## Nested Subspace Arrangement for Representation of Relational Data

### Nozomi Hata · Shizuo Kaji · Akihiro Yoshida · Katsuki Fujisawa

Keywords: [ Networks and Relational Learning ] [ Representation Learning ]

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Abstract: Studies of acquiring appropriate continuous representations of a discrete objects such as graph and knowledge based data have been conducted by many researches in the field of machine learning. In this paper, we introduce Nested SubSpace arrangement (NSS arrangement), a comprehensive framework for representation learning. We show that existing embedding techniques can be regarded as a member of NSS arrangement. Based on the concept of the NSS arrangement, we implemented Disk-ANChor ARrangement (DANCAR), a representation learning method specializing to reproduce general graphs. Numerical experiments have shown that DANCAR has successfully embedded WordNet in ${\mathbb R}^{20}$ with the F1 score of 0.993 in the reconstruction task. DANCAR is also suitable for visualization to understand the characteristics of graph.