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1. Ordinal Hyperplane Loss

   https://doi.org/10.1109/BigData.2018.8622079  

   Vanderheyden, Bob; Xie, Ying (December 2018, 2018 IEEE International Conference on Big Data (Big Data))

   The problem of ordinal classification occurs in a large and growing number of areas. Some of the most common source and applications of ordinal data include rating scales, medical classification scales, socio-economic scales, meaningful groupings of continuous data, facial emotional intensity, facial age estimation, etc. The problem of predicting ordinal classes is typically addressed by either performing n-1 binary classification for n ordinal classes or treating ordinal classes as continuous values for regression. However, the first strategy doesn't fully utilize the ordering information of classes and the second strategy imposes a strong continuous assumption to ordinal classes. In this paper, we propose a novel loss function called Ordinal Hyperplane Loss (OHPL) that is particularly designed for data with ordinal classes. The proposal of OHPL is a significant advancement in predicting ordinal class data, since it enables deep learning techniques to be applied to the ordinal classification problem on both structured and unstructured data. By minimizing OHPL, a deep neural network learns to map data to an optimal space where the distance between points and their class centroids are minimized while a nontrivial ordinal relationship among classes are maintained. Experimental results show that deep neural network with OHPL not only outperforms the state-of-the-art alternatives on classification accuracy but also scales well to large ordinal classification problems. 

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2. Distributional Adversarial Loss

   Ahmadi, Saba; Bhandari, Siddharth; Blum, Avrim; Dan, Chen; Jain, Prabhav (May 2025, Proceedings of The 28th International Conference on Artificial Intelligence and Statistics (AISTATS 2025))
3. Leaky Hinge Loss: The First Negatively Divergent Margin-based Loss Function forClassification

   Kwon, Oh-ran; Zou, Hui (January 2023, Journal of machine learning research)
4. Simulations of inner radiation belt proton loss during geomagnetic storms: PROTON BELT LOSS

   https://doi.org/10.1002/2015JA021568  

   Engel, M. A.; Kress, B. T.; Hudson, M. K.; Selesnick, R. S. (November 2015, Journal of Geophysical Research: Space Physics)
5. Estimating global genetic diversity loss

   https://doi.org/10.1126/science.add0007  

   Ruegg, Kristen; Turbek, Sheela (September 2022, Science)

   Preservation of genetic diversity is critical to the resilience of species in the face of global change. To meet international calls to preserve at least 90% of species’ genetic diversity, researchers and conservationists need a way to reliably predict genetic diversity loss resulting from human activities ( 1 ). On page 1431 of this issue, Exposito-Alonso et al. present a mathematical framework that elegantly bridges biodiversity and population genetics theory to model the relationship between genetic diversity and habitat loss ( 2 ). This approach builds on methods already used by biodiversity policy experts for predicting species extinctions based on habitat loss ( 3 ) and should be useful to those tasked with setting goals for preserving genetic diversity. 

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