# Learning the Hierarchical Parts of Objects by Deep Non-Smooth Nonnegative Matrix Factorization

arXiv: https://arxiv.org/abs/1803.07226 · HTML: https://mlsanity.com/paper/1803.07226/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Mar 2018.

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

- [AdaLomo: Low-memory Optimization with Adaptive Learning Rate](https://mlsanity.com/paper/2310.10195/) (2023)
- [Hyperspectral Unmixing Based on Nonnegative Matrix Factorization: A Comprehensive Review](https://mlsanity.com/paper/2205.09933/) (2022)
- [Input Guided Multiple Deconstruction Single Reconstruction neural network models for Matrix Factorization](https://mlsanity.com/paper/2405.13449/) (2024)
- [A Generalized Deep Non-negative Matrix Factorization Approach for SAR Automatic Target Recognition](https://mlsanity.com/paper/2607.09779/) (2026)

## Abstract (arXiv)

Nonsmooth Nonnegative Matrix Factorization (nsNMF) is capable of producing more localized, less overlapped feature representations than other variants of NMF while keeping satisfactory fit to data. However, nsNMF as well as other existing NMF methods is incompetent to learn hierarchical features of complex data due to its shallow structure. To fill this gap, we propose a deep nsNMF method coined by the fact that it possesses a deeper architecture compared with standard nsNMF. The deep nsNMF not only gives parts-based features due to the nonnegativity constraints, but also creates higher-level, more abstract features by combing lower-level ones. The in-depth description of how deep architecture can help to efficiently discover abstract features in dnsNMF is presented. And we also show that the deep nsNMF has close relationship with the deep autoencoder, suggesting that the proposed model inherits the major advantages from both deep learning and NMF. Extensive experiments demonstrate the standout performance of the proposed method in clustering analysis.