Joint Feature and Differentiable $ k $-NN Graph Learning using Dirichlet Energy

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 the new feature subspace during the training process using selected features. We employ the Gumbel Softmax technique and the Optimal Transport theory to address the non-differentiability issues of learning discrete FS results and learning $ k $-NN graphs in neural networks, which theoretically makes our model applicable to other graph neural networks. 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.