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A Parameterized Complexity Analysis of Combinatorial Feature Selection Problems

  • Vincent Froese
  • René van Bevern
  • Rolf Niedermeier
  • Manuel Sorge
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8087)

Abstract

We examine the algorithmic tractability of NP-hard combinatorial feature selection problems in terms of parameterized complexity theory. In combinatorial feature selection, one seeks to discard dimensions from high-dimensional data such that the resulting instances fulfill a desired property. In parameterized complexity analysis, one seeks to identify relevant problem-specific quantities and tries to determine their influence on the computational complexity of the considered problem. In this paper, for various combinatorial feature selection problems, we identify parameterizations and reveal to what extent these govern computational complexity. We provide tractability as well as intractability results; for example, we show that the Distinct Vectors problem on binary points is polynomial-time solvable if each pair of points differs in at most three dimensions, whereas it is NP-hard otherwise.

Keywords

Feature Selection Cluster Graph Alphabet Size Complexity Dichotomy Parameterized Reduction 
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-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Vincent Froese
    • 1
  • René van Bevern
    • 1
  • Rolf Niedermeier
    • 1
  • Manuel Sorge
    • 1
  1. 1.Institut für Softwaretechnik und Theoretische InformatikTU BerlinGermany

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