 or lowdimensional manifolds. By learning the affinity matrix in the form of sparse reconstruction, techniques proposed in this vein often considerably boost the performance in subspace settings where traditional SC can fail. Despite the success, there are fundamental problems that have been left unsolved: the spectrum property of the learned affinity matrix cannot be gauged in advance, and there is often one ugly symmetrization step that postprocesses the affinity for SC input. Hence we advocate to enforce the symmetric positive semidefinite constraint explicitly during learning (LowRank Representation with Positive SemiDefinite constraint, or LRRPSD), and show that factually it can be solved in an exquisite scheme efficiently instead of generalpurpose SDP solvers that usually scale up poorly. We provide rigorous mathematical derivations to show that, in its canonical form, LRRPSD is equivalent to the recently proposed LowRank Representation (LRR) scheme [1], and hence offer theoretic and practical insights to both LRRPSD and LRR, inviting future research. As per the computational cost, our proposal is at most comparable to that of LRR, if not less. We validate our theoretic analysis and optimization scheme by experiments on both synthetic and real data sets. Keywordsspectral clustering, affinity matrix learning, rank minimization, robust estimation, eigenvalue thresholding I.
Clustering and Community Detection in Directed Networks: A Survey
, 2013
"... Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed – in the sense that there is directionality on the edges, making the semantics of the edges non symmetric as ..."
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Networks (or graphs) appear as dominant structures in diverse domains, including sociology, biology, neuroscience and computer science. In most of the aforementioned cases graphs are directed – in the sense that there is directionality on the edges, making the semantics of the edges non symmetric as the source node transmits some property to the target one but not vice versa. An interesting feature that real networks present is the clustering or community structure property, under which the graph topology is organized into modules commonly called communities or clusters. The essence here is that nodes of the same community are highly similar while on the contrary, nodes across communities present low similarity. Revealing the underlying community structure of directed complex networks has become a crucial and interdisciplinary topic with a plethora of relevant application domains. Therefore, naturally there is a recent wealth of research production in the area of mining directed graphs – with clustering being the primary method sought and the primary tool for community detection and evaluation. The goal of this paper is to offer an indepth comparative review of the methods presented so far for clustering directed networks along with the relevant necessary methodological background and also related applications. The survey commences by offering a concise review of the fundamental concepts and methodological base on which graph clustering algorithms
Backhaulconstrained multicell cooperation using compressive sensing and spectral clustering
 in Proc. Signal Processing Advances in Wireless Communications (SPAWC
, 2012
"... Multicell cooperative processing with limited backhaul traffic is considered for cellular uplinks. To parsimoniously select a set of cooperating base stations, a sparse multicell receivefilter is obtained through convex optimization using compressive sensing techniques. Clustered cooperation is ..."
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Multicell cooperative processing with limited backhaul traffic is considered for cellular uplinks. To parsimoniously select a set of cooperating base stations, a sparse multicell receivefilter is obtained through convex optimization using compressive sensing techniques. Clustered cooperation is also considered, where sparsity is promoted on intercluster feedback. A joint equalizer design and dynamic partitioning problem is formulated and solved using an iterative spectral clustering approach. Numerical tests verify the efficacy of proposed methods. 1.
Multiway Spectral Clustering: A Marginbased Perspective
, 2008
"... Spectral clustering is a broad class of clustering procedures in which an intractable combinatorial optimization formulation of clustering is “relaxed ” into a tractable eigenvector problem, and in which the relaxed solution is subsequently “rounded ” into an approximate discrete solution to the ori ..."
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Cited by 7 (3 self)
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Spectral clustering is a broad class of clustering procedures in which an intractable combinatorial optimization formulation of clustering is “relaxed ” into a tractable eigenvector problem, and in which the relaxed solution is subsequently “rounded ” into an approximate discrete solution to the original problem. In this paper we present a novel marginbased perspective on multiway spectral clustering. We show that the marginbased perspective illuminates both the relaxation and rounding aspects of spectral clustering, providing a unified analysis of existing algorithms and guiding the design of new algorithms. We also present connections between spectral clustering and several other topics in statistics, specifically minimumvariance clustering, Procrustes analysis and Gaussian intrinsic autoregression.
