1 research outputs found
An Unsupervised Framework for Comparing Graph Embeddings
Graph embedding is a transformation of vertices of a graph into set of
vectors. Good embeddings should capture the graph topology, vertex-to-vertex
relationship, and other relevant information about graphs, subgraphs, and
vertices. If these objectives are achieved, they are meaningful,
understandable, and compressed representations of networks. They also provide
more options and tools for data scientists as machine learning on graphs is
still quite limited. Finally, vector operations are simpler and faster than
comparable operations on graphs.
The main challenge is that one needs to make sure that embeddings well
describe the properties of the graphs. In particular, the decision has to be
made on the embedding dimensionality which highly impacts the quality of an
embedding. As a result, selecting the best embedding is a challenging task and
very often requires domain experts.
In this paper, we propose a ``divergence score'' that can be assign to
various embeddings to distinguish good ones from bad ones. This general
framework provides a tool for an unsupervised graph embedding comparison. In
order to achieve it, we needed to generalize the well-known Chung-Lu model to
incorporate geometry which is interesting on its own rights. In order to test
our framework, we did a number of experiments with synthetic networks as well
as real-world networks, and various embedding algorithms