  Generative adversarial networks (GANs) have shown remarkable success in
generation of data from natural data manifolds such as images. In several
scenarios, it is desirable that generated data is well-clustered, especially
when there is severe class imbalance. In this paper, we focus on the problem of
clustering in generated space of GANs and uncover its relationship with the
characteristics of the latent space. We derive from first principles, the
necessary and sufficient conditions needed to achieve faithful clustering in
the GAN framework: (i) presence of a multimodal latent space with adjustable
priors, (ii) existence of a latent space inversion mechanism and (iii)
imposition of the desired cluster priors on the latent space. We also identify
the GAN models in the literature that partially satisfy these conditions and
demonstrate the importance of all the components required, through ablative
studies on multiple real world image datasets. Additionally, we describe a
procedure to construct a multimodal latent space which facilitates learning of
cluster priors with sparse supervision.

Machine Learning;Machine Learning