# A Novel Equivariant Self-Supervised Vector Network for Three-Dimensional Point Clouds
## 4 Experiment
### Few-Shot Learning  
In order to reflect the powerful learning ability of our network, we conduct experiments with small samples on the ModelNet40 dataset. We follow the previous work and adopt the \(n\)-way, \(m\)-shot setting, where \(n\) is the number of randomly selected categories from the dataset and \(m\) is the number of randomly collected objects from the \(n\) classes. At training time, only these objects are used for training, i.e., there are only \(n\times m\) training samples. Then, in the subsequent testing session, we randomly select 20 unlearned objects from \(n\) classes for evaluation.  
Table 3 shows the test results of different settings in \(n\in\{5,10\}\) and \(m\in\{10,20\}\). Meanwhile, we perform 10 independent experiments for each setting, following the standard protocol, and report the average accuracy with standard deviation. Due to the excellent transfer capability of self-supervised learning, our network achieves significant improvements in accuracy and greatly reduced bias across three different settings. This indicates that our network can achieve the performance of other networks trained on a larger samples with only a small number of data. Furthermore, we further validate the network performance in a rotation scenario. The vector neurons in the network give it excellent rotation equivariance, which makes it lose only a small amount of accuracy when processing rotated data. This result fully proves that our network is extremely robust to rotated point clouds.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Methods** & **i** & **z** & **SO(3)** \\ \hline \multirow{6}{*}{Traditional network} & Point-BERT [19] & 84.1 & - & - \\  & Point-MAE [20] & 84.2 & - & - \\  & GPSFormer [42] & **85.4** & - & - \\  & ShellNet [37] & 82.8 & - & - \\  & PointNet [38] & 80.4 & 80.4 & 62.3 \\  & PointNet++ [16] & 81.9 & 81.9 & 76.7 \\  & DGCNN [17] & 82.4 & 82.3 & 78.6 \\ \hline \multirow{6}{*}{Equivariant network} & GC-Conv [29] & - & - & 77.3 \\  & VN-PointNet [15] & - & - & 72.8 \\ \cline{1-1}  & VN-DGCNN [15] & - & - & 81.4 \\ \cline{1-1}  & Ours & 84.8 & **82.8** & **81.5** \\ \hline \hline \end{tabular}
\end{table}
Table 2: Segmentation on ShapeNetPart. The results are reported in terms of the overall average category mean IoU (%) over 16 categories in three train/test scenarios. We bolded the results of the best performing networks.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Rotation** & **Methods** & **5-Way, 10-Shot** & **5-Way, 20-Shot** & **10-Way, 10-Shot** & **10-Way, 20-Shot** \\ \hline \multirow{6}{*}{i} & DGCNN-rand [17] & 31.6 \(\pm\) 2.8 & 40.8 \(\pm\) 4.6 & 19.9 \(\pm\) 2.1 & 16.9 \(\pm\) 1.5 \\  & DGCNN-Oco [17] & 90.6 \(\pm\) 2.8 & 92.5 \(\pm\) 1.9 & 82.9 \(\pm\) 1.3 & 86.5 \(\pm\) 2.2 \\  & Transformer-rand [19] & 87.8 \(\pm\) 5.2 & 93.3 \(\pm\) 4.3 & 84.6 \(\pm\) 5.5 & 89.4 \(\pm\) 6.3 \\  & Transformer-Oco [19] & 94.0 \(\pm\) 3.6 & 95.9 \(\pm\) 2.3 & 89.4 \(\pm\) 5.1 & 92.4 \(\pm\) 4.6 \\  & Point-BERT [19] & 94.6 \(\pm\) 3.1 & 96.3 \(\pm\) 2.7 & 91.0 \(\pm\) 5.4 & 92.7 \(\pm\) 5.1 \\  & Point-MAE [20] & 96.3 \(\pm\) 2.5 & 97.8 \(\pm\) 1.8 & **92.6 \(\pm\) 4.1** & 95.0 \(\pm\) 3.0 \\  & GPSFormer [42] & 90.2 \(\pm\) 2.3 & 91.7 \(\pm\) 1.1 & 82.5 \(\pm\) 2.1 & 86.1 \(\pm\) 3.5 \\  & Ours & **99.8 \(\pm\) 0.4** & **99.0 \(\pm\) 0.0** & 88.3 \(\pm\) 0.9 & **95.5 \(\pm\) 0.4** \\ \hline z & Ours & 96.8 \(\pm\) 1.3 & 96.4 \(\pm\) 0.7 & 81.3 \(\pm\) 1.1 & 91.2 \(\pm\) 0.6 \\ \hline SO(3) & Ours & 94.7 \(\pm\) 0.8 & 94.3 \(\pm\) 0.7 & 78.5 \(\pm\) 1.1 & 91.6 \(\pm\) 0.5 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Few-shot object classification on ModelNet40. We conduct 10 independent experiments for each setting and report mean accuracy (%) with standard deviation. We bolded the results of the best performing networks.