# The Incremental Multiresolution Matrix Factorization Algorithm

arXiv: https://arxiv.org/abs/1705.05804 · HTML: https://mlsanity.com/paper/1705.05804/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 May 2017.

## Built on by (most cited first, 4 of 4)

- [Multi Resolution Analysis (MRA) for Approximate Self-Attention](https://mlsanity.com/paper/2207.10284/) (2022)
- [Fast Temporal Wavelet Graph Neural Networks](https://mlsanity.com/paper/2302.08643/) (2023)
- [Learning Multiresolution Matrix Factorization and its Wavelet Networks on Graphs](https://mlsanity.com/paper/2111.01940/) (2021)
- [Learning to Solve Multiresolution Matrix Factorization by Manifold Optimization and Evolutionary Metaheuristics](https://mlsanity.com/paper/2406.00469/) (2024)

## Abstract (arXiv)

Multiresolution analysis and matrix factorization are foundational tools in computer vision. In this work, we study the interface between these two distinct topics and obtain techniques to uncover hierarchical block structure in symmetric matrices -- an important aspect in the success of many vision problems. Our new algorithm, the incremental multiresolution matrix factorization, uncovers such structure one feature at a time, and hence scales well to large matrices. We describe how this multiscale analysis goes much farther than what a direct global factorization of the data can identify. We evaluate the efficacy of the resulting factorizations for relative leveraging within regression tasks using medical imaging data. We also use the factorization on representations learned by popular deep networks, providing evidence of their ability to infer semantic relationships even when they are not explicitly trained to do so. We show that this algorithm can be used as an exploratory tool to improve the network architecture, and within numerous other settings in vision.