# Structural Hierarchy-Enhanced Network Representation Learning
## 4 Experiments
### Experimental Results  
**Main Results.** The main results are shown in Figures 3-5. We can have several observations. First, DeepWalk, node2 vec, and LINE enhanced by the proposed SHE can get significant performance improvement (i.e., red vs. blue curves) in both tasks of NC and LP across datasets. The improvement margin is around 60% and 30% for NC and LP (these two improvement percentages are obtained by averaging the differences of MAF and AUC scores between red and blue curves over all training percentages on Citeseer and Cora datasets for node classification and link prediction, respectively), respectively. Second, SHE can further outperform the state-of-the-art methods HARP and Marc while both have already led to apparent improvement from the original DeepWalk and node2 vec. We think the reason is that SHE not only leverages community knowledge, but also brings both fine-grained and coarse-grained information into the learning of different levels' NRLs. Besides, the superiority of SHE is more obvious in node classification than in link prediction. Third, when the training percentage increases, SHE is able to consistently outperform the other hierarchical NRL enhancement methods. Such results prove the effectiveness of SHE.  
Figure 3: Results on DeepWalk (DW) by varying the training percentage. The left and right columns are on node classification and link prediction, respectively. The top and bottom rows are using Citeseer and Cora datasets, respectively.  
The reason that the proposed SHE can outperform state-of-the-art methods is two-fold. On one hand, regarding constructing the hierarchy, HARP collapses nodes based on edge and star connections and Marc consider 3-cliques as super nodes. However, neither connection collapsing nor clique structure in both HARP and Marc can depict the semantic correlation between nodes, i.e., the community knowledge in networks. In our SHE, the obtained communities are used to form the hierarchy so that the fine-grained community information with respect to every node can be encoded into the learning of its embedding. On the other hand, different-level's node embeddings are learned independently in HARP and Marc. That said, higher-level NRL cannot utilize node embeddings to learn the hierarchy.  
Figure 4: Results on node2 vec (n2v) by varying the training percentage. The left and right columns are on node classification and link prediction, respectively. The top and bottom rows are using Citeseer and Cora datasets, respectively.  
Figure 5: Performance comparison on Pubmed data. Left: node classification by MAF scores. Right: link prediction by AUC scores. Compared methods include the combinations of node embedding methods DeepWalk (DW), node2 vec (n2v), and LINE with hierarchical NRL methods: original (original NRL method), HARP, Marc, and our proposed SHE.  
embeddings derived from lower-level NRL, and lower-level NRL cannot be enhanced by high-level coarse-grained semantics. Therefore, less informed node embeddings lead to worse performance, comparing to our SHE method that jointly learns and exploits node embeddings at different levels in the hierarchy.  
**Level Analysis.** We aim to understand how the number of hierarchy levels affects the performance improvement of the proposed SHE. We vary the number of levels as 0, 0-1, and 0-2, which indicate no hierarchy (NRL on the original network), only one additional level in the hierarchy, and adopting a three-level hierarchy, respectively. The results of level analysis are exhibited in Figure 6. We can find that the hierarchy with only one additional level is enough to bring significant performance improvement. In addition, the performance of the hierarchy with two additional levels is nearly the same as that with one additional level. We can draw an insight from such results. Using only the community knowledge obtained from the original network is sufficient for SHE to boost the effectiveness of NRL.