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

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.