A reductive approach to hypergraph clustering: An application to image segmentation

Ducournau, Aurélien; Bretto, Alain; Rital, Soufiane; Laget, Bernard

doi:10.1016/j.patcog.2012.01.005

Cited by 47 publications

(21 citation statements)

References 33 publications

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“…The task of clustering is to partition a given data set into groups of homogeneous data that may reveal meaningful information for advanced data analysis, such as data mining, signal processing, and image analysis [1], [2], [3], [4]. For clustering analysis, three issues are considered [5], i.e., clustering tendency assessment, cluster analysis, and cluster validation.…”

Section: Introductionmentioning

confidence: 99%

A New Fuzzy Clustering Validity Index With a Median Factor for Centroid-Based Clustering

Ouyang

Chen

et al. 2015

IEEE Trans. Fuzzy Syst.

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Determining the number of clusters, which is usually approved by domain experts or evaluated by clustering validity indexes, is an important issue in clustering analysis. This study discusses on the effectiveness of clustering validity indexes for centroid-based partitional clustering algorithms. Most general-purpose clustering validity indexes take the minimum/maximum distance between a pair of data objects, a pair of cluster centroids, or an object and a centroid as an important evaluation factor; however, they may present unstable results especially when two centroids are allocated closely. To alleviate this problem, a new clustering validity index, termed as WLI, is proposed in this paper. Our proposed WLI partially allows, to some extent, the existence of closely allocated centroids in the clustering results by considering not only the minimum but also the median distances between a pair of centroids and therefore possesses the better stability. The performances of WLI and some existing clustering validity indexes are evaluated and compared by running the fuzzy c-means algorithm for clustering various types of data sets, including artificial data sets, UCI data sets, and images. Experimental results have shown that WLI has the more accurate and satisfactory performance than other indexes.

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Section: Introductionmentioning

confidence: 99%

A New Fuzzy Clustering Validity Index With a Median Factor for Centroid-Based Clustering

Ouyang

Chen

et al. 2015

IEEE Trans. Fuzzy Syst.

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“…For more information, we refer the reader to [27]. Recently, in [13], two algorithms of hypergraph reduction have been proposed. The first algorithm, called HR-IH, uses hyperedge intersections.…”

Section: Hypergraph Reductionmentioning

confidence: 99%

Frequent Itemset Border Approximation by Dualization

Durand

Quafafou

2016

Transactions on Large-Scale Data- And Knowledge-Centered Systems XXVI

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The approach F IBAD is introduced with the purpose of computing approximate borders of frequent itemsets by leveraging dualization and computation of approximate minimal transversals of hypergraphs. The distinctiveness of the F IBAD's theoretical foundations is the approximate dualization where a new function f is defined to compute the approximate negative border. From a methodological point of view, the function f is implemented by the method AM T HR that consists of a reduction of the hypergraph and a computation of its minimal transversals. For evaluation purposes, we study the sensibility of F IBAD to AM T HR by replacing this latter by two other algorithms that compute approximate minimal transversals. We also compare our approximate dualization-based method with an existing approach that computes directly, without dualization, the approximate borders. The experimental results show that our method outperforms the other methods as it produces borders that have the highest quality.

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“…Hypergraphs are increasingly used to model complex discrete systems in many areas, including ecology [12], quantum computing [17], social networks [2], computer science [7], medicine [18] and chemistry [10]. However, there are relatively few asymptotic enumeration results for hypergraphs.…”

Section: Introductionmentioning

confidence: 99%

Enumerating sparse uniform hypergraphs with given degree sequence and forbidden edges

Aldosari

Greenhill

2019

European Journal of Combinatorics

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For n ≥ 3 and r = r(n) ≥ 3, let k = k(n) = (k 1 , . . . , k n ) be a sequence of non-negative integers with sum M (k) = n j=1 k j . We assume that M (k) is divisible by r for infinitely many values of n, and restrict our attention to these values. Let X = X(n) be a simple r-uniform hypergraph on the vertex set V = {v 1 , v 2 , . . . , v n } with t edges. We denote by H r (k) the set of all simple r-uniform hypergraphs on the vertex set V with degree sequence k, and let H r (k, X) be the set of all hypergraphs in H r (k) which contain no edge of X. We give an asymptotic enumeration formula for the size of H r (k, X). This formula holds when r 4 k 3 max = o(M (k)), t k 3 max = o(M (k) 2 ) and r t k 4 max = o(M (k) 3 ). Our proof involves the switching method. As a corollary, we obtain an asymptotic formula for the number of hypergraphs in H r (k) which contain every edge of X. We apply this result to find asymptotic expressions for the expected number of perfect matchings and loose Hamilton cycles in a random hypergraph in H r (k) in the regular case.

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A reductive approach to hypergraph clustering: An application to image segmentation

Cited by 47 publications

References 33 publications

A New Fuzzy Clustering Validity Index With a Median Factor for Centroid-Based Clustering

A New Fuzzy Clustering Validity Index With a Median Factor for Centroid-Based Clustering

Frequent Itemset Border Approximation by Dualization

Enumerating sparse uniform hypergraphs with given degree sequence and forbidden edges

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