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Iteratively reweighted least squares classifier and its l2- and l1-regularized Kernel versions

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Języki publikacji
EN
Abstrakty
EN
This paper introduces a new classifier design method based on regularized iteratively reweighted least squares criterion function. The proposed method uses various approximations of misclassification error, including: linear, sigmoidal, Huber and logarithmic. Using the represented theorem a kernel version of classifier design method is introduced. The conjugate gradient algorithm is used to minimize the proposed criterion function. Furthermore, .1-regularized kernel version of the classifier is introduced. In this case, the gradient projection is used to optimize the criterion function. Finally, an extensive experimental analysis on 14 benchmark datasets is given to demonstrate the validity of the introduced methods.
Rocznik
Strony
171--182
Opis fizyczny
Bibliogr. 35 poz., rys., tab.
Twórcy
autor
  • Institute of Electronics, Silesian University of Technology, 16 Akademicka St., 44-100 Gliwice, Poland, jleski@polsl.pl
Bibliografia
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  • [9] O.L. Mangasarian and D.R. Musicant, “Lagrangian support vector machines”, J. Mach. Learn. Res. 1 (1), 161–177 (2001).
  • [10] J.A.K. Suykens and J. Vandewalle, “Least squares support vector machine classifiers”, Neur. Proc. Lett. 9 (3), 293–300 (1999).
  • [11] I.W. Tsang, J.T. Kwok, and P.-M. Cheung, “Core vector machines: Fast SVM training on very large data sets”, J. Mach. Learn. Res. 6 (1), 363–392 (2005).
  • [12] I.W. Tsang, J.T. Kwok, and J.M. Zurada, “Generalized core vector machines”, IEEE Trans. Neur. Net. 17 (5), 1126–1140 (2006).
  • [13] I.W. Tsang, A. Kocsor, and J.T. Kwok, “Large-scale maximum margin discriminant analysis using core vector machines”, IEEE Trans. Neur. Net. 19 (4), 610–623 (2008).
  • [14] S. Mika, G. R¨atsch, J. Weston, S. Sch¨olkopf, and K.-R. M¨uller, “Fisher discriminant analysis with kernels”, in: Neur. Net. Sig. Proc. IX, pp. 41–48, eds. Y-H. Hu, J. Larsen, E. Wilson, S. Douglas, IEEE Press, New York, 1999.
  • [15] W. Zheng and L. Zou, “Foley-Sammon optimal discriminant vectors using kernel approach”, IEEE Trans. Neur. Net. 16 (1), 1–9 (2005).
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  • [17] J.-H. Chen and C.-S. Chen, “Fuzzy kernel perceptron”, IEEE Trans. Neu. Net. 13 (6), 1364–1373 (2002).
  • [18] E. Pękalska, P. Paclik, and R.P.W. Duin, “A generalized kernel approach to dissimilarity-based classification”, J. Mach. Learn. Res. 2 (1), 175–211 (2001).
  • [19] Y.-C. Ho and R.L. Kashyap, “An algorithm for linear inequalities and its applications”, IEEE Trans. Elec. Comp. 14 (5), 683–688 (1965).
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  • [23] J.M. Łęski, “Kernel Ho-Kashyap classifier with generalization control”, Int. J. App. Math. Comp. Sci. 14 (1), 53–62 (2004).
  • [24] Z. Wang, S. Chen, J. Liu, and D. Zhang, “Pattern representation in feature extraction and classifier design: matrix versus vector”, IEEE Trans. Neu. Net. 19 (5), 758–769 (2008).
  • [25] Z. Wang, S. Chen, and T. Sun, “MultiK-MHKS: a novel multiple kernel learning algorithm”, IEEE Trans. Patt. Ana. Mach. Intel. 30 (2), 348–353 (2008).
  • [26] C.-W. Hsu and C.-J. Lin, “A comparison of methods for multiclass support vector machines”, IEEE Trans. Neu. Net. 13 (2), 415–425 (2002).
  • [27] P.J. Huber, Robust Statistics, Wiley, New York, 1981.
  • [28] S. Haykin, Neural Networks: a Comprehensive Foundation, Prentice Hall, Upper Saddle River, 1999.
  • [29] T. Blumensath and M.E. Davies, “Gradient pursuit”, IEEE Trans. Sig. Proc. 56 (6), 2370–2382 (2008).
  • [30] M.A.T. Figueiredo, R.D. Nowak, and S.J. Wright, “Gradient projection for sparse reconstruction: application to compressed sensing and other inverse problems”, IEEE J. Select. Top. Sig. Proc. 1 (4), 586–597 (2007).
  • [31] B. Efron, T. Hastie, I. Johnstone, and R. Tibshirani, “Least angle regression”, The Annals of Statistics 32 (2), 407–451 (2004).
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  • [33] S.-J. Kim, K. Koh, M. Lustig, S. Boyd, and D. Gorinevsky, “An interior-point method for large-scale l1-regularized least squares”, IEEE J. Select. Top. Sig. Proc. 1 (4), 606–617 (2007).
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPG8-0020-0018
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