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Hyperspectral unmixing is an essential research topic for spectral data analysis due to the existence of mixed pixels. Recently, many methods based on sparse nonnegative matrix factorization (NMF) have been widely used for unmixing by incorporating similarity preserving. However, most of them conduct the similarity learning and unmixing by using two separate steps, which may lead to the case that the learned similarity matrix is not the optimal one for unmixing. Thus, the performance of unmixing would be influenced and become undesirable. To alleviate this problem, we propose an adaptive relationship preserving-based sparse NMF (ARP-NMF) for hyperspectral unmixing. Typically, we regard similarity learning and unmixing as an alternative optimization process. During this process, the learned similarity weights and unmixing results can be mutually improved. Thus, our proposed method can learn the optimal similarity weights for unmixing and obtain better generalization ability for different hyperspectral images than traditional methods. Moreover, by using the spectral and spatial local structure, our ARP-NMF method effectively preserves structure consistency between pixels and abundances. Experimental results both on the synthetic data and the real data reveal that our proposed method outperforms several representative sparse NMF-based methods. [ABSTRACT FROM AUTHOR]

Nonnegative matrix factorization (NMF) is one of the most popular data representation methods in the field of computer vision and pattern recognition. High-dimension data are usually assumed to be sampled from the submanifold embedded in the original high-dimension space. To preserve the locality geometric structure of the data, k-nearest neighbor (k-NN) graph is often constructed to encode the near-neighbor layout structure. However, k-NN graph is based on Euclidean distance, which is sensitive to noise and outliers. In this article, we propose a refined-graph regularized nonnegative matrix factorization by employing a manifold regularized least-squares regression (MRLSR) method to compute the refined graph. In particular, each sample is represented by the whole dataset regularized with ℓ2-norm and Laplacian regularizer. Then a MRLSR graph is constructed based on the representative coefficients of each sample. Moreover, we present two optimization schemes to generate refined-graphs by employing a hard-thresholding technique. We further propose two refined-graph regularized nonnegative matrix factorization methods and use them to perform image clustering. Experimental results on several image datasets reveal that they outperform 11 representative methods. [ABSTRACT FROM AUTHOR]

Hyperspectral unmixing (HU) is regarded as an indispensable preprocessing procedure for many field of spectral data analysis because of the existence of mixed pixels. However, the unmixing algorithms are implemented under the presupposition of special mixing models. In other words, any unmixing algorithm only works on a special mixing model of the spectra. This leads to low generalization performance of most unmixing algorithms. To mitigate this problem, a robust unmixing method is proposed, which exploits dual views with adaptive weights for HU (AwDvHU). The proposed method utilizes multi-kernel learning to construct a high-dimensional space that can reflect the nonlinear interaction between spectra optimally. Then, through fusing the unmixing object of original data and the mapped high-dimensional features, the AwDvHU method takes full advantage of the complementary characteristics of features in dual views. Moreover, the AwDvHU method automatically learns the weights for dual views according to the importance of different feature spaces. Its effectiveness in unmixing is verified by experimental results both on the synthetic and real data. [ABSTRACT FROM AUTHOR]