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Some recent studies have suggested using Generative Adversarial Network (GAN) for numeric data over-sampling, which is to generate data for completing the imbalanced numeric data. Compared with the conventional over-sampling methods, taken SMOTE as an example, the recently-proposed GAN schemes fail to generate distinguishable augmentation results for classifiers. In this paper, we discuss the reason for such failures, based on which we further study the restrained conditions between $G$ and $D$ theoretically, and propose a quantitative indicator of the restrained structure, called Similarity of the Restrained Condition (SRC) to measure the restrained conditions. Practically, we propose several candidate solutions, which are isomorphic (IWGAN) mirror (MWGAN) and self-symmetric WGAN (SWGAN) for restrained conditions. Besides, the restrained WGANs enhance the classification performance in AUC on five classifiers compared with the original data as the baseline, conventional SMOTE, and other GANs add up to 20 groups of experiments in four datasets. The restrained WGANs outperform all others in 17/20 groups, among which IWGAN accounted for 15/17 groups and the SRC is an effective measure in evaluating the restraints so that further GAN structures with G-D restrains could be designed on SRC. Multidimensional scaling (MDS) is introduced to eliminate the impact of datasets and evaluation of the AUC in a composite index and IWGAN decreases the MDS distance by 20% to 40%. Moreover, the convergence speed of IWGAN is increased, and the initial error of loss function is reduced.

Study of Restrained Network Structures for Wasserstein Generative Adversarial Networks (WGANs) on Numeric Data Augmentation