Block-wise missing data poses significant challenges in real-world data imputation tasks. Compared to scattered missing data, block-wise gaps exacerbate adverse effects on subsequent analytic and machine learning tasks, as the lack of local neighboring elements significantly reduces the interpolation capability and predictive power. However, this issue has not received adequate attention. Most SOTA matrix completion methods appeared less effective, primarily due to overreliance on neighboring elements for predictions. We systematically analyze the issue and propose a novel matrix completion method ``BlockEcho" for a more comprehensive solution. This method creatively integrates Matrix Factorization (MF) within Generative Adversarial Networks (GAN) to explicitly retain long-distance inter-element relationships in the original matrix. Besides, we incorporate an additional discriminator for GAN, comparing the generator's intermediate progress with pre-trained MF results to constrain high-order feature distributions. Subsequently, we evaluate BlockEcho on public datasets across three domains. Results demonstrate superior performance over both traditional and SOTA methods when imputing block-wise missing data, especially at higher missing rates. The advantage also holds for scattered missing data at high missing rates. We also contribute on the analyses in providing theoretical justification on the optimality and convergence of fusing MF and GAN for missing block data.

提出一种名为“BlockEcho”的新型矩阵补全方法，通过在生成对抗网络中创造性地整合矩阵分解和鉴别器，以解决分块缺失数据的问题，并在公共数据集上验证其在高缺失率下优于传统和现有方法的性能表现。

BlockEcho: 维持长程依赖性以对块级缺失数据进行补全