  This paper presents an unsupervised learning approach for simultaneous sample
and feature selection, which is in contrast to existing works which mainly
tackle these two problems separately. In fact the two tasks are often
interleaved with each other: noisy and high-dimensional features will bring
adverse effect on sample selection, while informative or representative samples
will be beneficial to feature selection. Specifically, we propose a framework
to jointly conduct active learning and feature selection based on the CUR
matrix decomposition. From the data reconstruction perspective, both the
selected samples and features can best approximate the original dataset
respectively, such that the selected samples characterized by the features are
highly representative. In particular, our method runs in one-shot without the
procedure of iterative sample selection for progressive labeling. Thus, our
model is especially suitable when there are few labeled samples or even in the
absence of supervision, which is a particular challenge for existing methods.
As the joint learning problem is NP-hard, the proposed formulation involves a
convex but non-smooth optimization problem. We solve it efficiently by an
iterative algorithm, and prove its global convergence. Experimental results on
publicly available datasets corroborate the efficacy of our method compared
with the state-of-the-art.
