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7 - Clustering Nodes

Published online by Cambridge University Press:  05 July 2016

François Fouss
Affiliation:
Université Catholique de Louvain, Belgium
Marco Saerens
Affiliation:
Université Catholique de Louvain, Belgium
Masashi Shimbo
Affiliation:
Nara Institute of Science and Technology, Japan
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Summary

Introduction

This chapter introduces several methods of clustering the nodes of a graph into a partition. In multivariate statistics and data analysis [413, 429, 560], pattern recognition [418, 761, 807], data mining [361, 372], or machine learning [23, 91], clustering means grouping a set of objects into subsets, or clusters, such that those belonging to the same cluster are more “related” than those belonging to different clusters.1 In other words, a clustering provides a partition of the set of objects into disjoint clusters such that members of a cluster are highly “similar” while objects belonging to different clusters are dissimilar [264, 303, 418, 821, 824]. Of course, this supposes three different ingredients:

  1. ▸ a measure of similarity or dissimilarity between the objects

  2. ▸ a criterion, also called cost, loss, or objective function, measuring the quality of a partition

  3. ▸ an optimization technique, or procedure, for computing a high-quality partition, according to the criterion being considered

The similarity measure could, for instance, be the similarity provided by a kernel on a graph, or simply whether the nodes are connected. In addition, the criterion could be the total within-cluster inertia induced by the kernel on a graph in the embedding space, as in the case of a simple k-means clustering.

However, most of the clustering algorithms, such as the k-means, assume that the user provides a priori the number of clusters, which is not very realistic because this number is, in general, not known in advance. There exists, however, a number of heuristic procedures to suggest a “natural” number of clusters (see for instance [576]). Thus, some clustering algorithms do not need this assumption and are therefore able to detect a number of clusters as well. These are often called community detection algorithms in the context of node clustering. One popular example of a community detection algorithm is modularity optimization, which is described in this chapter.

There exist several different types of clustering algorithms [6, 264, 303, 418, 761, 821, 824], the most prominent ones being the following:

  1. Top-down, divisive, techniques, also called partitioning or splitting methods. These methods start from an initial situation where all the nodes of the graph are contained in only one cluster.

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Publisher: Cambridge University Press
Print publication year: 2016

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  • Clustering Nodes
  • François Fouss, Université Catholique de Louvain, Belgium, Marco Saerens, Université Catholique de Louvain, Belgium, Masashi Shimbo
  • Book: Algorithms and Models for Network Data and Link Analysis
  • Online publication: 05 July 2016
  • Chapter DOI: https://doi.org/10.1017/CBO9781316418321.008
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  • Clustering Nodes
  • François Fouss, Université Catholique de Louvain, Belgium, Marco Saerens, Université Catholique de Louvain, Belgium, Masashi Shimbo
  • Book: Algorithms and Models for Network Data and Link Analysis
  • Online publication: 05 July 2016
  • Chapter DOI: https://doi.org/10.1017/CBO9781316418321.008
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Clustering Nodes
  • François Fouss, Université Catholique de Louvain, Belgium, Marco Saerens, Université Catholique de Louvain, Belgium, Masashi Shimbo
  • Book: Algorithms and Models for Network Data and Link Analysis
  • Online publication: 05 July 2016
  • Chapter DOI: https://doi.org/10.1017/CBO9781316418321.008
Available formats
×