Feature selection is a core area of data mining with a recent innovation of graph-driven unsupervised feature selection for linked data. In this setting we have a dataset $mathbf{Y}$ consisting of $n$ instances each with $m$ features and a corresponding $n$ node graph (whose adjacency matrix is $mathbf{A}$) with an edge indicating that the two instances are similar. Existing efforts for unsupervised feature selection on attributed networks have explored either directly regenerating the links by solving for $f$ such that $f(mathbf{y}_i,mathbf{y}_j) approx mathbf{A}_{i,j}$ or finding community structure in $mathbf{A}$ and using the features in $mathbf{Y}$ to predict these communities. However, graph-driven unsupervised feature selection remains an understudied area with respect to exploring more complex guidance. Here we take the novel approach of first building a block model on the graph and then using the block model for feature selection. That is, we discover $mathbf{F}mathbf{M}mathbf{F}^T approx mathbf{A}$ and then find a subset of features $mathcal{S}$ that induces another graph to preserve both $mathbf{F}$ and $mathbf{M}$. We call our approach Block Model Guided Unsupervised Feature Selection (BMGUFS). Experimental results show that our method outperforms the state of the art on several real-world public datasets in finding high-quality features for clustering.
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