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Node Embeddings <3 (Ideas, Nice to Haves (Performance on Adversarial…

- - - - Locally Linear Embedding (LLE) [1]
        
        Every node is a linear combination of its neighbors
        Obtain embedding ϕ(Y)=∑i|Yi−∑jWijYj|2, where Yi≈∑jWijYj
      - Laplacian Eigenmaps [1], [2]
        
        Earliest, DEC(zi,zj)=||zi-zj||^2), L=SUM(DEC(zi,zj)*sg(vi,vj)))
      - Cauchy Graph Embedding [1]
        
        With quadratic penalty in Laplacian Eigenmaps, preservation of dissimilarity is emphasized compared to similarity, Use |Yi−Yj|2|Yi−Yj|2+σ2 instead, Emphasis on similar nodes rather than dissimilar
      - Structure Preserving Embedding (SPE) [1]
        
        Perfectly reconstruct the graph, Use PSD Kernel Matrix K and a connectivity algorithm G, Introduce slack variable for noise handling
      - Graph Factorization (GF) [1], [2]
        
        HOPE, GF, GraRep are inner product based -> DEC(zi,zj)=ziTzj
        Proximity measure Aij
      - GraRep [1],[2]
        
        HOPE, GF, GraRep are inner product based -> DEC(zi,zj)=ziTzj
        Proximity measure Aij, Aij^2, ..., Aij^k
      - HOPE [1],[2]
        
        HOPE, GF, GraRep are inner product based -> DEC(zi,zj)=ziTzj
        general Proximity measure
    - - DeepWalk [1], [2]
        
        direct encoding, decoder based on inner product, approximate loss with hierarchical softmax to compute norm. factor, binary tree structure for acceleration
      - Node2Vec [1], [2]
        
        direct encoding, decoder based on inner product approximate loss with negative sampling
      - Hierarchical Representation Learning for Networks (HARP) [1], [2]
        
        graph preprocessing, collapse related nodes into supernodes, then other Random Walk based method
      - Walklets [1]
        
        Combine idea of explicit modelling (Fact. Based) and random walks, Modifies DeepWalk by skipping nodes, Performed in different skip lengths, analogous to factorizing Ak in GraRep, Results are used to train similar to DeepWalk
    - - Structural Deep Network Embedding (SDNE)
      - Deep Neural Networks for Learning Graph Representations (DNGR)
      - Graph Convolutional Networks (GCN)
      - Variational Graph Auto-Encoders (VGAE)
    - - LINE
        
        Two encoder-decoder objectives that optim "first order" and "second order" graph proximity respectively
        use decoder based on sigmoid
        
        proximity sg(vi,vj)=Aij
        
        proximity two hop adjacency neighborhoods