  Expectation maximization (EM) algorithm is to find maximum likelihood
solution for models having latent variables. A typical example is Gaussian
Mixture Model (GMM) which requires Gaussian assumption, however, natural images
are highly non-Gaussian so that GMM cannot be applied to perform clustering
task on pixel space. To overcome such limitation, we propose a GAN based EM
learning framework that can maximize the likelihood of images and estimate the
latent variables with only the constraint of L-Lipschitz continuity. We call
this model GAN-EM, which is a framework for image clustering, semi-supervised
classification and dimensionality reduction. In M-step, we design a novel loss
function for discriminator of GAN to perform maximum likelihood estimation
(MLE) on data with soft class label assignments. Specifically, a conditional
generator captures data distribution for $K$ classes, and a discriminator tells
whether a sample is real or fake for each class. Since our model is
unsupervised, the class label of real data is regarded as latent variable,
which is estimated by an additional network (E-net) in E-step. The proposed
GAN-EM achieves state-of-the-art clustering and semi-supervised classification
results on MNIST, SVHN and CelebA, as well as comparable quality of generated
images to other recently developed generative models.
