  A Triangle Generative Adversarial Network ($\Delta$-GAN) is developed for
semi-supervised cross-domain joint distribution matching, where the training
data consists of samples from each domain, and supervision of domain
correspondence is provided by only a few paired samples. $\Delta$-GAN consists
of four neural networks, two generators and two discriminators. The generators
are designed to learn the two-way conditional distributions between the two
domains, while the discriminators implicitly define a ternary discriminative
function, which is trained to distinguish real data pairs and two kinds of fake
data pairs. The generators and discriminators are trained together using
adversarial learning. Under mild assumptions, in theory the joint distributions
characterized by the two generators concentrate to the data distribution. In
experiments, three different kinds of domain pairs are considered, image-label,
image-image and image-attribute pairs. Experiments on semi-supervised image
classification, image-to-image translation and attribute-based image generation
demonstrate the superiority of the proposed approach.
