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Weighted clustering of attributed multi-graphs


An information network modeled as an attributed multi-graph contains objects described by heterogeneous attributes and connected by multiple types of edges. In this paper we study the problem of identifying groups of related objects, namely clusters, in an attributed multi-graph. It is a challenging task since a good balance between the structural and attribute properties of the objects must be achieved, while each edge-type and each attribute contains different information and is of different importance to the clustering task. We propose a unified distance measure for attributed multi-graphs which is the first to consider simultaneously the individual importance of each object property, i.e. attribute and edge-type, as well as the balance between the sets of attributes and edges. Based on this, we design an iterative parallelizable algorithm for CLustering Attributed Multi-graPhs called CLAMP, which automatically balances the structural and attribute properties of the vertices, and clusters the network such that objects in the same cluster are characterized by similar attributes and connections. Extensive experimentation on synthetic and real-world datasets demonstrates the superiority of the proposed approach over several state-of-the-art clustering methods.

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  1. 1.

    Similarly, overlapping clustering assigns an object to multiple clusters with binary memberships [32]. Though, membership probabilities provide more information, i.e. importance of an object in a cluster [14].

  2. 2.

    This dataset is available online at EU Open Data Portal—

  3. 3.

    Edge weights have been scaled to [0, 1].

  4. 4.

    Type-similar Connectivity can be calculated on directed graphs as well.

  5. 5.

    Other distance functions such as Minkowski or Semantic could be adopted as well.

  6. 6.

    Hence, \(\mathscr {C}_k\) is a valid parameter to Eqs. (1)–(6).

  7. 7.

    Also, it is suitable for our problem since Eq. (8) is differentiable. Alternatively, optimization techniques such as simulated annealing and Newton’s optimization method could be adopted. However, these techniques may impose new parameters to the model, i.e. temperature parameter, or require expensive computations at each iteration, i.e. second order derivatives, while they do not guarantee better results.

  8. 8.

    Alternatively, several centroid initialization methods could be extended and used in the proposed approach, such as the works of Bahmani et al. [3] and Shen and Meng [23], to preprocess the network aiming to reduce the number of iterations and/or improve clustering accuracy.

  9. 9.

    The full DBLP dataset is available at


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This work was partially supported by the EU Commission in terms of the PaaSport 605193 FP7 Project (FP7-SME-2013).

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Correspondence to Andreas Papadopoulos.

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Papadopoulos, A., Pallis, G. & Dikaiakos, M.D. Weighted clustering of attributed multi-graphs. Computing 99, 813–840 (2017).

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  • Clustering
  • Information networks
  • Attributed multi-graphs

Mathematics Subject Classification

  • 05C22
  • 05C40
  • 05C78
  • 68W10
  • 68W15
  • 62H30
  • 91C20