Nested Subspace Arrangement for Representation of Relational Data
This work provides a foundational framework for representation learning in machine learning, potentially impacting various domains that use relational data, though it appears incremental as it builds upon existing techniques.
The paper tackles the problem of learning continuous representations for relational data like graphs and knowledge bases by introducing the Nested SubSpace (NSS) arrangement framework, which generalizes existing embedding techniques, and implements DANCAR, a method that achieved an F1 score of 0.993 in reconstructing WordNet in ℝ²⁰.
Studies on acquiring appropriate continuous representations of discrete objects, such as graphs and knowledge base data, have been conducted by many researchers in the field of machine learning. In this study, we introduce Nested SubSpace (NSS) arrangement, a comprehensive framework for representation learning. We show that existing embedding techniques can be regarded as special cases of the NSS arrangement. Based on the concept of the NSS arrangement, we implement a Disk-ANChor ARrangement (DANCAR), a representation learning method specialized to reproducing general graphs. Numerical experiments have shown that DANCAR has successfully embedded WordNet in ${\mathbb R}^{20}$ with an F1 score of 0.993 in the reconstruction task. DANCAR is also suitable for visualization in understanding the characteristics of graphs.