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    • An affine eigenvalue problem on the nonnegative orthantPeer reviewedClosed access 

      2005, Blondel, Vincent; Ninove, Laure; Van Dooren, Paul, HE Léonard de Vinci
      Article scientifique
      In this paper, we consider the conditional affine eigenvalue problem where A is an n × n nonnegative matrix, b a nonnegative vector, and ∥·∥ a monotone vector norm. Under suitable hypotheses, we prove the existence and uniqueness of the solution (λ∗, x∗) and give its expression as the Perron root and vector of a matrix , where c∗ has a maximizing property depending on the considered norm. The equation ...

    • Dominant vectors of nonnegative matrices : application to information extraction in large graphsClosed access 

      21 janvier 2008, NINOVE, Laure, HE Léonard de Vinci
      TFE
      Objects such as documents, people, words or utilities, that are related in some way, for instance by citations, friendship, appearance in definitions or physical connections, may be conveniently represented using graphs or networks. An increasing number of such relational databases, as for instance theWorldWideWeb, digital libraries, social networking web sites or phone calls logs, are available. ...