Accurate Interpolation of Scattered Data Via Learning Relation Graph

Shizhe Ding, Boyang Xia, Jingyan Sui, Dongbo Bu

Abstract: Interpolation of scattered data is crucial across various domains, and neural networks have proved effective in developing accurate interpolators. While these neural network-based approaches excel in capturing data distributions, their failure to leverage inherent locality in computations can lead to overly dense correlation modeling. This might result in capturing spurious correlations and thereby affecting accuracy. To address these shortcomings, we propose a relation-aware interpolation framework named REIN. REIN uses a relational inference module to efficiently identify neighboring observed data points for each interpolation location, and integrate the relation graph as constraints into a neural interpolator. Experimental results on both synthetic and real-world datasets show that REIN outperforms the existing interpolation methods, even those employing heuristic local constraints. The analysis also suggests that compared with the widely-used heuristic local constraints, the learned local relation graphs exhibit improved adaptability and interpretability.