Learning-Related Complexity of Linear Ranking Functions

  • Atsuyoshi Nakamura
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4264)


In this paper, we study learning-related complexity of linear ranking functions from n-dimensional Euclidean space to {1,2,...,k}. We show that their graph dimension, a kind of measure for PAC learning complexity in the multiclass classification setting, is Θ(n+k). This graph dimension is significantly smaller than the graph dimension Ω(nk) of the class of {1,2,...,k}-valued decision-list functions naturally defined using k–1 linear discrimination functions. We also show a risk bound of learning linear ranking functions in the ordinal regression setting by a technique similar to that used in the proof of an upper bound of their graph dimension.


Function Class Collaborative Filter Ordinal Regression Graph Dimension Decision List 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Atsuyoshi Nakamura
    • 1
  1. 1.Graduate School of Information Science and TechnologyHokkaido UniversitySapporoJapan

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