# Hierarchical and Unsupervised Graph Representation Learning with Loukas's Coarsening
## 5 Evaluation
### Supervised Classification
#### 5.2.4 Results  
We note that get substantial improvements over Graph2 Vec baseline for many datasets, more specifically when the graph are big and carry high dimensional features.  
For FRANKENSTEIN, if we connect a randomly initialized two-layer CNN to the input of the model for better feature extraction, the results are improved and reach \(66.5\pm 0.4\%\) which is a noticeable improvement. Thanks to the end-to-end differentiability of the model, the CNN is trained with backpropagation, benefiting from the unsupervised loss signal.  
On the notably difficult REDDIT-B and REDDIT-5K we reach high results, comparable to SOTA. The coarsening operation is beneficial to these datasets, considering the size of the graphs. On datasets with smaller graphs, the results are less significant.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**DATASET** & **\#graphs \#nodes** & \begin{tabular}{c} **HG2V** \\ **(Ours)** \\ \end{tabular} & **Graph2 Vec** & **Infograph** & \begin{tabular}{c} **DiffPool** \\ **(Supervised)** \\ \end{tabular} & \begin{tabular}{c} **GIN** \\ **(Supervised)** \\ \end{tabular} & \begin{tabular}{c} **MinCutPool** \\ **(Supervised)** \\ \end{tabular} & \
\begin{tabular}{c} **WL-OA** \\ **(Kernel)** \\ \end{tabular} &
\begin{tabular}{c} **WWL** \\ **(Kernel)** \\ \end{tabular} \\ \hline IMDB-m & 1500 & 13 & \(47.9\pm 1.0\) & \(\mathbf{50.4\pm 0.9}\) & \(49.6\pm 0.5\) & \(45.6\pm 3.4\) & \(48.5\pm 3.3\) & ✗ & ✗ & ✗ \\ \hline PTC\_FR & 351 & 15 & \(\mathbf{67.5\pm 0.5}\) & \(60.2\pm 6.9\) & ✗ & ✗ & ✗ & ✗ & \(63.6\pm 1.5\) & ✗ \\ \hline FRANK & 4337 & 17 & \(\mathbf{65.3\pm 0.7}\) & \(60.4\pm 1.3\) & ✗ & ✗ & ✗ & ✗ & ✗ & ✗ \\ \hline MUTAG & 188 & 18 & \(81.8\pm 1.8\) & \(83.1\pm 9.2\) & \(\mathbf{89.0\pm 1.1}\) & ✗ & ✗ & ✗ & \(84.5\pm 1.7\) & \(87.3\pm 1.5\) \\ \hline IMDB-b & 1000 & 20 & \(71.3\pm 0.8\) & \(63.1\pm 0.1\) & \(73.0\pm 0.9\) & \(68.4\pm 3.3\) & \(71.2\pm 3.9\) & ✗ & ✗ & \(\mathbf{74.4\pm 0.8}\) \\ \hline NCI1 & 4110 & 30 & \(76.3\pm 0.8\) & \(73.2\pm 1.8\) & ✗ & \(76.9\pm 1.9\) & \(80.0\pm 1.4\) & ✗ & \(\mathbf{86.1\pm 0.2}\) & \(85.8\pm 0.2\) \\ \hline NCI109 & 4127 & 30 & \(75.6\pm 0.7\) & \(74.3\pm 1.5\) & ✗ & ✗ & ✗ & ✗ & \(\mathbf{86.3\pm 0.2}\) & ✗ \\ \hline ENZYMES & 600 & 33 & \(66.0\pm 2.5\) & \(51.8\pm 1.8\) & ✗ & \(59.5\pm 5.6\) & \(59.6\pm 4.5\) & ✗ & \(59.9\pm 1.1\) & \(\mathbf{73.3\pm 0.9}\) \\ \hline PROTEINS & 1113 & 39 & \(75.7\pm 0.7\) & \(73.3\pm 2.0\) & ✗ & \(73.7\pm 3.5\) & \(73.3\pm 4.0\) & \(76.5\pm 2.6\) & \(76.4\pm 0.4\) & \(\mathbf{77.9\pm 0.8}\) \\ \hline MNIST & 10000 & 151 & \(\mathbf{96.1\pm 0.2}\) & \(56.3\pm 0.7\) & ✗ & ✗ & ✗ & ✗ & ✗ \\ \hline D\&D & 1178 & 284 & \(79.2\pm 0.8\) & \(58.6\pm 0.1\) & ✗ & \(75.0\pm 3.5\) & \(75.3\pm 2.9\) & \(\mathbf{80.8\pm 2.3}\) & \(79.2\pm 0.4\) & \(79.7\pm 0.5\) \\ \hline REDDIT-b & 2000 & 430 & \(91.2\pm 0.6\) & \(75.7\pm 1.0\) & \(82.5\pm 1.4\) & \(87.8\pm 2.5\) & \(89.9\pm 1.9\) & \(\mathbf{91.4\pm 1.5}\) & \(89.3\) & ✗ \\ \hline DLA & 1000 & 501 & \(\mathbf{99.9\pm 0.1}\) & \(77.2\pm 2.5\) & ✗ & ✗ & ✗ & ✗ & ✗ \\ \hline REDDIT-5K & 4999 & 509 & \(55.5\pm 0.7\) & \(47.9\pm 0.3\) & \(53.5\pm 1.0\) & \(53.8\pm 1.4\) & \(\mathbf{56.1\pm 1.7}\) & ✗ & ✗ & ✗ \\ \hline \hline \end{tabular}
\end{table}
Table 2: Accuracy on classification tasks. HG2V is trained over both _TrainVal+Test_ splits, without using labels due to its unsupervised nature. Model selection of C-SVM and hyper-parameters of HG2V have been done with 5-cross validation over _TrainVal_ split. We report on the accuracy over the _Test_ split, averaged over 10 runs, and with standard deviation. Unavailable result marked as \(X\).