Representing Hierarchical Structured Data Using Cone Embedding

Extracting hierarchical structure in graph data is becoming an important problem in fields such as natural language processing and developmental biology. Hierarchical structures can be extracted by embedding methods in non-Euclidean spaces, such as Poincaré embedding and Lorentz embedding, and it is now possible to learn efficient embedding by taking advantage of the structure of these spaces. In this study, we propose embedding into another type of metric space called a metric cone by learning an only one-dimensional coordinate variable added to the original vector space or a pre-trained embedding space. This allows for the extraction of hierarchical information while maintaining the properties of the pre-trained embedding. The metric cone is a one-dimensional extension of the original metric space and has the advantage that the curvature of the space can be easily adjusted by a parameter even when the coordinates of the original space are fixed. Through an extensive empirical evaluation we have corroborated the effectiveness of the proposed cone embedding model. In the case of randomly generated trees, cone embedding demonstrated superior performance in extracting hierarchical structures compared to existing techniques, particularly in high-dimensional settings. For WordNet embeddings, cone embedding exhibited a noteworthy correlation between the extracted hierarchical structures and human evaluation outcomes.