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The Q-norm complexity measure and the minimum gradient method: a novel approach to the machine learning structural
D A G Vieira1, Ricardo H C Takahashi, Vasile Palade
1Department of Electrical Engineering, Federal University of Minas Gerais, Belo Horizonte, MG 31270-010, Brazil. douglas@cpdee.ufmg.br
Abstract:
This paper presents a novel approach for dealing with the structural risk minimization (SRM) applied to a general setting of the machine learning problem. The formulation is based on the fundamental concept that supervised learning is a bi-objective optimization problem in which two conflicting objectives should be minimized. The objectives are related to the empirical training error and the machine complexity. In this paper, one general Q-norm method to compute the machine complexity is presented, and, as a particular practical case, the minimum gradient method (MGM) is derived relying on the definition of the fat-shattering dimension. A practical mechanism for parallel layer perceptron (PLP) network training, involving only quasi-convex functions, is generated using the aforementioned definitions. Experimental results on 15 different benchmarks are presented, which show the potential of the proposed ideas.
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