Unsupervised feature selection by joint graph learning

The recent literature indicates that preserving local geometric structure of data graph becomes much more important for unsupervised feature selection and that many existing feature selection criteria essentially work in this way. Key to constructing a local geometric structure of data graph is to determine the elements of the similarity matrix from which it is derived. Thus, the performance of feature selection are highly determined by the effectiveness of data similarity learning. Because the process of constructing or learning the underlying data similarity and feature ranking are often conducted in two separated steps, the learned data similarity may not be the optimal one for subsequent feature ranking and lead to the suboptimal results. In this paper, we propose a unsupervised feature selection model to learn the data similarity and feature selection simultaneously. Moreover, besides preserving the local sample similarity of graph, our new model also preserve the uniformity (or smoothness) of graph by adding an entropy regularizer. An efficient algorithm based on augmented Lagrangian method will be derived to solve the above constrained optimization problem to find the stable local solution. Experimental results are provided which demonstrate the effectiveness of the method.