Generalization of clustering agreements and distances for overlapping clusters and network communities

Rabbany, Reihaneh; Zaı̈ane, Osmar R.

doi:10.1007/s10618-015-0426-x

Cited by 13 publications

(17 citation statements)

References 39 publications

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“…Extensions of the NMI measure for hierarchical community structure have been proposed by Perotti et al (2015) and for overlapping partitions by Fortunato (2009), McDaid et al (2011), and Rabbany and Zaïane (2015). Perotti et al (2015) generalized the MI to compare hierarchical structures represented as trees.…”

Section: Definitions and Related Workmentioning

confidence: 99%

“…Extensions of the NMI measure for hierarchical community structure have been proposed by Perotti et al () and for overlapping partitions by Lancichinetti and Fortunato (), McDaid et al (), and Rabbany and Zaïane ().…”

Section: Definitions and Related Workmentioning

confidence: 99%

“…Recently, Rabbany and Zaïane () proposed a generalized clustering distance that encompasses agreement measures belonging to the pair counting and information theoretic families. This distance is based on two functions η and ϕ , where the former quantifies the similarity between two partitions by building their contingency table, and the latter computes the dispersion in each row of this table.…”

Section: Definitions and Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Correction for Closeness: Adjusting Normalized Mutual Information Measure for Clustering Comparison

Amelio

Pizzuti

2016

Computational Intelligence

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Normalized mutual information (NMI) is a widely used measure to compare community detection methods. Recently, however, the need of adjustment for information theory-based measures has been argued because of the so-called selection bias problem, that is, they show the tendency in choosing clustering solutions with more communities. In this article, an experimental evaluation of these measures is performed to deeply investigate the problem, and an adjustment that scales the values of these measures is proposed. Experiments on synthetic networks, for which the ground-truth division is known, highlight that scaled NMI does not present the selection bias behavior. Moreover, a comparison among some well-known community detection methods on synthetic generated networks shows a fairer behavior of scaled NMI, especially when the network topology does not present a clear community structure. The experimentation also on two real-world networks reveals that the corrected formula allows to choose, among a set, the method finding a network division that better reflects the ground-truth structure.

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Section: Definitions and Related Workmentioning

confidence: 99%

Section: Definitions and Related Workmentioning

confidence: 99%

Section: Definitions and Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Correction for Closeness: Adjusting Normalized Mutual Information Measure for Clustering Comparison

Amelio

Pizzuti

2016

Computational Intelligence

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“…The selection is based on the entropy as a measure of quality of the obtained clusters [41,42]. This measure considers the overlaps between clusters P and E. The entropy of cluster P and E is H(P) and H(E).…”

Section: Coal Deposit Partitioning Modelmentioning

confidence: 99%

Multi-Attribute Technological Modeling of Coal Deposits Based on the Fuzzy TOPSIS and C-Mean Clustering Algorithms

Gligorić

Beljić

et al. 2016

Energies

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Abstract:The main aim of a coal deposit model is to provide an effective basis for mine production planning. The most applied approach is related to block modeling as a reasonable global representation of the coal deposit. By selection of adequate block size, deposits can be well represented. A block has a location in XYZ space and is characterized by adequate attributes obtained from drill holes data. From a technological point of view, i.e., a thermal power plant's requirements, heating value, sulfur and ash content are the most important attributes of coal. Distribution of attributes' values within a coal deposit can vary significantly over space and within each block as well. To decrease the uncertainty of attributes' values within blocks the concept of fuzzy triangular numbers is applied. Production planning in such an environment is a very hard task, especially in the presence of requirements. Such requirements are considered as target values while the values of block attributes are the actual values. To make production planning easier we have developed a coal deposit model based on clustering the relative closeness of actual values to the target values. The relative closeness is obtained by the TOPSIS method while technological clusters are formed by fuzzy C-mean clustering. Coal deposits are thus represented by multi-attribute technological mining cuts.

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“…In [45], the bipartite graph whose nodes are clusters with one weighted edge for two clusters sharing items is used to derive a general connected component-based decomposition formula, and it is shown that several existing measures are special cases. In a similar spirit, a generalization of clustering agreement measures is proposed in [36] based on a function ϕ(·) which quantifies the dispersion of the per-row and per-column distributions of the contingency table. Adjustments of mutual information measures have also been worked out in particular to reduce selection bias [38].…”

Section: Introductionmentioning

confidence: 99%

Comparing Two Clusterings Using Matchings between Clusters of Clusters

Cazals¹,

Mazauric²,

Tetley³

et al. 2019

ACM J. Exp. Algorithmics

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Clustering is a fundamental problem in data science, yet, the variety of clustering methods and their sensitivity to parameters make clustering hard. To analyze the stability of a given clustering algorithm while varying its parameters, and to compare clusters yielded by different algorithms, several comparison schemes based on matchings, information theory and various indices (Rand, Jaccard) have been developed. We go beyond these by providing a novel class of methods computing meta-clusters within each clustering-a meta-cluster is a group of clusters, together with a matching between these. Let the intersection graph of two clusterings be the edge-weighted bipartite graph in which the nodes represent the clusters, the edges represent the non empty intersection between two clusters, and the weight of an edge is the number of common items. We introduce the so-called D-family-matching problem on intersection graphs, with D the upper-bound on the diameter of the graph induced by the clusters of any meta-cluster. First we prove NP-completeness results and unbounded approximation ratio of simple strategies. Second, we design exact polynomial time dynamic programming algorithms for some classes of graphs (in particular trees). Then, we prove spanning-tree based efficient algorithms for general graphs. Our experiments illustrate the role of D as a scale parameter providing information on the relationship between clusters within a clustering and in-between two clusterings. They also show the advantages of our built-in mapping over classical cluster comparison measures such as the variation of information (VI). Comparer deux clusterings en utilisant des clusters de clustersRésumé :Le clustering est une tâche essentielle en analyse de données, mais la variété des méthodes disponibles rend celle-ci ardue. Diverses stratégies ont été proposées pour analyser la stabilité d'un clustering en fonction des paramètres de l'algorithme l'ayant généré, ou bien comparer des clusterings produits par des algorithmes différents. Nous allons au delà de celles-ci, en proposant une nouvelle classe de méthodes formant des groupes de clusters (meta-clusters) dans chaque clustering, et établissant une correspondance entre ceux-ci.Plus spécifiquement, définissons le graphe intersection de deux clusterings comme le graphe biparti dont les sommets sont les clusters, chaque arête étant pondérée par le nombre de points communs à deux clusters. Nous définissons le D-family-matching problème à partir du graphe intersection, D étant une borne supérieure sur le diamètre du graphe induit par les clusters des metaclusters. Dans un premier temps, nous établissons des résultats de difficulté et d'inaproximabilité. Dans un second temps, nous développons des algorithmes de programmation dynamique pour certaines classes de graphes (arbres en particulier). Enfin, nous concevons des algorithmes efficaces, basés sur des arbres couvrants, pour des graphes généraux.Nos résultats expérimentaux illustrent le rôle de D comme un paramètre d'échelle fournissant de l'i...

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Generalization of clustering agreements and distances for overlapping clusters and network communities

Cited by 13 publications

References 39 publications

Correction for Closeness: Adjusting Normalized Mutual Information Measure for Clustering Comparison

Correction for Closeness: Adjusting Normalized Mutual Information Measure for Clustering Comparison

Multi-Attribute Technological Modeling of Coal Deposits Based on the Fuzzy TOPSIS and C-Mean Clustering Algorithms

Comparing Two Clusterings Using Matchings between Clusters of Clusters

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