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A Second-Order Perceptron Algorithm

  • Nicolò Cesa-Bianchi
  • Alex Conconi
  • Claudio Gentile
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2375)

Abstract

We introduce a variant of the Perceptron algorithm called second-order Perceptron algorithm, which is able to exploit certain spectral properties of the data. We analyze the second-order Perceptron algorithm in the mistake bound model of on-line learning and prove bounds in terms of the eigenvalues of the Gram matrix created from the data. The performance of the second-order Perceptron algorithm is affected by the setting of a parameter controlling the sensitivity to the distribution of the eigenvalues of the Gram matrix. Since this information is not preliminarly available to on-line algorithms, we also design a refined version of the second-order Perceptron algorithm which adaptively sets the value of this parameter. For this second algorithm we are able to prove mistake bounds corresponding to a nearly optimal constant setting of the parameter.

Keywords

Unit Norm Vector Nonzero Eigenvalue Adaptive Parameter Forward Algorithm Hinge Loss 
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 2002

Authors and Affiliations

  • Nicolò Cesa-Bianchi
    • 1
  • Alex Conconi
    • 1
  • Claudio Gentile
    • 2
  1. 1.Dept. of Information TechnologiesUniversità di MilanoItaly
  2. 2.CRIIUniversità dell’InsubriaItaly

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