# A Lightweight Graph Neural Network Algorithm for Action Recognition Based on Self-Distillation
## 4 Experiments and Discussion
### Denser Representations  
There are 60 actions in NTU, which are hard to plot together; therefore, 8 actions are chosen for plotting. The chosen actions are drinking water, reading, taking off a shoe, making a phone call/answering phone, taking a selfie, sneezing/coughing, staggering and falling. The first six actions are daily activities, while the last two are actions that may be related to abnormal activities.  
To further evaluate the cluster qualities, three common cluster metrics are used to estimate their densities.  
* Davies-Bouldin [20]: The good clusters should have low intra-cluster distance and high inter-cluster distance, and therefore a small Davies-Bouldin index. The metric is defined as \[DB=\frac{1}{K}\sum_{i=1}^{K}\max_{j\
eq i}(\frac{\sigma_{i}+\sigma_{j}}{d(c_{ i},c_{j})}),\] (13) where \(K\) is the number of clusters, \(c_{i}\) is the centroid for the \(i\)-th cluster, \(\sigma_{i}\) is the average intra-class distance and \(d(c_{i},c_{j})\) is the distance between centroids \(c_{i},c_{j}\). It assumes a spherical shape with similar sizes and densities for each cluster.
* Dunn index [21; 22]: The clusters with a higher Dunn Index are more desirable. The formula is \[D=\frac{\min_{1\leq i\leq j\leq K}d(i,j)}{\max_{1\leq k\leq K}d^{\prime}(k)},\] (14) where \(d(i,j)\) is the inter-class distance between cluster \(C_{I},C_{J}\) and the distance between centroids \(c_{i},c_{j}\) and \(d^{\prime}(k)\) is the maximum distance between points in cluster \(C_{k}\). One issue for the Dunn Index is that if only one cluster is extremely stretched, while the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Block** & **ST 20** & **ST 12** & **ST 8** \\ \hline block 1 & 2.33\(\times\) & 3.43\(\times\) & **4.60\(\times\)** \\ block 2 & 1.42\(\times\) & 2.36\(\times\) & 2.90\(\times\) \\ block 3 & 1.00\(\times\) & 1.54\(\times\) & 2.03\(\times\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: The relative execution time for each sample compared with the block 3 of ST 20, which is the heaviest model. The ST 20, ST 12 and ST 8 denote ST-GCN 20, ST-GCN 12, and ST-GCN 8, respectively. Each sample has 300 frames.  
Figure 7: The percentage of the parameter size for each block compared with the corresponding whole backbone, where b1, b2, b3 denote block 1, block 2 and block 3, and ST 20, ST 12, ST 8 represent ST-GCN 20, ST-GCN 12 and ST-GCN 8, respectively. The parameter sizes of b1, b2, b3 differ because of the varied output dimensions shown in Figure 4. The size of b1 includes the preprocessing layer, and the size of b3 includes the FC layer.  
other clusters are tightly packed, the Dunn index will be low because of the max in the denominator.
* Silhouette coefficients [23]: The clusters with a high silhouette value are considered well clustered. The silhouette coefficients ranges in \([-1,1]\). Its formula is \[S(i)=\begin{cases}1-\frac{a(i)}{b(i)},\text{if }a(i)<b(i)\\ 0,\text{if }a(i)=b(i)\\ \frac{b(i)}{a(i)}-1,\text{if }a(i)=b(i)\end{cases}\] (15) where \(a(i)=\frac{1}{|C_{I}|-1}\sum\limits_{j\in C_{I},i\
eq j}d(i,j)\) and \(b(i)=\min\limits_{j\
eq I}\frac{1}{|C_{I}|}\sum\limits_{j\in C_{I}}d(i,j)\). \(|C_{I}|,|C_{J}|\) denote the number of points inside the clusters \(C_{I},C_{J}\). The geometric shape of the representation learned by self-distillation is estimated, and the differences of representations from different blocks are compared.