May 10 2007

SMO per Unsupervised Learning

Sequential Minimal Optimization è l’algoritmo per la risoluzione del problema di programmazione quadratica per l’addestramento di una SVM. Esiste una variante di questo algoritmo per il caso non supervisionato.

Riferimenti:

  • B. Schölkopf, J. Platt, J. Shawe-Taylor, A. Smola, and R. Williamson, "Estimating the support of a high-dimensional distribution," Microsoft Research, Redmond, WA, 99–87, 1999.
    @techreport{sch99estimating, Address = {Redmond, WA},
      Author = {B. Sch”olkopf and J. Platt and J. Shawe-Taylor and A. Smola and R. Williamson},
      Date-Added = {2007-05-07 12:48:36 +0200},
      Date-Modified = {2007-06-19 13:05:29 +0200},
      Institution = {Microsoft Research},
      Keywords = {svm, SMO, one-class},
      Number = {99–87},
      Title = {Estimating the support of a high-dimensional distribution},
      Url = {http://citeseer.ist.psu.edu/251593.html},
      Year = {1999},
      Bdsk-File-1 = {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},
      Bdsk-Url-1 = {http://citeseer.ist.psu.edu/251593.html}
    }
  • B. Schölkopf, R. C. Williamson, A. J. Smola, J. Shawe-Taylor, and J. Platt, "Support Vector Method for Novelty Detection," in Advances in Neural Information Processing Systems 12: Proceedings of the 1999 Conference, 2000.
    @inproceedings{scholkopf2000,
      author = {B. Sch”olkopf and R.C. Williamson and A.J. Smola and J. Shawe-Taylor and J. Platt},
      Booktitle = {Advances in Neural Information Processing Systems 12: Proceedings of the 1999 Conference},
      Date-Added = {2007-04-29 16:39:57 +0200},
      Date-Modified = {2007-08-10 14:18:50 +0200},
      Keywords = {SVM, clustering, SMO, one-class, novelty detection},
      Title = {Support Vector Method for Novelty Detection},
      Url = {http://axiom.anu.edu.au/~williams/papers/P126.pdf},
      Year = {2000},
      Bdsk-File-1 = {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},
      Bdsk-Url-1 = {http://axiom.anu.edu.au/~williams/papers/P126.pdf}
    }

Molto probabilmente libSVM implementa già tale variante; infatti libSVM supporta la one-class classification (distribution estimation) e per tale tipo di problema è necessaria la stessa variante di SMO.

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