Data imputation is a prevalent and important task due to the ubiquitousness of missing data. Many efforts try to first draft a completed data and second refine to derive the imputation results, or "draft-then-refine" for short. In this work, we analyze this widespread practice from the perspective of Dirichlet energy. We find that a rudimentary "draft" imputation will decrease the Dirichlet energy, thus an energy-maintenance "refine" step is in need to recover the overall energy. Since existing "refine" methods such as Graph Convolutional Network (GCN) tend to cause further energy decline, in this work, we propose a novel framework called Graph Laplacian Pyramid Network (GLPN) to preserve Dirichlet energy and improve imputation performance. GLPN consists of a U-shaped autoencoder and residual networks to capture global and local detailed information respectively. By extensive experiments on several real-world datasets, GLPN shows superior performance over state-of-the-art methods under three different missing mechanisms. Our source code is available at https://github.com/liguanlue/GLPN.

翻译：数据填补是一项普遍且重要的任务，因为缺失数据无处不在。许多研究尝试先勾勒出完整数据的初稿，再通过细化得到填补结果，简称“先勾勒后细化”。本文从狄利克雷能量的角度分析了这一普遍做法。我们发现，基础的“勾勒”填补会降低狄利克雷能量，因此需要一个维持能量的“细化”步骤来恢复整体能量。由于现有的“细化”方法（如图卷积网络）往往导致能量进一步下降，本文提出了一种名为图拉普拉斯金字塔网络（GLPN）的新型框架，以保持狄利克雷能量并提升填补性能。GLPN由U型自编码器和残差网络组成，分别捕获全局与局部细节信息。通过在多个真实数据集上的广泛实验，GLPN在三种不同缺失机制下均表现出优于现有最先进方法的性能。我们的源代码可在 https://github.com/liguanlue/GLPN 获取。