$\mathbf{f}$ as an optimization problem, which minimizes a weighted sum of the GLR and cross-entropy. We set this objective as the loss function of the proposed JLGCN to guide network model optimization, which employs a localized first-order approximation of spectral graph convolution as in [@Kipf2016SemiSupervisedCW]. Further, the learned graph at the previous layer is added to that of the current layer for multi-level feature learning. The proposed JLGCN can be integrated into any GCNN architecture for applications such as node classification and graph classification. To validate the effectiveness of the proposed JLGCN, we apply it to semi-supervised learning for citation networks and 3D point cloud learning problems. Extensive experimental results demonstrate the superiority and robustness of JLGCN compared with state-of-the-art methods on four datasets even with a small model size.

Our contributions can be summarized as follows:

-   We propose joint learning of underlying graphs and node features at each layer of a GCNN, which captures pairwise similarities of node features dynamically.

-   We cast the graph learning problem as distance metric learning with the Mahalanobis distance deployed. We further decompose the distance metric into a low-dimensional matrix for efficient implementation, which is optimized from both the GLR and cross 