Rank Matrix Factorisation

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9077)


We introduce the problem of rank matrix factorisation (RMF). That is, we consider the decomposition of a rank matrix, in which each row is a (partial or complete) ranking of all columns. Rank matrices naturally appear in many applications of interest, such as sports competitions. Summarising such a rank matrix by two smaller matrices, in which one contains partial rankings that can be interpreted as local patterns, is therefore an important problem.

After introducing the general problem, we consider a specific instance called Sparse RMF, in which we enforce the rank profiles to be sparse, i.e., to contain many zeroes. We propose a greedy algorithm for this problem based on integer linear programming. Experiments on both synthetic and real data demonstrate the potential of rank matrix factorisation.


Matrix factorisation Rank data Integer linear programming 


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This research was supported by the DBOF 10/044 Project, the Natural and Artifical Genetic Variation in Microbes project, Post-doctoral Fellowships of the Research Foundation Flanders (fwo) for Siegfried Nijssen and Matthijs van Leeuwen, and the EU FET Open project Inductive Constraint Programming.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Computer ScienceKU LeuvenLeuvenBelgium
  2. 2.Leiden Institute for Advanced Computer ScienceUniversiteit LeidenLeidenThe Netherlands

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