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Incremental p-margin algorithm for classification with arbitrary norm
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DOI：10.1016/j.patcog.2016.01.016.png)
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摘要
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This paper presents a new algorithm to approximate large margin solutions in binary classification problems with arbitrary q-norm or p-margin, where p and q are Holder conjugates. We begin by presenting the online fixed p-margin perceptron algorithm (FMPp) that solves linearly separable classification problems in primal variables and consists of a generalization of the fixed margin perceptron algorithm (FMP). This algorithm is combined with an incremental margin strategy called IMA(p), which computes an approximation of the maximal p-margin. To achieve this goal, IMA(p) executes FMPp several times with increasing p-margin values. One of the main advantages of this approach is its flexibility, which allows the use of different p-norms in the same primal formulation. For non-linearly separable problems, FMPp can be used with a soft margin in primal variables. The incremental learning strategy always guarantees a good approximation of the optimal p-margin and avoids the use of linear or higher order programming methods. IMA(p) was tested in different datasets obtaining similar results when compared to classical L-1 and L-infinity linear programming formulations. Also, the algorithm was compared to ALMA(p) and presents superior results. (C) 2016 Elsevier Ltd. All rights reserved.
Keyword:
Large margin classifiers
p-Norm
Perceptron algorithms
Binary classification
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