  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.