Graph Transduction as a Noncooperative Game
, 2012
"... Graph transduction is a popular class of semisupervised learning techniques that aims to estimate a classification function defined over a graph of labeled and unlabeled data points. The general idea is to propagate the provided label information to unlabeled nodes in a consistent way. In contrast t ..."
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Cited by 7 (2 self)
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Graph transduction is a popular class of semisupervised learning techniques that aims to estimate a classification function defined over a graph of labeled and unlabeled data points. The general idea is to propagate the provided label information to unlabeled nodes in a consistent way. In contrast to the traditional view, in which the process of label propagation is defined as a graph Laplacian regularization, this article proposes a radically different perspective, based on gametheoretic notions. Within the proposed framework, the transduction problem is formulated in terms of a noncooperative multiplayer game whereby equilibria correspond to consistent labelings of the data. An attractive feature of this formulation is that it is inherently a multiclass approach and imposes no constraint whatsoever on the structure of the pairwise similarity matrix, being able to naturally deal with asymmetric and negative similarities alike. Experiments on a number of realworld problems demonstrate that the proposed approach performs well compared with stateoftheart algorithms, and it can deal effectively with various types of similarity relations.
Community discovery in social networks: Applications, methods and emerging trends
 In Social Network Data Analytics
, 2011
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Axiomatic construction of hierarchical clustering in asymmetric networks,” https://fling.seas.upenn.edu/∼ssegarra/wiki/ index.php?n=Research.Publications
, 2012
"... We present an axiomatic construction of hierarchical clustering in asymmetric networks where the dissimilarity from node a to node b is not necessarily equal to the dissimilarity from node b to node a. The theory is built on the axioms of value and transformation which encode desirable properties co ..."
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We present an axiomatic construction of hierarchical clustering in asymmetric networks where the dissimilarity from node a to node b is not necessarily equal to the dissimilarity from node b to node a. The theory is built on the axioms of value and transformation which encode desirable properties common to any clustering method. Two hierarchical clustering methods that abide to these axioms are derived: reciprocal and nonreciprocal clustering. We further show that any clustering method that satisfies the axioms of value and transformation lies between reciprocal and nonreciprocal clustering in a well defined sense. We apply this theory to the formation of circles of trust in social networks. Index Terms — Clustering, asymmetric networks. 1.
Detecting Commmunities via Simultaneous Clustering of Graphs and Folksonomies
"... Abstract. We present a simple technique for detecting communities by utilizing both the link structure and folksonomy (or tag) information. A simple way to describe our approach is by defining a community as a set of nodes in a graph that link more frequently within this set than outside it and they ..."
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Abstract. We present a simple technique for detecting communities by utilizing both the link structure and folksonomy (or tag) information. A simple way to describe our approach is by defining a community as a set of nodes in a graph that link more frequently within this set than outside it and they share similar tags. Our technique is based on the Normalized Cut (NCut) algorithm and can be easily and efficiently implemented. We validate our method by using a real network of blogs and tag information obtained from a social bookmarking site. We also verify our results on a citation network for which we have access to ground truth cluster information. Our method, Simultaneous Cut (SimCut), has the advantage that it can group related tags and cluster the nodes simultaneously. 1
Directed graph learning via highorder colinkage analysis
 in Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part III
"... Abstract. Many real world applications can be naturally formulated as a directed graph learning problem. How to extract the directed link structures of a graph and use labeled vertices are the key issues to infer labels of the remaining unlabeled vertices. However, directed graph learning is not we ..."
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Abstract. Many real world applications can be naturally formulated as a directed graph learning problem. How to extract the directed link structures of a graph and use labeled vertices are the key issues to infer labels of the remaining unlabeled vertices. However, directed graph learning is not well studied in data mining and machine learning areas. In this paper, we propose a novel Colinkage Analysis (CA) method to process directed graphs in an undirected way with the directional information preserved. On the induced undirected graph, we use a Green’s function approach to solve the semisupervised learning problem. We present a new zeromode free Laplacian which is invertible. This leads to an Improved Green’s Function (IGF) method to solve the classification problem, which is also extended to deal with multilabel classification problems. Promising results in extensive experimental evaluations on real data sets have demonstrated the effectiveness of our approach. 1
Ganc: Greedy agglomerative normalized cut
 Pattern Recognition, 2011, In Press, Accepted Manuscript. [Online]. Available: http://arxiv.org/abs/1105.0974
"... ar ..."