Suzuki, Atsushi, Wang, Jing, Tian, Feng, Nitanda, Atsushi and Yamanishi, Kenji (2019) Hyperbolic ordinal embedding. In: Asian Conference on Machine Learning, 17-19 November 2019, Nagoya, Japan. Proceedings of Machine Learning Research, 101 . MIR, Moscow, Russia, pp. 1065-1080.

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Abstract

Given ordinal relations such as the object i is more similar to j than k is to l, ordinal embedding is to embed these objects into a low-dimensional space with all ordinal constraints preserved. Although existing approaches have preserved ordinal relations in Euclidean space, whether Euclidean space is compatible with true data structure is largely ignored, although it is essential to effective embedding. Since real data often exhibit hierarchical structure, it is hard for Euclidean space approaches to achieve effective embeddings in low dimensionality, which incurs high computational complexity or overfitting. In this paper we propose a novel hyperbolic ordinal embedding (HOE) method to embed objects in hyperbolic space. Due to the hierarchy-friendly property of hyperbolic space, HOE can effectively capture the hierarchy to achieve embeddings in an extremely low-dimensional space. We have not only theoretically proved the superiority of hyperbolic space and the limitations of Euclidean space for embedding hierarchical data, but also experimentally demonstrated that HOE significantly outperforms Euclidean-based methods.

Item Type:	Conference Proceedings
Title of Proceedings:	Asian Conference on Machine Learning, 17-19 November 2019, Nagoya, Japan
Uncontrolled Keywords:	Ordinal embedding, hyperbolic space, hierarchical structure, low-dimensionality
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Faculty / School / Research Centre / Research Group:	Faculty of Engineering & Science > School of Computing & Mathematical Sciences (CMS) Faculty of Engineering & Science
Related URLs:	Publisher
Last Modified:	04 Mar 2022 13:06
URI:	http://gala.gre.ac.uk/id/eprint/30533

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