Hyperspectral remote sensing technology, as a new type of earth observation technology, provides rich spectral information of features and can identify and finely classify feature targets. A single pixel in hyperspectral images contains multiple features as limited by the spatial resolution. As a result, the mixed pixels become widespread. Ultimately, the accuracy of pixel-level applications is difficult to improve. Nonnegative Matrix Factorization (NMF), with its clear physical meaning, lays the foundation for the development of unsupervised linear spectral unmixing. Thus, traditional NMF often uses Euclidean distance as a similarity measure method. On the one hand, hyperspectral data have manifold distribution. Thus, simple linear measurement between two points cannot accurately represent the distance between data. This problem makes the sample internal features weakly correlated, which results in the NMF algorithm having an inaccurate prediction of the high-dimensional spatial inaccurate prediction of the translational noise in high-dimensional space. On the other hand, the objective function constructed based on this method ignores the correlation characteristics in the image space, which inhibits the performance of the algorithm.Method Considering the correlation between data manifolds and features, this study proposes a nonnegative matrix factorization unmixing algorithm based on Sinkhorn distance and graph regularization constraint (SDGNMF). On the basis of fully exploiting the advantages of EMD, the algorithm imposes entropy regularization constraint on EMD, improves EMD to Sinkhorn distance, and takes it as the standard of measuring error, which effectively reduces the computational complexity. In addition, EMD with entropy regularization constraint, that is, the representation of the model by Sinkhorn distance, can better model the relationship between different dimensional features and fully utilize the correlation of features. In particular, this study introduces the graph regularity constraint based on the Sinkhorn distance to further characterize the manifold structure of data. Compared with the unmixing model constructed by Euclidean distance, SDGNMF is relatively insensitive to the noise in hyperspectral data and can better extract the internal structural information of the data, which improves the unmixing accuracy.Result An experiment was conducted on simulated and real datasets. Experimental results prove that the proposed algorithm proposed has achieved excellent subspace learning results and has good robustness. Compared with several other algorithms, SDGNMF can retain the similar structure after iteration. The correlation between the endmember features is also fully considered in SDGNMF. Thus, the similar substances distributed in adjacent regions can be separated. Therefore, SDGNMF can better display the details of local abundance and obtain a more realistic and perfect abundance map.Conclusion In general, the proposed unmixing model can overcome noise and consider the correlation of features and data manifold structure simultaneously. Experimental results show that the proposed algorithm can effectively improve the unmixing accuracy of most hyperspectral remote sensing data, especially those with high feature correlation. However, the proposed algorithm has high computational complexity. In addition, the algorithm only considers the prior knowledge of abundance. Therefore, future work will focus on solving these problems.

hyperspectral unmixing;nonnegative matrix factorization (NMF);Sinkhorn distance;entropy regularization;graph regularization