# Matrix Decomposition on Graphs: A Functional View

arXiv: https://arxiv.org/abs/2102.03233 · HTML: https://mlsanity.com/paper/2102.03233/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 39 references that are in the map.
- First posted on arXiv 5 Feb 2021.

## Builds on (most cited first, 7 of 7)

- [Implicit Regularization in Deep Matrix Factorization](https://mlsanity.com/paper/1905.13655/) (2019)
- [Zero-shot Recognition via Semantic Embeddings and Knowledge Graphs](https://mlsanity.com/paper/1803.08035/) (2018)
- [Geometric Matrix Completion with Recurrent Multi-Graph Neural Networks](https://mlsanity.com/paper/1704.06803/) (2017)
- [Generating Classification Weights with GNN Denoising Autoencoders for Few-Shot Learning](https://mlsanity.com/paper/1905.01102/) (2019)
- [Matrix Completion on Graphs](https://mlsanity.com/paper/1408.1717/) (2014)
- [Fast Robust PCA on Graphs](https://mlsanity.com/paper/1507.08173/) (2015)
- [Robust Principal Component Analysis on Graphs](https://mlsanity.com/paper/1504.06151/) (2015)

## Built on by (most cited first, 2 of 2)

- [Learning Canonical Embedding for Non-rigid Shape Matching](https://mlsanity.com/paper/2110.02994/) (2021)
- [Joint Symmetry Detection and Shape Matching for Non-Rigid Point Cloud](https://mlsanity.com/paper/2112.02713/) (2021)

## Abstract (arXiv)

We propose a functional view of matrix decomposition problems on graphs such as geometric matrix completion and graph regularized dimensionality reduction. Our unifying framework is based on the key idea that using a reduced basis to represent functions on the product space is sufficient to recover a low rank matrix approximation even from a sparse signal. We validate our framework on several real and synthetic benchmarks (for both problems) where it either outperforms state of the art or achieves competitive results at a fraction of the computational effort of prior work.