  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.
