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Graph Convolution Networks (GCNs) have been shown to be very effective in utilizing pair-wise relationships across samples. They have been successfully applied to solve various machine learning problems in practice. In many applications, the construction of GCNs involves more than one layer. However, their generalization and stability analysis are limited. The main aim of this paper is to analyze GCNs with two layers. The formulation is based on transductive semi-supervised learning and the filtering is done in the eigen-domain. We show the uniform stability of the neural network and the convergence of the generalization gap to zero. The analysis of two-layer GCN is more involved than the single-layer case and requires some new estimates of the neural network's quantities. The analysis confirms the usefulness of GCNs. It also sheds light on the design of the neural network, for instance, how the data should be scaled to achieve the uniform stability of the learning process. Some experimental results on benchmark datasets are presented to illustrate the theory. [ABSTRACT FROM AUTHOR]

This paper proposes a novel inverse method based on the deep convolutional neural network (ConvNet) to extract snow's layer thickness and temperature via passive microwave remote sensing (PMRS). The proposed ConvNet is trained using simulated data obtained through conventional computational electromagnetic methods. Compared with the traditional inverse method, the trained ConvNet can predict the result with higher accuracy. Besides, the proposed method has a strong tolerance for noise. The proposed ConvNet composes three pairs of convolutional and activation layers with one additional fully connected layer to realize regression, i.e., the inversion of snow parameters. The feasibility of the proposed method in learning the inversion of snow parameters is validated by numerical examples. The inversion results indicate that the correlation coefficient ( R 2 ) ratio between the proposed ConvNet and conventional methods reaches 4.8, while the ratio for the root mean square error (RMSE) is only 0.18. Hence, the proposed method experiments with a novel path to improve the inversion of passive microwave remote sensing through deep learning approaches. [ABSTRACT FROM AUTHOR]

Recently, deep-learning-based denoising methods for hyperspectral images (HSIs) have been comprehensively studied and achieved impressive performance because they can effectively extract complex and nonlinear image features. Compared with deep-learning-based methods, the nonlocal similarity-based denoising methods are more suitable for images containing edges or regular textures. We propose a powerful HSI denoising method, termed non-local 3-D convolutional neural network (NL-3DCNN), combining traditional machine learning and deep learning techniques. NL-3DCNN exploits the high spectral correlation of an HSI using subspace representation, and the corresponding representation coefficients are termed eigenimages. The high spatial correlation in eigenimages is exploited by grouping nonlocal similar patches, which are denoised by a 3-D convolutional neural network. The numerical and graphical denoising results of the simulated and real data show that the proposed method is superior to the state-of-the-art methods. [ABSTRACT FROM AUTHOR]