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Co-Clustering Under the Maximum Norm

  • Laurent Bulteau
  • Vincent Froese
  • Sepp Hartung
  • Rolf Niedermeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8889)

Abstract

Co-clustering, that is, partitioning a matrix into “homogeneous” submatrices, has many applications ranging from bioinformatics to election analysis. Many interesting variants of co-clustering are NP-hard. We focus on the basic variant of co-clustering where the homogeneity of a submatrix is defined in terms of minimizing the maximum distance between two entries. In this context, we spot several NP-hard as well as a number of relevant polynomial-time solvable special cases, thus charting the border of tractability for this challenging data clustering problem. For instance, we provide polynomial-time solvability when having to partition the rows and columns into two subsets each (meaning that one obtains four submatrices). When partitioning rows and columns into three subsets each, however, we encounter NP-hardness even for input matrices containing only values from \(\{ 0,1,2\}\).

Keywords

Input Matrix Boolean Formula Cluster Boundary Column Block Generalize Maximum Entropy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Laurent Bulteau
    • 1
  • Vincent Froese
    • 1
  • Sepp Hartung
    • 1
  • Rolf Niedermeier
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinBerlinGermany

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