  Generative adversarial networks (GANs) have shown remarkable success in
generating realistic data from some predefined prior distribution (e.g.,
Gaussian noises). However, such prior distribution is often independent of real
data and thus may lose semantic information (e.g., geometric structure or
content in images) of data. In practice, the semantic information might be
represented by some latent distribution learned from data. However, such latent
distribution may incur difficulties in data sampling for GANs. In this paper,
rather than sampling from the predefined prior distribution, we propose an
LCCGAN model with local coordinate coding (LCC) to improve the performance of
generating data. First, we propose an LCC sampling method in LCCGAN to sample
meaningful points from the latent manifold. With the LCC sampling method, we
can exploit the local information on the latent manifold and thus produce new
data with promising quality. Second, we propose an improved version, namely
LCCGAN++, by introducing a higher-order term in the generator approximation.
This term is able to achieve better approximation and thus further improve the
performance. More critically, we derive the generalization bound for both
LCCGAN and LCCGAN++ and prove that a low-dimensional input is sufficient to
achieve good generalization performance. Extensive experiments on four
benchmark datasets demonstrate the superiority of the proposed method over
existing GANs.
