The paper on generative graph

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