# Properties of Vector Embeddings in Social Networks
## 3 Related Work
### Techniques for Inspecting Embeddings  
Graph embeddings usually create vectors of several 100 dimensions per node in the graph. While eigenvalue based decomposition methods give some formal guarantees on the retained network properties, random-walk based methods are stochastic in nature and depend heavily on hyper-parameter settings. Therefore, analyzing the retained graph properties requires either applying the embeddings to particular graph analysis tasks, like node classification, clustering, community detection or link prediction, or to visualize structural relationships. For example, if two nodes \(u\) and \(v\) are directly connected in the graph, they should appear close to each other when in a visualized embedding space. In this section, we review different methods to inspect graph embeddings in order to motivate the development of our own approach.  
* **Visualization:** To gain insight into binary relationships between objects, the relations are often coded into a graph, which is then visualized. The visualization is usually split in the layout and the drawing phase. The layout is a mapping of graph elements to points in \(\mathbb{R}^{d}\). The drawing assigns graphical shapes to the graph elements and draws them using the positions computed in the layout [30]. The effectiveness of DeepWalk is illustrated by visualizing the Zachary's Karate Club network [12]. The authors of LINE visualized the DataBase systems and Logic Programming (DBLP) co-authorship network, and showed that LINE is able to cluster together authors in the same field. Structural Deep Network Embedding (SDNE) [31] was applied on a 20-Newsgroup document similarity network to obtain clusters of documents based on topics.
* **Network Compression:** The idea in network compression is to reconstruct the graph with a smaller number of edges [23]. Graph embedding can also be interpreted as a compression of the graph. [PERSON] et al. [31] and [PERSON] et al. [32] tested this hypothesis explicitly by reconstructing the original graph from the embedding and evaluating the reconstruction error. They show that a low-dimensional representation for each node suffices to reconstruct the graph with high precision.
* **Classification:** Often in social networks, a fraction of nodes are labeled which indicate interests, beliefs, or demographics, but the rest are missing labels. Missing labels can be inferred using the labeled nodes through links in the network. The task of predicting these missing labels is also known as node classification. Recent work [10; 12; 14; 31] has evaluated the predictive power of embedding on various information networks including language, social, biology and collaboration graphs. The authors in [15] predict the social circles for a new node added into the network.
* **Clustering:** Graph clustering in social networks aim to detect social communities. In [33], the authors evaluated the effectiveness of embedding representations of DeepWalk and LINE on network clustering. Both approaches showed nearly the same performance.
* **Link Prediction:** Social networks are constructed from the observed interactions between entities, which may be incomplete or inaccurate. The challenge often lies in predicting missing interactions. Link prediction refers to the task of predicting either missing interactions or links that may appear in the future in an evolving network. Link prediction is used to predict probable friendships, which can be used for recommendation and lead to a more satisfactory user experience. [PERSON] et al. [34] used link prediction to evaluate node2 vec and LINE. Node2 vec outperforms LINE in terms of area under the Receiver Operating Characteristic (ROC) curve.