  Some recent studies have suggested using GANs for numeric data generation
such as to generate data for completing the imbalanced numeric data.
Considering the significant difference between the dimensions of the numeric
data and images, as well as the strong correlations between features of numeric
data, the conventional GANs normally face an overfitting problem, consequently
leads to an ill-conditioning problem in generating numeric and structured data.
This paper studies the constrained network structures between generator G and
discriminator D in WGAN, designs several structures including isomorphic,
mirror and self-symmetric structures. We evaluates the performances of the
constrained WGANs in data augmentations, taking the non-constrained GANs and
WGANs as the baselines. Experiments prove the constrained structures have been
improved in 17/20 groups of experiments. In twenty experiments on four UCI
Machine Learning Repository datasets, Australian Credit Approval data, German
Credit data, Pima Indians Diabetes data and SPECT heart data facing five
conventional classifiers. Especially, Isomorphic WGAN is the best in 15/20
experiments. Finally, we theoretically proves that the effectiveness of
constrained structures by the directed graphic model (DGM) analysis.
