# Embedding Semantic Hierarchy in Discrete Optimal Transport for Risk Minimization

arXiv: https://arxiv.org/abs/2105.00101 · HTML: https://mlsanity.com/paper/2105.00101/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 27 references that are in the map.
- First posted on arXiv 30 Apr 2021.

## Builds on (most cited first, 11 of 11)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Cost Sensitive Learning of Deep Feature Representations from Imbalanced Data](https://mlsanity.com/paper/1508.03422/) (2015)
- [Evaluation Measures for Hierarchical Classification: a unified view and novel approaches](https://mlsanity.com/paper/1306.6802/) (2013)
- [Importance-Aware Semantic Segmentation in Self-Driving with Discrete Wasserstein Training](https://mlsanity.com/paper/2010.12440/) (2020)
- [Hierarchical Novelty Detection for Visual Object Recognition](https://mlsanity.com/paper/1804.00722/) (2018)
- [Unimodal-uniform Constrained Wasserstein Training for Medical Diagnosis](https://mlsanity.com/paper/1911.02475/) (2019)
- [Dependency-aware Attention Control for Unconstrained Face Recognition with Image Sets](https://mlsanity.com/paper/1907.03030/) (2019)
- [Conservative Wasserstein Training for Pose Estimation](https://mlsanity.com/paper/1911.00962/) (2019)
- [Embedding Visual Hierarchy with Deep Networks for Large-Scale Visual Recognition](https://mlsanity.com/paper/1707.02406/) (2017)
- [HiNet: Hierarchical Classification with Neural Network](https://mlsanity.com/paper/1705.11105/) (2017)

## Built on by (most cited first, 4 of 4)

- [Deep Unsupervised Domain Adaptation: A Review of Recent Advances and Perspectives](https://mlsanity.com/paper/2208.07422/) (2022)
- [Inducing Neural Collapse to a Fixed Hierarchy-Aware Frame for Reducing Mistake Severity](https://mlsanity.com/paper/2303.05689/) (2023)
- [Recursively Conditional Gaussian for Ordinal Unsupervised Domain Adaptation](https://mlsanity.com/paper/2107.13467/) (2021)
- [Learning Structured Representations by Embedding Class Hierarchy with Fast Optimal Transport](https://mlsanity.com/paper/2410.03052/) (2024)

## Abstract (arXiv)

The widely-used cross-entropy (CE) loss-based deep networks achieved significant progress w.r.t. the classification accuracy. However, the CE loss can essentially ignore the risk of misclassification which is usually measured by the distance between the prediction and label in a semantic hierarchical tree. In this paper, we propose to incorporate the risk-aware inter-class correlation in a discrete optimal transport (DOT) training framework by configuring its ground distance matrix. The ground distance matrix can be pre-defined following a priori of hierarchical semantic risk. Specifically, we define the tree induced error (TIE) on a hierarchical semantic tree and extend it to its increasing function from the optimization perspective. The semantic similarity in each level of a tree is integrated with the information gain. We achieve promising results on several large scale image classification tasks with a semantic tree structure in a plug and play manner.