A matrix factorization approach to graph compression with partial information

  • Farshad Nourbakhsh
  • Samuel Rota BulòEmail author
  • Marcello Pelillo
Original Article


We address the problem of encoding a graph of order \(\mathsf {n}\) into a graph of order \(\mathsf {k}<\mathsf {n}\) in a way to minimize reconstruction error. This encoding is characterized in terms of a particular factorization of the adjacency matrix of the original graph. The factorization is determined as the solution of a discrete optimization problem, which is for convenience relaxed into a continuous, but equivalent, one. Our formulation does not require to have the full graph, but it can factorize the graph also in the presence of partial information. We propose a multiplicative update rule for the optimization task resembling the ones introduced for nonnegative matrix factorization, and convergence properties are proven. Experiments are conducted to assess the effectiveness of the proposed approach.


Matrix factorization Graph compression Stochastic blockmodel 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Farshad Nourbakhsh
    • 1
  • Samuel Rota Bulò
    • 2
    Email author
  • Marcello Pelillo
    • 1
  1. 1.DAIS, Università Ca’ Foscari VeneziaVenezia MestreItaly
  2. 2.Fondazione Bruno KesslerPovoItaly

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