Spectral Unmixing is an important technique in remote sensing used to analyze hyperspectral images to identify endmembers and estimate abundance maps. Over the past few decades, performance of techniques for endmember extraction and fractional abundance map estimation have significantly improved. This article presents an ensemble model workflow called Autoencoder Graph Ensemble Model (AEGEM) designed to extract endmembers and fractional abundance maps. An elliptical kernel is applied to measure spectral distances, generating the adjacency matrix within the elliptical neighborhood. This information is used to construct an elliptical graph, with centroids as senders and remaining pixels within the geometry as receivers. The next step involves stacking abundance maps, senders, and receivers as inputs to a Graph Convolutional Network, which processes this input to refine abundance maps. Finally, an ensemble decision-making process determines the best abundance maps based on root mean square error metric. The proposed AEGEM is assessed with benchmark datasets such as Samson, Jasper, and Urban, outperforming results obtained by baseline algorithms. For the Samson dataset, AEGEM excels in three abundance maps: water, tree and soil yielding values of 0.081, 0.158, and 0.182, respectively. For the Jasper dataset, results are improved for the tree and water endmembers with values of 0.035 and 0.060 in that order, as well as for the mean average of the spectral angle distance metric 0.109. For the Urban dataset, AEGEM outperforms previous results for the abundance maps of roof and asphalt, achieving values of 0.135 and 0.240, respectively. Additionally, for the endmembers of grass and roof, AEGEM achieves values of 0.063 and 0.094.

Deep Nonnegative Matrix Factorization (deep NMF) has recently emerged as a valuable technique for extracting multiple layers of features across different scales. However, all existing deep NMF models and algorithms have primarily centered their evaluation on the least squares error, which may not be the most appropriate metric for assessing the quality of approximations on diverse datasets. For instance, when dealing with data types such as audio signals and documents, it is widely acknowledged that $\beta$-divergences offer a more suitable alternative. In this paper, we develop new models and algorithms for deep NMF using $\beta$-divergences. Subsequently, we apply these techniques to the extraction of facial features, the identification of topics within document collections, and the identification of materials within hyperspectral images.

The dictionary-aided sparse regression (SR) approach has recently emerged as a promising alternative to hyperspectral unmixing (HU) in remote sensing. By using an available spectral library as a dictionary, the SR approach identifies the underlying materials in a given hyperspectral image by selecting a small subset of spectral samples in the dictionary to represent the whole image. A drawback with the current SR developments is that an actual spectral signature in the scene is often assumed to have zero mismatch with its corresponding dictionary sample, and such an assumption is considered too ideal in practice. In this paper, we tackle the spectral signature mismatch problem by proposing a dictionary-adjusted nonconvex sparsity-encouraging regression (DANSER) framework. The main idea is to incorporate dictionary correcting variables in an SR formulation. A simple and low per-iteration complexity algorithm is tailor-designed for practical realization of DANSER. Using the same dictionary correcting idea, we also propose a robust subspace solution for dictionary pruning. Extensive simulations and real-data experiments show that the proposed method is effective in mitigating the undesirable spectral signature mismatch effects.