Isomorphic Wasserstein Generative Adversarial Network for Numeric Data Augmentation

GAN-based schemes are one of the most popular methods designed for image generation. Some recent studies have suggested using GAN for numeric data augmentation that is to generate data for completing the imbalanced numeric data. Compared to the conventional oversampling methods, taken SMOTE as an example, the proposed GAN schemes fail to generate distinguishable augmentation result for classifiers. This paper introduces an isomorphic structure between generator G and discriminator D to the conventional WGAN, and hence develops an Isomorphic Wasserstein Generative Adversarial Networks (IWGAN). DGM-based analysis proves that the isomorphic structure establishes an additional restriction from D to G in learning G and verse vice. Hence, the isomorphic structure enhances the classification performance in AUC on four datasets on five classifiers compared with three other GANs, and the conventional SMOTE methods add up to 20 groups of experiments. IWGAN outperforms all others in 15/20 groups. Introduction At present, multiple Generative Adversarial Network (GAN) schemes [1] have achieved significant progress in generating images and enhanced the accuracy of the classifier, where some of the GANs can produce almost indistinguishable images from human visional examination. In recent two years, several GAN models have been proposed for numeric data augmentation, which aims to generate samples to improve detection rates form multiple classifiers on the credit card fraud dataset [2, 3] and the telecom fraud dataset [4]. However, compared to the conventional augmentation methods, taken Synthetic Minority Over-Sampling Technique (SMOTE) [5] as an example, the GAN based methods have not exhibited many advantages [6]. Motivated by isomorphism in abstract algebra, we design an IWGAN for data argumentation. We define an isomorphic structure for the G and D pair. Here the isomorphic structure is defined as that the two networks have the same number of layers, each layer has the same number of nodes, and every two neighboring layers have the same connection. The two networks will be considered isomorphic or in same layers for the short of the definitions to satisfy requirements as mentioned above. Beneficial from the Wasserstein distance as the loss function, we technically setup the isomorphic network pairs, and the DGM analysis theoretically proves that this isomorphism provides an additional restriction in learning G from D, and verse vice, respectively. In evaluating of GAN-based augmentation, we compared IWGAN to three other GANs: conventional Wasserstein Generative Adversarial Network (WGAN) [6], adapted GAN proposed in 2017 [3], and GAN-DAE in 2018 [4]. In addition, the most widely used oversampling method, SMOTE [5], and is also employed in the evaluation as the baseline of data augmentation. Experiments are carried out on four widely studied datasets [8] and five classifiers, including Artificial Neural Network (ANN), Support Vector Machine (SVM), k-Nearest Neighbor (KNN), Gradient Boosting Classifier (GBC) and RF. In the common metrics, AUC in four datasets on five classifiers compared with three other GANs, and the conventional SMOTE methods add up to 20