# Go Wider: An Efficient Neural Network for Point Cloud Analysis via Group Convolutions
## 4 Experiments
### Classification
#### 4.1.4 Ablation Study  
Finally, we tested our classification model using different hyperparameter settings on the ModelNet40 benchmark dataset [36].  
Table 2 shows the change in performance for different number of groups. In order to evenly split the feature channels, the initial input of the SGC unit shares the same edge feature \(\mathbf{e_{ij}}=(\mathbf{x_{i}},\mathbf{x_{i}}-\mathbf{x_{ij}})\) for all groups. The results highlight how the use of multiple groups (e.g., \(g=2,4\)) is beneficial with respect to having no grouping operation (i.e., \(g=1\)), as multiple groups help with capturing more information for a given complexity. However, when the group number becomes too large (e.g., \(g=8\)), the performance decreases. Hence, it is likely that the usefulness of the feature information becomes limited for each group when we split feature channels into many groups, leading to the fact that the neural network is unlikely to learn useful information from individual groups. The number of parameters and FLOPs only show a slight drop with respect to the number of groups because of Equations (1) and (2). The reason is that standard MLP operations (e.g., global feature extraction) and the fully-connected layers take almost 95% of the computational cost and are not influenced by the group number. The forward time also increases when the group number becomes larger, as more groups need more time to store corresponding features and parameters to the cache [32].  
As shown in Table 2, when we split feature channels into two groups and disable channel shuffling operation, the performance of overall accuracy drops significantly to 91.9%. We discuss the fact that, when we disable shuffling operation, center point features and corresponding neighbouring points features are captured, respectively, but still will concatenate before the max pooling layer. As a result, without shuffling, only the last MLP layer contributes to exploiting local features from both center points and corresponding neighbouring points.  
Table 3 shows different settings for the number of points, low-level edge features \(e_{ij}\), and grouping methods. It indicates that there is no improvement when we add neighbour features to represent local features, and edge features connecting center point to corresponding neighbourhood is beneficial for better results. In addition, \(k\)-NN searching slightly outperforms radius searching. We discuss the reason that \(k\)-NN searching is more efficient when the layout of dataset can be more or less treated as uniform distribution.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Groups** & **Shuffling** & **OA (\%)** & **Params** & **FLOPs** & **Time** \\ \hline \(g=1\) & \(\times\) & 91.8 & 1.20 M & 946 M & 15.3 ms \\ \(g=2\) & ✓ & 92.5 & 1.17 M & 770 M & 16.7 ms \\ \(g=2\) & \(\times\) & 91.9 & 1.17 M & 770 M & 16.7 ms \\ \(g=4\) & ✓ & 92.3 & 1.15 M & 692 M & 19.5 ms \\ \(g=8\) & ✓ & 91.5 & 1.14 M & 650 M & 22.7 ms \\ \hline \hline \end{tabular}
\end{table}
Table 2: Model complexity and accuracy for different groups.