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

Jul 16, 2026

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Proposes a generalized deep non-negative matrix factorization (G-DNMF) method to improve the interpretability and accuracy of deep-learning features for synthetic aperture radar (SAR) automatic target recognition. Unlike existing layer-by-layer DNMF that can accumulate errors and fall into local optima as layers increase, G-DNMF removes layer-by-layer decomposition, targets global optimality, and derives parameter update rules via Lagrangian multipliers. Experiments on MSTAR and OpenSARship verify improved stability, recognition performance, additive multi-layer feature understanding, and clearer reconstruction-based interpretability.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages13

Reading Time33 min

Introduction

Deep learning and interpretability challenges in SAR ATR

Deep non-negative matrix factorization and layered feature modeling

Sparsity-regularized DNMF variants in prior work

arXiv :2607 .09779v 1 [ cs .CV] 8 Jul 2026 A Generalized Deep Non-negative Matrix Factorization Approach for SAR Automatic Target Recognition Yunhong Zhang, Changjie Cao*, Member, IEEE, Zhongli Zhou, Bingli Liu, Zongjie Cao, Member, IEEE, Zongyong Cui, Member, IEEE, Ying Yang Abstract—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. Index Terms—Deep Non-negative Matrix Factorization, Automatic Target Recognition, Lagrangian Multiplier, Synthetic Aperture Radar ~~ ~~ ✦ ~~ ~~ 1 INTRODUCTION S YNTHETIC cover and aperture radar(SAR) can penetrate cloud operate continuously regardless of time or weather conditions, delivering essential data for earth observation [1–3] . Among the many applications of SAR, the automatic target recognition (ATR) technology is the critical mean of SAR image interpretation [4–6] . In general, the performance of SAR ATR methods is heavily contingent upon the selection of data representation strategy. The conventional approach to acquiring SAR target data representation is through feature extraction, which involves the design of elaborate algorithms for implementing transformations on SAR target data in support of ATR tasks [7–9] . Among them, deep learning algorithms have become a important area of research by progressively constructing feature representations with discriminability and generalization capabilities [10–12], leveraging multi-layer representations of target samples [13–15] . However, the security implications of applying deep learning methods, such as convolutional neural networks (CNNs), to SAR ATR have become increasingly concerning due to lack transparency in internal logic processes [16– 19] . Specifically, SAR imagery pixel values are inherently This work was supported by the National Science and Technology Major Projects of China(2025ZD1008203), the National Natural Science Foundation of China(42572389), the Sichuan Natural Science Foundation(2026NSFSC0238) positive, whereas CNNs-extracted features can take on both positive and negative values. These features clearly do not align with the human understanding of SAR imagery content, which is based on the hierarchical additive understanding of nonlinear transformation. Therefore, conventional CNN algorithms often lack transparency in explaining their fe

FAQs

What problem does G-DNMF address in SAR automatic target recognition?

It targets the low interpretability of deep learning methods for extracting multilayer features from SAR targets, and it also addresses error accumulation and local optima caused by existing layer-by-layer DNMF strategies as the number of layers grows.

How does G-DNMF differ from existing DNMF approaches?

G-DNMF discards the layer-by-layer decomposition strategy, aims for global optimality, and derives update rules for parameters using the Lagrangian multiplier method.

What evidence supports G-DNMF’s effectiveness and interpretability?

Experiments provide feature images extracted from each layer and reconstructed original images, demonstrating a pure additive understanding of multilayer features. Results on MSTAR and OpenSARship show improved stability and recognition performance over existing DNMF algorithms and derivatives.

Jul 16, 2026

Upload by Violet