  Unsupervised feature selection is an important method to reduce dimensions of
high dimensional data without labels, which is benefit to avoid ``curse of
dimensionality'' and improve the performance of subsequent machine learning
tasks, like clustering and retrieval. How to select the uncorrelated and
discriminative features is the key problem of unsupervised feature selection.
Many proposed methods select features with strong discriminant and high
redundancy, or vice versa. However, they only satisfy one of these two
criteria. Other existing methods choose the discriminative features with low
redundancy by constructing the graph matrix on the original feature space.
Since the original feature space usually contains redundancy and noise, it will
degrade the performance of feature selection. In order to address these issues,
we first present a novel generalized regression model imposed by an
uncorrelated constraint and the $\ell_{2,1}$-norm regularization. It can
simultaneously select the uncorrelated and discriminative features as well as
reduce the variance of these data points belonging to the same neighborhood,
which is help for the clustering task. Furthermore, the local intrinsic
structure of data is constructed on the reduced dimensional space by learning
the similarity-induced graph adaptively. Then the learnings of the graph
structure and the indicator matrix based on the spectral analysis are
integrated into the generalized regression model. Finally, we develop an
alternative iterative optimization algorithm to solve the objective function. A
series of experiments are carried out on nine real-world data sets to
demonstrate the effectiveness of the proposed method in comparison with other
competing approaches.
