July 09 2007

SVC: prestazioni del cluster assignment

With regard of this document, recently we have performed the test described at the paragraph 5 with all of two cluster assignment algorithms implemented: Complete Graph Cluster Labeling (CGCL, the classic one) and the Cone Cluster Labeling, respectively presented in

  • A. Ben-Hur, D. Horn, H. T. Siegelmann, and V. Vapnik, "Support Vector Clustering," Journal of Machine Learning Research, vol. 2, pp. 125-137, 2001.
    @article{svc,
      author = {A. Ben-Hur and D. Horn and H. T. Siegelmann and V. Vapnik},
      Date-Modified = {2007-06-19 14:44:40 +0200},
      Journal = {Journal of Machine Learning Research},
      Keywords = {clustering, SVM, gaussian kernel},
      Pages = {125-137},
      Title = {Support Vector Clustering},
      Url = {http://citeseer.ist.psu.edu/hur01support.html},
      Volume = 2, Year = 2001, Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGBwpZJGFyY2hpdmVyWCR2ZXJzaW9uVCR0b3BYJG9iamVjdHNfEA9OU0tleWVkQXJjaGl2ZXISAAGGoNEICVRyb290gAGoCwwXGBkaHiVVJG51bGzTDQ4PEBMWWk5TLm9iamVjdHNXTlMua2V5c1YkY2xhc3OiERKABIAFohQVgAKAA4AHXHJlbGF0aXZlUGF0aFlhbGlhc0RhdGFfEDUuLi8uLi8uLi9QYXBlcnMvQmVuLUh1ci9TdXBwb3J0IFZlY3RvciBDbHVzdGVyaW5nLnBkZtIbDxwdV05TLmRhdGFPEQHqAAAAAAHqAAIAAAlEb2N1bWVudHMAAAAAAAAAAAAAAAAAAAAAAAC+zniuSCsAAAA3IEUdU3VwcG9ydCBWZWN0b3IgQ2×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},
      Bdsk-Url-1 = {http://citeseer.ist.psu.edu/hur01support.html}
    }

and

  • S. Lee and K. M. Daniels, "Cone Cluster Labeling for Support Vector Clustering," in Proceedings of 6th SIAM Conference on Data Mining, 2006, pp. 484-488.
    @inproceedings{cone2006,
      author = {Sei-Hyung Lee and Karen M. Daniels},
      Booktitle = {Proceedings of 6th SIAM Conference on Data Mining},
      Date-Added = {2007-04-29 16:58:13 +0200},
      Date-Modified = {2007-06-19 18:52:22 +0200},
      Keywords = {SVM, clustering},
      Month = {May},
      Pages = {484–488},
      Title = {Cone Cluster Labeling for Support Vector Clustering},
      Url = {http://www.siam.org/meetings/sdm06/proceedings/046lees.pdf},
      Year = {2006},
      Bdsk-File-1 = {YnBsaXN0MDDUAQIDBAUGBwpZJGFyY2hpdmVyWCR2ZXJzaW9uVCR0b3BYJG9iamVjdHNfEA9OU0tleWVkQXJjaGl2ZXISAAGGoNEICVRyb290gAGoCwwXGBkaHiVVJG51bGzTDQ4PEBMWWk5TLm9iamVjdHNXTlMua2V5c1YkY2xhc3OiERKABIAFohQVgAKAA4AHXHJlbGF0aXZlUGF0aFlhbGlhc0RhdGFfEEsuLi8uLi8uLi9QYXBlcnMvTGVlL0NvbmUgQ2×1c3RlciBMYWJlbGluZyBmb3IgU3VwcG9ydCBWZWN0b3IgQ2×1c3RlcmluZy5wZGbSGw8cHVdOUy5kYXRhTxECLgAAAAACLgACAAAJRG9jdW1lbnRzAAAAAAAAAAAAAAAAAAAAAAAAvs54rkgrAAAANyVBH0NvbmUgQ2×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},
      Bdsk-Url-1 = {http://www.siam.org/meetings/sdm06/proceedings/046lees.pdf}
    }

In the first case we have a total execution time of 280.87 seconds; in the second case only 0.47 seconds was taken. In both cases, 0.25 seconds was taken in the domain description by the SVM. So, we can say that the classic algorithm was slower than CCL about of 99.92%.

The clustering results are the same and they are reported in the document mentioned above.

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