Node Embedding

Definition

The goal of node embedding is finding an encoder mapping nodes into embedding space preserving the similarity of the nodes. ${\mathbf{z}}_u=\mathrm{ENC}(u)\text{subject to}\mathrm{similarity}(u,v)\approx {\mathbf{z}}_v^{⊺}{\mathbf{z}}_u$

The encoder $\mathrm{ENC}:V\to {\mathbb{R}}^d$ maps node to embedding and the decoder $\mathrm{DEC}:{\mathbb{R}}^d\times {\mathbb{R}}^d\to {\mathbb{R}}^{+}$ extracts useful-information such as local neighbor and classification label of the corresponding node from embedding, where $d$ is the dimension of the embedded vectors. .