Radu Ioan Bot, Andre Heinrich, Gert Wanka: Employing different loss functions for the classification of images via supervised learning

Author(s):

Radu Ioan Bot
Andre Heinrich
Gert Wanka

Title:

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

Electronic source:

application/pdf

Preprint series:

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 15, 2011

Mathematics Subject Classification:

49N15	[]
90C25	[]
49N15	[]

Abstract:

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 the 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 special problem.

Keywords:

machine learning, Tikhonov regularization, conjugate duality, image classification

Language:

English

Publication time:

07/2011