The forgetron: A kernel-based perceptron on a budget

Ofer Dekel, Shalev Shwartz Shai, Yoram Singer

Research output: Contribution to journalArticlepeer-review

142 Scopus citations


The Perceptron algorithm, despite its simplicity, often performs well in online classification tasks. The Perceptron becomes especially effective when it is used in conjunction with kernel functions. However, a common difficulty encountered when implementing kernel-based online algorithms is the amount of memory required to store the online hypothesis, which may grow unboundedly as the algorithm progresses. Moreover, the running time of each online round grows linearly with the amount of memory used to store the hypothesis. In this paper, we present the Forgetron family of kernel-based online classification algorithms, which overcome this problem by restricting themselves to a predefined memory budget. We obtain different members of this family by modifying the kernel-based Perceptron in various ways. We also prove a unified mistake bound for all of the Forgetron algorithms. To our knowledge, this is the first online kernel-based learning paradigm which, on one hand, maintains a strict limit on the amount of memory it uses and, on the other hand, entertains a relative mistake bound. We conclude with experiments using real datasets, which underscore the merits of our approach.

Original languageEnglish (US)
Pages (from-to)1342-1372
Number of pages31
JournalSIAM Journal on Computing
Issue number5
StatePublished - 2007

All Science Journal Classification (ASJC) codes

  • General Computer Science
  • General Mathematics


  • Kernel methods
  • Learning theory
  • Online classification
  • The Perceptron algorithm


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