  Feature selection (FS) plays an important role in machine learning, which
extracts important features and accelerates the learning process. In this
paper, we propose a deep FS method that simultaneously conducts feature
selection and differentiable $ k $-NN graph learning based on the Dirichlet
Energy. The Dirichlet Energy identifies important features by measuring their
smoothness on the graph structure, and facilitates the learning of a new graph
that reflects the inherent structure in new feature subspace. We employ Optimal
Transport theory to address the non-differentiability issue of learning $ k
$-NN graphs in neural networks, which theoretically makes our method applicable
to other graph neural networks for dynamic graph learning. Furthermore, the
proposed framework is interpretable, since all modules are designed
algorithmically. We validate the effectiveness of our model with extensive
experiments on both synthetic and real-world datasets.
