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.

翻译：特征选择（FS）在机器学习中具有重要作用，能够提取关键特征并加速学习过程。本文提出一种基于Dirichlet能量的深度特征选择方法，该方法同步执行特征选择与可微分$k$-NN图学习。Dirichlet能量通过衡量特征在图结构上的平滑性来识别重要特征，并促进学习能够反映新特征子空间中内在结构的图模型。针对神经网络中$k$-NN图学习不可微的问题，本文采用最优传输理论予以解决，从理论上使该方法可应用于其他图神经网络的动态图学习。此外，由于所有模块均基于算法设计，所提框架具有可解释性。通过在合成数据集和真实数据集上的大量实验，我们验证了模型的有效性。