  Deep metric learning (DML) aims to automatically construct task-specific
distances or similarities of data, resulting in a low-dimensional
representation. Several significant metric-learning methods have been proposed.
Nonetheless, 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 aging
level in face recognition. This study proposes a novel angular triangle
distance (ATD) and ordinal triplet network (OTD) 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 OTD learns its
ordinal projection. We also demonstrated that our new distance measure
satisfies the distance metric properties mathematically. The proposed method
was assessed using real-world data with an ordinal nature, such as biomedical,
facial, and hand-gestured images. 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.
Moreover, we also demonstrate that our proposed method outperforms the
state-of-the-art ordinal metric learning method.
