  Unsupervised graph-level representation learning plays a crucial role in a
variety of tasks such as molecular property prediction and community analysis,
especially when data annotation is expensive. Currently, most of the
best-performing graph embedding methods are based on Infomax principle. The
performance of these methods highly depends on the selection of negative
samples and hurt the performance, if the samples were not carefully selected.
Inter-graph similarity-based methods also suffer if the selected set of graphs
for similarity matching is low in quality. To address this, we focus only on
utilizing the current input graph for embedding learning. We are motivated by
an observation from real-world graph generation processes where the graphs are
formed based on one or more global factors which are common to all elements of
the graph (e.g., topic of a discussion thread, solubility level of a molecule).
We hypothesize extracting these common factors could be highly beneficial.
Hence, this work proposes a new principle for unsupervised graph representation
learning: Graph-wise Common latent Factor EXtraction (GCFX). We further propose
a deep model for GCFX, deepGCFX, based on the idea of reversing the
above-mentioned graph generation process which could explicitly extract common
latent factors from an input graph and achieve improved results on downstream
tasks to the current state-of-the-art. Through extensive experiments and
analysis, we demonstrate that, while extracting common latent factors is
beneficial for graph-level tasks to alleviate distractions caused by local
variations of individual nodes or local neighbourhoods, it also benefits
node-level tasks by enabling long-range node dependencies, especially for
disassortative graphs.
