GENERATIVE GRAPH CONVOLUTIONAL NETWORK FOR GROWING GRAPHS.pptx
- 1. GENERATIVE GRAPH CONVOLUTIONAL NETWORK FOR GROWING GRAPHS Walmart Labs, Sunnyvale, California, USA https://arxiv.org/pdf/1903.02640.pdf
- 2. CONTENTS Introduction Background Variational Autoencoder Graph Convolutional Network Graph convolutional Autoencoder Proposed method Experimental results Discussions
- 3. ITNRODUCTION The paper tackles the problem of network growing, which lies in the same line with our work Observed undirected graph 𝐺 = (𝑉, 𝐸) Adjacency matrix 𝑨 Node attributes 𝑿 ∈ 𝑅𝑛×𝑑0 New nodes 𝑉𝑛𝑒𝑤 with attributes 𝑿𝑛𝑒𝑤 The proposed approach learns the generation of overall adjacency matrix 𝑨𝑛𝑒𝑤 for 𝑉 ∪ 𝑉𝑛𝑒𝑤 New node comes in With known attributes
- 4. VARIATIONAL AUTOENCODERS (VAE) 𝑥𝑖 𝑞𝜙(𝑧|𝑥𝑖) 𝑧 𝑥𝑖 𝑝𝜃(𝑥𝑖|𝑧) 𝑥𝑖 𝑞𝜙(𝑧|𝑥𝑖) 𝑧 𝑥𝑖 𝑝𝜃(𝑥𝑖|𝑧) 𝑝(𝑧) A well-known deep generative model Consist of 2 neural networks: Encoder Decoder The key idea is to model the latent variable as a Gaussian distribution so we can draw a sample from it. Loss function for a datapoint 𝑥𝑖 𝑙𝑖 𝜃, 𝜙 = − E𝑧~𝑞𝜃 𝑧 𝑥𝑖 log 𝑝𝜙 𝑥𝑖 𝑧
- 5. Input Layer 1 Layer 2 Layer 3 Output Weight matrix W1 Weight matrix W2 Weight matrix W3 GRAPH CONVOLUTIONAL NETWORK (GCN)
- 6. GRAPH CONVOLUTIONAL AUTOENCODER (GAE) 𝐙 ∈ 𝑅𝑛×𝑘: isotrophic Gaussian X GCN Mean Z Varianc eZ Z A 𝐀 X
- 7. GENERATIVE GRAPH CONVOLUTIONAL NETWORK (G- GCN) Objective function: 𝑖=1 𝑛−1 Reconstruction loss (i − th step) + 𝛽 𝑖=1 𝑛−1 KL (i − th step) treating incoming nodes as being added one-by-one into the graph
- 8. EXPERIMENTAL RESULTS a growing graph is constructed by randomly sampling an observed subgraph containing 70% of all nodes. Link prediction performance
- 9. DISCUSSIONS The problem is of interest to our research The paper is not fully written The notations are confusing lack of information on the experimental section There seems to be an underlying assumption that the growth of nodes follows a Gaussian distribution The method may contain flaws