Angular triangle distance for ordinal metric learning

Imam Mustafa Kamal, Hyerim Bae, Ling Liu

Abstract: Deep metric learning (DML) aims to automatically construct task-specific distances or similarities between data, resulting in a low-dimensional representation. Several significant DML methods have been proposed. However, no approach guarantees the preservation of the ordinal nature of the original data in a low-dimensional space. Ordinal data are ubiquitous in real-world problems, such as the severity of symptoms in biomedical cases, production quality in manufacturing, rating level in businesses, and ageing level in face recognition. This study proposes a novel angular triangle distance (ATD) and ordinal triplet network (OTN) to obtain an accurate and meaningful embedding space representation for ordinal data. The ATD projects the ordinal relation of data in the angular space, whereas the OTN learns its ordinal projection. We also demonstrate that our new distance measure mathematically satisfies the distance metric properties. The proposed method was assessed using various benchmarks with an ordinal nature in both dependent and independent variables. Extensive experiments have been conducted, and the results show that our proposed method not only semantically preserves the ordinal nature but is also more accurate than existing DML models. Furthermore, our study demonstrates that our proposed method can effectively address ordinal regression tasks, producing competitive outcomes achieved by current state-of-the-art techniques.

External IDs:dblp:journals/apin/KamalBL25