# Learning nonnegative matrix factorizations from compressed data

arXiv: https://arxiv.org/abs/2409.04994 · HTML: https://mlsanity.com/paper/2409.04994/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 51 references that are in the map.
- First posted on arXiv 8 Sep 2024.

## Builds on (most cited first, 17 of 17)

- [Sketching as a Tool for Numerical Linear Algebra](https://mlsanity.com/paper/1411.4357/) (2014)
- [Frequent Directions : Simple and Deterministic Matrix Sketching](https://mlsanity.com/paper/1501.01711/) (2015)
- [Practical sketching algorithms for low-rank matrix approximation](https://mlsanity.com/paper/1609.00048/) (2016)
- [The Why and How of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1401.5226/) (2014)
- [A Statistical Perspective on Randomized Sketching for Ordinary Least-Squares](https://mlsanity.com/paper/1406.5986/) (2014)
- [Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review](https://mlsanity.com/paper/2205.09933/) (2022)
- [Lower Memory Oblivious (Tensor) Subspace Embeddings with Fewer Random Bits: Modewise Methods for Least Squares](https://mlsanity.com/paper/1912.08294/) (2019)
- [Block majorization-minimization with diminishing radius for constrained nonsmooth nonconvex optimization](https://mlsanity.com/paper/2012.03503/) (2020)
- [On a Guided Nonnegative Matrix Factorization](https://mlsanity.com/paper/2010.11365/) (2020)
- [Compressed Nonnegative Matrix Factorization is Fast and Accurate](https://mlsanity.com/paper/1505.04650/) (2015)
- [Randomized Nonnegative Matrix Factorization](https://mlsanity.com/paper/1711.02037/) (2017)
- [Fast and Secure Distributed Nonnegative Matrix Factorization](https://mlsanity.com/paper/2009.02845/) (2020)
- [COVID-19 Literature Topic-Based Search via Hierarchical NMF](https://mlsanity.com/paper/2009.09074/) (2020)
- [Sparseness-constrained Nonnegative Tensor Factorization for Detecting Topics at Different Time Scales](https://mlsanity.com/paper/2010.01600/) (2020)
- [Randomized Algorithms for Symmetric Nonnegative Matrix Factorization](https://mlsanity.com/paper/2402.08134/) (2024)
- [Compressed Factorization: Fast and Accurate Low-Rank Factorization of Compressively-Sensed Data](https://mlsanity.com/paper/1706.08146/) (2017)
- [Gaussian Compression Stream: Principle and Preliminary Results](https://mlsanity.com/paper/2011.05390/) (2020)

## Abstract (arXiv)

We propose a flexible and theoretically supported framework for scalable nonnegative matrix factorization. The goal is to find nonnegative low-rank components directly from compressed measurements, accessing the original data only once or twice. We consider compression through randomized sketching methods that can be adapted to the data, or can be oblivious. We formulate optimization problems that only depend on the compressed data, but which can recover a nonnegative factorization which closely approximates the original matrix. The defined problems can be approached with a variety of algorithms, and in particular, we discuss variations of the popular multiplicative updates method for these compressed problems. We demonstrate the success of our approaches empirically and validate their performance in real-world applications.