  Feature selection is an important data preprocessing in data mining and
machine learning which can be used to reduce the feature dimension without
deteriorating model's performance. Since obtaining annotated data is laborious
or even infeasible in many cases, unsupervised feature selection is more
practical in reality. Though lots of methods for unsupervised feature selection
have been proposed, these methods select features independently, thus it is no
guarantee that the group of selected features is optimal. What's more, the
number of selected features must be tuned carefully to obtain a satisfactory
result. To tackle these problems, we propose a joint adaptive graph and
structured sparsity regularization unsupervised feature selection (JASFS)
method in this paper, in which a $l_{2,0}$-norm regularization term with
respect to transformation matrix is imposed in the manifold learning for
feature selection, and a graph regularization term is incorporated into the
learning model to learn the local geometric structure of data adaptively. An
efficient and simple iterative algorithm is designed to solve the proposed
optimization problem with the analysis of computational complexity. After
optimized, a subset of optimal features will be selected in group, and the
number of selected features will be determined automatically. Experimental
results on eight benchmarks demonstrate the effectiveness and efficiency of the
proposed method compared with several state-of-the-art approaches.
