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Kernel multilogit algorithm for multiclass classification

Author

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  • Dalmau, Oscar
  • Alarcón, Teresa E.
  • González, Graciela

Abstract

An algorithm for multi-class classification is proposed. The soft classification problem is considered, where the target variable is a multivariate random variable. The proposed algorithm transforms the original target variable into a new space using the multilogit function. Assuming Gaussian noise on this transformation and using a standard Bayesian approach the model yields a quadratic functional whose global minimum can easily be obtained by solving a set of linear system of equations. In order to obtain the classification, the inverse multilogit-based transformation should be applied and the obtained result can be interpreted as a ‘soft’ or probabilistic classification. Then, the final classification is obtained by using the ‘Winner takes all’ strategy. A Kernel-based formulation is presented in order to consider the non-linearities associated with the feature space of the data. The proposed algorithm is applied on real data, using databases available online. The experimental study shows that the algorithm is competitive with respect to other classical algorithms for multiclass classification.

Suggested Citation

  • Dalmau, Oscar & Alarcón, Teresa E. & González, Graciela, 2015. "Kernel multilogit algorithm for multiclass classification," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 199-206.
    • Handle: RePEc:eee:csdana:v:82:y:2015:i:c:p:199-206
    DOI: 10.1016/j.csda.2014.09.007
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    References listed on IDEAS

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    1. Dankmar Böhning, 1992. "Multinomial logistic regression algorithm," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 44(1), pages 197-200, March.
    2. Caudill, Steven B, 1988. "An Advantage of the Linear Probability Model over Probit or Logit," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 50(4), pages 425-427, November.
    3. Gray, J. Brian & Fan, Guangzhe, 2008. "Classification tree analysis using TARGET," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1362-1372, January.
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