Employing different loss functions for the classification of images via supervised learning

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• 作者：Radu Ioan Bo? (1)
  André Heinrich (2)
  Gert Wanka (2)
  
• 关键词：47A52 ; 90C25 ; 49N15 ; Machine learning ; Tikhonov regularization ; Conjugate duality ; Image classification
• 刊名：Central European Journal of Mathematics
• 出版年：2014
• 出版时间：February 2014
• 年：2014
• 卷：12
• 期：2
• 页码：381-394
• 全文大小：
• 作者单位：Radu Ioan Bo? (1)
  André Heinrich (2)
  Gert Wanka (2)
  
  1. Faculty of Mathematics, University of Vienna, 1090, Vienna, Austria
  2. Department of Mathematics, Chemnitz University of Technology, 09017, Chemnitz, Germany
  
• ISSN：1644-3616

文摘

Supervised learning methods are powerful techniques to learn a function from a given set of labeled data, the so-called training data. In this paper the support vector machines approach is applied to an image classification task. Starting with the corresponding Tikhonov regularization problem, reformulated as a convex optimization problem, we introduce a conjugate dual problem to it and prove that, whenever strong duality holds, the function to be learned can be expressed via the dual optimal solutions. Corresponding dual problems are then derived for different loss functions. The theoretical results are applied by numerically solving a classification task using high dimensional real-world data in order to obtain optimal classifiers. The results demonstrate the excellent performance of support vector classification for this particular problem.