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Abstract-Hyperspectral unmixing, the process of estimating a common set of spectral bases and their corresponding composite percentages at each pixel, is an important task for hyperspectral analysis, visualization and understanding. From an unsupervised learning perspective, this problem is very challenging-both the spectral bases and their composite percentages are unknown, making the solution space too large. To reduce the solution space, many approaches have been proposed by exploiting various priors. In practice, these priors would easily lead to some unsuitable solution. This is because they are achieved by applying an identical strength of constraints to all the factors, which does not hold in practice. To overcome this limitation, we propose a novel sparsity based method by learning a data-guided map to describe the individual mixed level of each pixel. Through this data-guided map, the p (0 < p < 1) constraint is applied in an adaptive manner. Such implementation not only meets the practical situation, but also guides the spectral bases toward the pixels under highly sparse constraint. What's more, an elegant optimization scheme as well as its convergence proof have been provided in this paper. Extensive experiments on several datasets also demonstrate that the data-guided map is feasible, and high quality unmixing results could be obtained by our method.

Hyperspectral Unmixing (HU) has received increasing attention in the past decades due to its ability of unveiling information latent in hyperspectral data. Unfortunately, most existing methods fail to take advantage of the spatial information in data. To overcome this limitation, we propose a Structured Sparse regularized Nonnegative Matrix Factorization (SS-NMF) method from the following two aspects. First, we incorporate a graph Laplacian to encode the manifold structures embedded in the hyperspectral data space. In this way, the highly similar neighboring pixels can be grouped together. Second, the lasso penalty is employed in SS-NMF for the fact that pixels in the same manifold structure are sparsely mixed by a common set of relevant bases. These two factors act as a new structured sparse constraint. With this constraint, our method can learn a compact space, where highly similar pixels are grouped to share correlated sparse representations. Experiments on real hyperspectral data sets with different noise levels demonstrate that our method outperforms the state-of-the-art methods significantly.

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Graph Convolutional Neural Networks (Graph CNNs) are generalizations of classical CNNs to handle graph data such as molecular data, point could and social networks. Current filters in graph CNNs are built for fixed and shared graph structure. However, for most real data, the graph structures varies in both size and connectivity. The paper proposes a generalized and flexible graph CNN taking data of arbitrary graph structure as input. In that way a task-driven adaptive graph is learned for each graph data while training. To efficiently learn the graph, a distance metric learning is proposed. Extensive experiments on nine graph-structured datasets have demonstrated the superior performance improvement on both convergence speed and predictive accuracy.

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