\end{split}$$ Altogether, the network is trained end-to-end by minimizing the following joint loss function $$L = L_{local} + \gamma L_{global},$$ where $\gamma$ ($\gamma=1$) is the proportion of two part errors.

Experiments
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In this section, we first investigate how some key parameters affect the performance of L2G-AE in the shape classification task on ModelNet10 [@wu20153d]. Then, an ablation study is done to show the effectiveness of each module in L2G-AE. Finally, we further evaluate the performances of L2G-AE in multiple applications including 3D shape classification, 3D shape retrieval and point cloud upsampling.

Network Configuration
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In L2G-AE, we first sample $M = 256$ points as the centroids of local regions by FPS. Then, around each centroid, a kNN searching algorithm selects $T=4$ scale areas with $[K_1=16, K_2=32, K_3=64, K_4=128]$ points inside each area. In the multi-level feature propagation process, we initialize the feature dimension $C = M/8 = 32$ and $D = 256$. The encoder learns a 1024-dimension global feature for the input point cloud through hierarchical feature extraction. Similarly, the decoder hierarchically reconstructs local scales and global point cloud. In the RNN decoding layer, we adopt LSTM as the default RNN cell with hidden state dimension $h = D 