Geometric Matrix Completion: A Functional View
This work addresses matrix completion in geometric contexts, offering a more efficient and interpretable solution for applications like recommendation systems or data imputation, though it appears incremental in its domain-specific focus.
The paper tackles the geometric matrix completion problem by introducing a novel regularization method inspired by functional maps, which is more interpretable and theoretically sound. On synthetic tasks with strong geometric structure, it outperforms state-of-the-art methods by two orders of magnitude, and on real datasets, it achieves state-of-the-art results with significantly less computational effort.
We propose a totally functional view of geometric matrix completion problem. Differently from existing work, we propose a novel regularization inspired from the functional map literature that is more interpretable and theoretically sound. On synthetic tasks with strong underlying geometric structure, our framework outperforms state of the art by a huge margin (two order of magnitude) demonstrating the potential of our approach. On real datasets, we achieve state-of-the-art results at a fraction of the computational effort of previous methods. Our code is publicly available at https://github.com/Not-IITian/functional-matrix-completion