Journal of Applied and Numerical Optimization

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DOI: 10.23952/jano.7.2025.2.01
Volume 7, Issue 2, 1 August 2025, Pages 141-148

 

Abstract. In the context of unsupervised deep metric learning of image features, Kan, Cen, Mladenovic and He [1] introduced a relative order relation, which is helpful for the comparison of two images in relation to a given special image also called anchor image. This short paper embeds the idea of a relative order relation into a more general mathematical framework. It turns out that this order relation has a strong mathematical structure, which leads to important results on minimality and strong minimality known from vector optimization. Properties of relative order matrices introduced in [1] are also obtained in this general mathematical setting. Among other things, characterizations of strongly minimal objects are given using relative order matrix elements.

 

How to Cite this Article:
J. Jahn, Some notes about a relative order relation used in unsupervised deep learning, J. Appl. Numer. Optim. 7 (2025), 141-148.