Persistent Homology and Graphs Representation Learning
This provides a method for understanding topological invariants in graph representation learning, which is incremental as it applies existing tools to a specific domain.
The authors tackled the problem of analyzing topological properties in graph node embeddings by applying persistent homology to real-valued embeddings from algorithms like DeepWalk, Node2Vec, and Diff2Vec, resulting in a unique persistence-based descriptor for graphs and nodes.
This article aims to study the topological invariant properties encoded in node graph representational embeddings by utilizing tools available in persistent homology. Specifically, given a node embedding representation algorithm, we consider the case when these embeddings are real-valued. By viewing these embeddings as scalar functions on a domain of interest, we can utilize the tools available in persistent homology to study the topological information encoded in these representations. Our construction effectively defines a unique persistence-based graph descriptor, on both the graph and node levels, for every node representation algorithm. To demonstrate the effectiveness of the proposed method, we study the topological descriptors induced by DeepWalk, Node2Vec and Diff2Vec.