(Local), global loss only (Global) and two losses together (Local + Global) are listed. The local loss function is very important in capturing local patterns of point clouds. And the two loss functions together can further enhance the classification performances of our neural network. In addition, Figure \[fig:loss\_compare\] shows the reconstruction results of our L2G-AE with only local loss and only global loss, respectively. From the results of the reconstructed point clouds, L2G-AE can reconstruct the input point cloud with only part of the joint loss function. In particular, the local reconstructed result in Figure \[fig:loss\_compare\] is a dense point cloud.

   Metric    Local   Global   Local+Global
  --------- ------- -------- --------------
   Acc (%)   94.71   92.84     **95.37**

  : The effects of the two loss functions $L_{local}$ and $L_{global}$ on ModelNet10.[]{data-label="table:loss"}

       Methods        Supervised     MN40        MN10     
  ------------------ ------------ ----------- ----------- --
       PointNet          Yes         89.20         -      
      PointNet++         Yes         90.70         -      
   ShapeContextNet       Yes         90.00         -      
        Kd-Net           Yes         91.80       94.00    
        KC-Net           Yes         91.00       94.4     
       PointCNN          Yes         92.20         -      
        DGCNN            Yes         92.20         -      
        SO-Net           Yes         90.90       94.1     
    Point2Sequence       Yes         92.60       95.30    
       MAP-VAE            No         90.15       94.82    
         LGAN             No         85.70       95.30    
      LGAN(MN40)          No         87.27       92.18    
      FoldingNet          No         88.40       94.40    
   FoldingNet(MN40)       No         84.36       91.85    
         Our              No       **90.64**   **95.37**  

  : The comparison of 