In the paper, we propose a deep nonsmooth nonnegative matrix factorization (nsNMF) network with semi-supervised learning for synthetic aperture radar (SAR) image change detection. In most of the existing deep-NMF-based models, the nonnegative matrix is linearly decomposed layer by layer, which may fail to characterize the nonlinearities in complex data. As such, a nonlinear deep nsNMF model is first built for learning hierarchical, nonlinear, and localized data representations. Meanwhile, in view of its good generalization performance and low computational complexity, extreme learning machine (ELM) is integrated into the nonlinear deep nsNMF model to construct a deep nsNMF network for satisfactory classification. More importantly, since it is difficult to acquire more labeled samples in practice, semi-supervised learning strategy is proposed to make use of partially labeled data for training. The learning process of the proposed network consists of pretraining stage and fine-tuning stage, in which the former pretrains all decomposed matrices layer by layer and the latter aims to reduce the total reconstruction error by using the mini-batch gradient descent algorithm. The experimental results on four pairs of SAR images demonstrate the effectiveness of the proposed method.

在本文中，我们提出了一种具有半监督学习的深非光滑非负矩阵分解（nsNMF）网络，用于合成孔径雷达（SAR）图像变化检测。在大多数现有的基于深度NMF的模型中，非负矩阵是逐层线性分解的，这可能无法描述复杂数据中的非线性。因此，首先建立了非线性深度nsNMF模型，用于学习分层，非线性和局部数据表示。同时，鉴于其良好的泛化性能和较低的计算复杂度，将极限学习机（ELM）集成到了非线性的深nsNMF模型中，以构建令人满意的分类的深nsNMF网络。更重要的是，由于实际上很难获取更多带标签的样本，提出了一种半监督学习策略，以利用部分标记的数据进行训练。拟议网络的学习过程包括预训练阶段和微调阶段，前者逐层对所有分解的矩阵进行预训练，而后者旨在通过使用小批量梯度下降算法来减少总的重构误差。在四对SAR图像上的实验结果证明了该方法的有效性。