Title: Unsupervised Learning of Mixture Models with a Uniform Background Component,
Abstract: Gaussian Mixture Models are one of the most studied and mature models in
unsupervised learning. However, outliers are often present in the data and
could influence the cluster estimation. In this paper, we study a new model
that assumes that data comes from a mixture of a number of Gaussians as well as
a uniform "background" component assumed to contain outliers and other
non-interesting observations. We develop a novel method based on robust loss
minimization that performs well in clustering such GMM with a uniform
background. We give theoretical guarantees for our clustering algorithm to
obtain best clustering results with high probability. Besides, we show that the
result of our algorithm does not depend on initialization or local optima, and
the parameter tuning is an easy task. By numeric simulations, we demonstrate
that our algorithm enjoys high accuracy and achieves the best clustering
results given a large enough sample size. Finally, experimental comparisons
with typical clustering methods on real datasets witness the potential of our
algorithm in real applications.