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Abstract

The idea of using the Choquet integral as an aggregation operator in machine learning has gained increasing attention in recent years, and a number of corresponding methods have already been proposed. Complementing these contributions from a more theoretical perspective, this paper addresses the following question: What is the VC dimension of the (discrete) Choquet integral when being used as a binary classifier? The VC dimension is a key notion in statistical learning theory and plays an important role in estimating the generalization performance of a learning method. Although we cannot answer the above question exactly, we provide a first interesting result in the form of (relatively tight) lower and upper bounds.

Keywords

Model Class Decision Boundary Generalization Performance Aggregation Operator Fuzzy Measure 
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 2012

Authors and Affiliations

  • Eyke Hüllermeier
    • 1
  • Ali Fallah Tehrani
    • 1
  1. 1.Department of Mathematics and Computer ScienceUniversity of MarburgGermany

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