  The problem of feature selection has raised considerable interests in the
past decade. Traditional unsupervised methods select the features which can
faithfully preserve the intrinsic structures of data, where the intrinsic
structures are estimated using all the input features of data. However, the
estimated intrinsic structures are unreliable/inaccurate when the redundant and
noisy features are not removed. Therefore, we face a dilemma here: one need the
true structures of data to identify the informative features, and one need the
informative features to accurately estimate the true structures of data. To
address this, we propose a unified learning framework which performs structure
learning and feature selection simultaneously. The structures are adaptively
learned from the results of feature selection, and the informative features are
reselected to preserve the refined structures of data. By leveraging the
interactions between these two essential tasks, we are able to capture accurate
structures and select more informative features. Experimental results on many
benchmark data sets demonstrate that the proposed method outperforms many state
of the art unsupervised feature selection methods.
