have been receiving increasing attention as a powerful tool for irregularly structured data on graphs, such as citation networks, social networks and 3D point clouds. The construction of an appropriate graph topology plays a critical role in GCNNs for efficient feature learning. In settings where the graph is inaccurate or even not readily available, it is necessary to infer or learn a graph topology from data before it is used for guiding graph convolution in GCNNs.

Most of the previous studies construct underlying graphs from data empirically, such as $k$-Nearest-Neighbor ($k$-NN) graphs [@wang2019dgcnn; @te2018rgcnn], which may lead to sub-optimal solutions. Few methods exploit *graph learning* for optimized representation [@Jiang2018GraphLN; @li2018adaptive; @shi2018non; @li2019spatio], which learns a fixed and shared graph for all instances, or an individual graph for each instance, or a combination of shared and individual graphs. However, only *one fixed* graph is learned and applied to all layers of the entire network, which may not well capture the underlying structure of node features in different layers dynamically.

Extending on these previous studies, we propose a Joint Learning Graph Convolutional Network (JLGCN), which exploits *dynamic* learning of graphs and node features *jointly* in GCNNs. In particular, we optimize an underlying 