# A Generalized Deep Non-negative Matrix Factorization Approach for SAR Automatic Target Recognition

arXiv: https://arxiv.org/abs/2607.09779 · HTML: https://mlsanity.com/paper/2607.09779/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 46 references that are in the map.
- First posted on arXiv 8 Jul 2026.

## Builds on (most cited first, 12 of 12)

- [A Survey on Neural Network Interpretability](https://mlsanity.com/paper/2012.14261/) (2020)
- [On Interpretability of Artificial Neural Networks: A Survey](https://mlsanity.com/paper/2001.02522/) (2020)
- [Transparency of Deep Neural Networks for Medical Image Analysis: A Review of Interpretability Methods](https://mlsanity.com/paper/2111.02398/) (2021)
- [Deep Learning Meets SAR](https://mlsanity.com/paper/2006.10027/) (2020)
- [A deep matrix factorization method for learning attribute representations](https://mlsanity.com/paper/1509.03248/) (2015)
- [Truncated Cauchy Non-negative Matrix Factorization](https://mlsanity.com/paper/1906.00495/) (2019)
- [Spectral Unmixing of Hyperspectral Imagery using Multilayer NMF](https://mlsanity.com/paper/1408.2810/) (2014)
- [Distributionally Robust and Multi-Objective Nonnegative Matrix Factorization](https://mlsanity.com/paper/1901.10757/) (2019)
- [Quadratic Matrix Factorization with Applications to Manifold Learning](https://mlsanity.com/paper/2301.12965/) (2023)
- [Tackling Interpretability in Audio Classification Networks with Non-negative Matrix Factorization](https://mlsanity.com/paper/2305.07132/) (2023)
- [Learning the Hierarchical Parts of Objects by Deep Non-Smooth Nonnegative Matrix Factorization](https://mlsanity.com/paper/1803.07226/) (2018)
- [Sparse Deep Nonnegative Matrix Factorization](https://mlsanity.com/paper/1707.09316/) (2017)

## Abstract (arXiv)

The deep nonnegative matrix factorization (DNMF) technique is proposed to address the low interpretability of deep learning-based methods in extracting multilayer features from synthetic aperture radar (SAR) target samples. However, existing DNMF methods employ a layer-by-layer decomposition strategy, which is prone to causing error accumulation and local optimum, thereby hindering a consistent improvement in recognition accuracy as the number of layer increases. In this paper, a robust multilayer feature extraction method, termed generalized deep non-negative matrix factorization (G-DNMF), is proposed to address the above challenges in SAR automatic target recognition (ATR). The G-DNMF aims global optimality and derives the update rules for each parameter using lagrangian multiplier method. The new update formula indicates that both the DNMF method based on the encoding matrix and the mixing matrix are special cases of the proposed method, theoretically demonstrating the universality of proposed method. In general, the proposed method discards the layer-by-layer decomposition strategy, thereby effectively mitigating the risk of local optima and eliminating error accumulation, leading to a significant improvement in DNMF's multi-layer feature extraction capability. The experimental results, by presenting the feature images extracted from each layer by G-DNMF and the reconstructed original images, verified the proposed method's pure additive understanding of multi-layer features and demonstrated its interpretability. The experimental results based on MSTAR and OpenSARship datasets show that G-DNMF outperforms existing DNMF algorithms and their derivatives in terms of stability and recognition performance.