Novel linear programming approach for building a piecewise nonlinear binary classifier with a priori accuracy |
Abstract:
This paper describes a novel approach to build a piecewise (non)linear surface that separates individualsfrom two classes with an a priori classification accuracy. In particular, total classification with a good generalizationlevel can be obtained, provided no individual belongs to both classes. The method is iterative: ateach iteration a new piece of the surface is found via the solution of a Linear Programming model. Theoretically,the larger the number of iterations, the better the classification accuracy in the training set; numerically,we also found that the generalization ability does not deteriorate on the cases tested. Nonetheless, wehave included a procedure that computes a lower bound to the number of errors that will be generated inany given validation set. If needed, an early stopping criterion is provided. We also showed that each pieceof the discriminating surface is equivalent to a neuron of a feed forward neural network (FFNN); so as abyproduct we are providing a novel training scheme for FFNNs that avoids the minimization of non convexfunctions which, in general, present many local minima.We compare this algorithm with a new linear SVM that needs no pre tuning and has an excellent performanceon standard and synthetic data. Highly encouraging numerical results are reported on synthetic examples,on the Japanese Bank dataset, and on medium and small datasets from the Irvine repository of machine
learning databases. |
| Keywords: |
Binary classification Support vector machines Artificial neural networks Classification trees Linear programming Piecewise discriminator |
| Author(s): |
Ubaldo M. García-Palomares, Orestes Manzanilla-Salazar |
| Source: |
Decision Support Systems 52 (2012) 717–728 |
| Subject: |
تحقیق در عملیات |
| Category: |
مقاله مجله |
| Release Date: |
2012 |
| No of Pages: |
12 |
| Price(Tomans): |
0 |
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