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Trainable monotone combiner

Neurocomputing, ISSN: 0925-2312, Vol: 417, Page: 86-105
2020
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We consider a binary classification problem in which the class label is given in the form of a discriminant function that satisfies a monotone constraint. That is, the degree of confidence that an object belongs to a class can not decrease as one of the input features increases. This manuscript examines how such a discriminant function can be trained on the basis of a labeled data set. Two alternative quality measures are considered. One of them is the AUC, which is based on the ROC analysis. The second is encouraged by the Neyman-Pearson lemma, which aims to maximize the ratio of correctly classified to misclassified examples. We propose an approach in which feature space is partitioned into quality layers that can then effectively compute the discriminant function. We prove that the resulting discriminant function is optimal with respect to the two quality measures mentioned, which indicates, among other things, the equivalence of these two quality measures. We also show that the associated optimal partitioning of feature space is unique, and provide a polynomial training algorithm for generating this partitioning.

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