node classification and point cloud classification, which are discussed in order as follows.

Semi-supervised node classification
-----------------------------------

### Datasets

We test our method on three citation network datasets, *i.e.*, Citeseer, Cora and Pubmed [@sen2008collective]. The statistics of the datasets are summarized in Tab. \[tab:citation\_datasets\].

  **Dataset**   **Nodes**   **Edges**   **Classes**   **Features**   **Label Ratio**
  ------------- ----------- ----------- ------------- -------------- -----------------
  Citeseer      3,327       4,732       6             3,703          0.036
  Cora          2,708       5,429       7             1,433          0.052
  Pubmed        19,717      44,338      3             500            0.003

  : Summary of citation network datasets.[]{data-label="tab:citation_datasets"}

### Experimental settings

We follow the experimental setup of previous work [@yang2016revisiting; @Kipf2016SemiSupervisedCW; @velivckovic2017graph], and use the same data partition as in [@yang2016revisiting]. The features are $L2$-normalized before fed into the network. Since our method builds a dense adjacency matrix among all nodes, we sub-sample 10,000 nodes for Pubmed dataset to evaluate our model due to memory limitation. We set the number of JLGCN layers in our network to 2, and the number of hidden units in each layer to 16. For the dimension of the Mahalanobis distance metric matrix $\mathbf{R}\in \mathbb{R}^{K\times S}$, we set $S$ to 16 for both layers and initialize it randomly if not specified. We apply dropout with $p=0.5$ for both layer’s input, and use 