A More Relaxed Model for Graph-Based Data Clustering: s-Plex Editing

Guo, Jiong; Komusiewicz, Christian; Niedermeier, Rolf; Uhlmann, Johannes

doi:10.1007/978-3-642-02158-9_20

Cited by 10 publications

(18 citation statements)

References 19 publications

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“…In addition, a weighted version of Cluster Editing has been considered to capture the fact that the costs of fixing false positives and of false negatives can differ [2]. Other variants to tackle data sets containing a large number of false negatives have been proposed [12,11]. The p-Defective Clique Editing problem is introduced by Guo et al [11]: modify a given graph by adding and deleting at most k edges to obtain a disjoint union of p-defective cliques, where a p-defective clique is a graph missing at most p edges from being a clique.…”

Section: Introductionmentioning

confidence: 99%

Generalized Graph Clustering: Recognizing (p,q)-Cluster Graphs

Heggernes

Lokshtanov

Nederlof

et al. 2010

Lecture Notes in Computer Science

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Cluster Editing is a classical graph theoretic approach to tackle the problem of data set clustering: it consists of modifying a similarity graph into a disjoint union of cliques, i.e, clusters. As pointed out in a number of recent papers, the cluster editing model is too rigid to capture common features of real data sets. Several generalizations have thereby been proposed. In this paper, we introduce (p, q)-cluster graphs, where each cluster misses at most p edges to be a clique, and there are at most q edges between a cluster and other clusters. Our generalization is the first one that allows a large number of false positives and negatives in total, while bounding the number of these locally for each cluster by p and q. We show that recognizing (p, q)-cluster graphs is NP-complete when p and q are input. On the positive side, we show that (0, q)-cluster, (p, 1)-cluster, (p, 2)-cluster, and (1, 3)-cluster graphs can be recognized in polynomial time.

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Section: Introductionmentioning

confidence: 99%

Generalized Graph Clustering: Recognizing (p,q)-Cluster Graphs

Heggernes

Lokshtanov

Nederlof

et al. 2010

Lecture Notes in Computer Science

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“…• to require the similarities in a cluster to form an S -plex [ 13 ], where S = sN+1 , the number of elements in the cluster being N , and 0 < s < 1 is a constant. In an S -plex, every element is of degree at least N − S .…”

Section: Resultsmentioning

confidence: 99%

Gene families as soft cliques with backbones: Amborellacontrasted with other flowering plants

et al. 2014

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BackgroundChaining is a major problem in constructing gene families.ResultsWe define a new kind of cluster on graphs with strong and weak edges: soft cliques with backbones (SCWiB). This differs from other definitions in how it controls the "chaining effect", by ensuring clusters satisfy a tolerant edge density criterion that takes into account cluster size. We implement algorithms for decomposing a graph of similarities into SCWiBs. We compare examples of output from SCWiB and the Markov Cluster Algorithm (MCL), and also compare some curated Arabidopsis thaliana gene families with the results of automatic clustering. We apply our method to 44 published angiosperm genomes with annotation, and discover that Amborella trichopoda is distinct from all the others in having substantially and systematically smaller proportions of moderate- and large-size gene families.ConclusionsWe offer several possible evolutionary explanations for this result.

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“…Fourth, the polynomial-time approximability of our problems remains unexplored. Fifth and finally, it seems promising to study overlaps in the context of the more general correlation clustering problems (see [1]) or by relaxing the demand for (maximal) cliques in cluster graphs by the demand for some reasonably dense subgraphs (as recently considered in the context of clustering without overlaps [18,19,21]).…”

Section: Resultsmentioning

confidence: 99%

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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A More Relaxed Model for Graph-Based Data Clustering: s-Plex Editing

Cited by 10 publications

References 19 publications

Generalized Graph Clustering: Recognizing (p,q)-Cluster Graphs

Generalized Graph Clustering: Recognizing (p,q)-Cluster Graphs

Gene families as soft cliques with backbones: Amborellacontrasted with other flowering plants

Graph-based data clustering with overlaps

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