NP-hard Approximation Problems in Overlapping Clustering

Barthélemy, Jean‐Pierre; Brucker, François

doi:10.1007/s00357-001-0014-1

Cited by 33 publications

(20 citation statements)

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“…For each m, each triangle (u, v, w) of G is covered by C m if all three vertices are included in C m and none of their non-neighbors are chosen. Therefore, the probability that (u, v, w) is covered by C m is at least 1 (d + 1) 3…”

Section: Proof Of the Upper Bound On The Edge-triangle Clique Cover Nmentioning

confidence: 99%

“…The problem of clustering vertices of graphs has received significant attention in physics, biology and computer science due to the fact that it reveals important properties regarding the community structure of the underlying networks [1,2]. Clustering may result in a partition of the vertices, or a decomposition of the vertex set into intersecting subsets that are often referred to as overlapping communities [3]. In most machine learning settings, one focuses on spectral clustering methods [4] and assumes that the number of clusters or an upper bound on the number of clusters is known beforehand, or that the parameters of the model may be learned efficiently [5,6].…”

Section: Introductionmentioning

confidence: 99%

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Motif clustering and overlapping clustering for social network analysis

Pan

Dau

Puleo

et al. 2017

IEEE INFOCOM 2017 - IEEE Conference on Computer Communications

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Motivated by applications in social network community analysis, we introduce a new clustering paradigm termed motif clustering. Unlike classical clustering, motif clustering aims to minimize the number of clustering errors associated with both edges and certain higher order graph structures (motifs) that represent "at omic units" of social organizations. Our contributions are two-fold: We first introduce motif correlation clustering, in which the goal is to agnostically partition the vertices of a weighted complete graph so that certain predetermined "important" social subgraphs mostly lie within the same cluster, while "less relevant" social subgraphs are allowed to lie across clusters. We then proceed to introduce the notion of motif covers, in which the goal is to cover the vertices of motifs via the smallest number of (near) cliques in the graph. Motif cover algorithms provide a natural solution for overlapping clustering and they also play an important role in latent feature inference of networks. For both motif correlation clustering and its extension introduced via the covering problem, we provide hardness results, algorithmic solutions and community detection results for two well-studied social networks.

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Section: Proof Of the Upper Bound On The Edge-triangle Clique Cover Nmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Motif clustering and overlapping clustering for social network analysis

Pan

Dau

Puleo

et al. 2017

IEEE INFOCOM 2017 - IEEE Conference on Computer Communications

View full text Add to dashboard Cite

show abstract

“…A diamond is the graph that results from a four-vertex clique by deleting one edge. Diamond-free graphs, that is, graphs containing no diamond as an induced subgraph, are a natural graph class and have been already studied in earlier work [2,34]. Proposition 1.…”

Section: Definition 1 (S-vertex-overlap Property and S-edge-overlap Pmentioning

confidence: 99%

“…The base case t = 1 is thus equivalent to Cluster Editing. Among other things, Barthélemy and Brucker [2] showed that 2-Zahn Clustering is NP-hard. The model of Barthélemy and Brucker [2] allows, for constant t, for vertices and edges to be in an unbounded number of maximal cliques.…”

Section: Introductionmentioning

confidence: 99%

“…Among other things, Barthélemy and Brucker [2] showed that 2-Zahn Clustering is NP-hard. The model of Barthélemy and Brucker [2] allows, for constant t, for vertices and edges to be in an unbounded number of maximal cliques. In contrast, our model limits the number of maximal cliques that a vertex or clique is contained in, but already for constant s there can be maximal cliques that intersect in an unbounded number of vertices.…”

Section: Introductionmentioning

confidence: 99%

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Graph-based data clustering with overlaps

Fellows

Guo

Komusiewicz

et al. 2011

Discrete Optimization

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We introduce overlap cluster graph modification problems where, other than in most previous work, the clusters of the target graph may overlap. More precisely, the studied graph problems ask for a minimum number of edge modifications such that the resulting graph consists of clusters (that is, maximal cliques) that may overlap up to a certain amount specified by the overlap number s. In the case of s-vertex-overlap, each vertex may be part of at most s maximal cliques; s-edge-overlap is analogously defined in terms of edges. We provide a complexity dichotomy (polynomial-time solvable versus NP-hard) for the underlying edge modification problems, develop forbidden subgraph characterizations of "cluster graphs with overlaps", and study the parameterized complexity in terms of the number of allowed edge modifications, achieving fixed-parameter tractability (in case of constant s-values) and parameterized hardness (in case of unbounded s-values).

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Computational Biology in microRNA

Zhang

2015

WIREs RNA

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MicroRNA (miRNA) is a class of small endogenous noncoding RNA species, which regulate gene expression post-transcriptionally by forming imperfect base-pair at the 3' untranslated regions of the messenger RNAs. Since the 1993 discovery of the first miRNA let-7 in worms, a vast number of studies have been dedicated to functionally characterizing miRNAs with a special emphasis on their roles in cancer. A single miRNA can potentially target ∼ 400 distinct genes, and there are over a 1000 distinct endogenous miRNAs in the human genome. Thus, miRNAs are likely involved in virtually all biological processes and pathways including carcinogenesis. However, functionally characterizing miRNAs hinges on the accurate identification of their mRNA targets, which has been a challenging problem due to imperfect base-pairing and condition-specific miRNA regulatory dynamics. In this review, we will survey the current state-of-the-art computational methods to predict miRNA targets, which are divided into three main categories: (1) sequence-based methods that primarily utilizes the canonical seed-match model, evolutionary conservation, and binding energy; (2) expression-based target prediction methods using the increasingly available miRNA and mRNA expression data measured for the same sample; and (3) network-based method that aims identify miRNA regulatory modules, which reflect their synergism in conferring a global impact to the biological system of interest. We hope that the review will serve as a good reference to the new comers to the ever-growing miRNA research field as well as veterans, who would appreciate the detailed review on the technicalities, strength, and limitations of each representative computational method.

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NP-hard Approximation Problems in Overlapping Clustering

Cited by 33 publications

References 0 publications

Motif clustering and overlapping clustering for social network analysis

Motif clustering and overlapping clustering for social network analysis

Graph-based data clustering with overlaps

Computational Biology in microRNA

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