Representing Hierarchical Structure by Using Cone Embedding
This work addresses a specific issue in graph embedding for hierarchical structure representation, offering an incremental improvement over existing methods.
The paper tackles the problem of arbitrary origin choice in graph embedding methods like Poincaré embedding, which is undesirable when using distance from the origin as a hierarchy indicator, by proposing cone embedding in a metric cone; the result is a method that provides a natural hierarchical indicator and can extract hierarchy from other embeddings with additional one-dimensional parameters.
Graph embedding is becoming an important method with applications in various areas, including social networks and knowledge graph completion. In particular, Poincaré embedding has been proposed to capture the hierarchical structure of graphs, and its effectiveness has been reported. However, most of the existing methods have isometric mappings in the embedding space, and the choice of the origin point can be arbitrary. This fact is not desirable when the distance from the origin is used as an indicator of hierarchy, as in the case of Poincaré embedding. In this paper, we propose cone embedding, embedding method in a metric cone, which solve these problems, and we gain further benefits: 1) we provide an indicator of hierarchical information that is both geometrically and intuitively natural to interpret, and 2) we can extract the hierarchical structure from a graph embedding output of other methods by learning additional one-dimensional parameters.