Abstract
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 image 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. We call this model GAN-EM, which is
a framework for image clustering, semi-supervised
classification and dimensionality reduction. In Mstep, 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 stateof-the-art clustering and semi-supervised classifi-
cation results on MNIST, SVHN and CelebA, as
well as comparable quality of generated images to
other recently developed generative models