Nested Subspace Arrangement for Representation of Relational Data

TL;DR

This paper introduces the Nested SubSpace (NSS) arrangement framework for representation learning of relational data, unifying existing methods and demonstrating a new approach called DANCAR that effectively embeds graphs like WordNet.

Contribution

The paper proposes the NSS arrangement as a unified framework for representation learning and introduces DANCAR, a specialized method for graph embedding, showing its effectiveness on WordNet.

Findings

DANCAR successfully embedded WordNet with an F1 score of 0.993.

NSS arrangement generalizes existing embedding techniques.

DANCAR is effective for graph visualization.

Abstract

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.