# Stratified-NMF for Heterogeneous Data

arXiv: https://arxiv.org/abs/2311.10789 · HTML: https://mlsanity.com/paper/2311.10789/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 29 references that are in the map.
- First posted on arXiv 17 Nov 2023.

## Builds on (most cited first, 5 of 5)

- [Handling Incomplete Heterogeneous Data using VAEs](https://mlsanity.com/paper/1807.03653/) (2018)
- [The Why and How of Nonnegative Matrix Factorization](https://mlsanity.com/paper/1401.5226/) (2014)
- [Semi-supervised NMF Models for Topic Modeling in Learning Tasks](https://mlsanity.com/paper/2010.07956/) (2020)
- [On a Guided Nonnegative Matrix Factorization](https://mlsanity.com/paper/2010.11365/) (2020)
- [Sparseness-constrained Nonnegative Tensor Factorization for Detecting Topics at Different Time Scales](https://mlsanity.com/paper/2010.01600/) (2020)

## Built on by (most cited first, 1 of 1)

- [Stratified Non-Negative Tensor Factorization](https://mlsanity.com/paper/2411.18805/) (2024)

## Abstract (arXiv)

Non-negative matrix factorization (NMF) is an important technique for obtaining low dimensional representations of datasets. However, classical NMF does not take into account data that is collected at different times or in different locations, which may exhibit heterogeneity. We resolve this problem by solving a modified NMF objective, Stratified-NMF, that simultaneously learns strata-dependent statistics and a shared topics matrix. We develop multiplicative update rules for this novel objective and prove convergence of the objective. Then, we experiment on synthetic data to demonstrate the efficiency and accuracy of the method. Lastly, we apply our method to three real world datasets and empirically investigate their learned features.