# CORE: Learning Consistent Ordinal REpresentations for Image Ordinal Estimation

arXiv: https://arxiv.org/abs/2301.06122 · HTML: https://mlsanity.com/paper/2301.06122/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 54 references that are in the map.
- First posted on arXiv 15 Jan 2023.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Grad-CAM: Visual Explanations from Deep Networks via Gradient-based Localization](https://mlsanity.com/paper/1610.02391/) (2016)
- [RISE: Randomized Input Sampling for Explanation of Black-box Models](https://mlsanity.com/paper/1806.07421/) (2018)
- [Deep Ordinal Regression Network for Monocular Depth Estimation](https://mlsanity.com/paper/1806.02446/) (2018)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Score-CAM: Score-Weighted Visual Explanations for Convolutional Neural Networks](https://mlsanity.com/paper/1910.01279/) (2019)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Explaining NonLinear Classification Decisions with Deep Taylor Decomposition](https://mlsanity.com/paper/1512.02479/) (2015)
- [Photo Aesthetics Ranking Network with Attributes and Content Adaptation](https://mlsanity.com/paper/1606.01621/) (2016)
- [Gradient Estimation with Stochastic Softmax Tricks](https://mlsanity.com/paper/2006.08063/) (2020)
- [Learning Probabilistic Ordinal Embeddings for Uncertainty-Aware Regression](https://mlsanity.com/paper/2103.13629/) (2021)
- [Group-CAM: Group Score-Weighted Visual Explanations for Deep Convolutional Networks](https://mlsanity.com/paper/2103.13859/) (2021)
- [Deep Regression Forests for Age Estimation](https://mlsanity.com/paper/1712.07195/) (2017)
- [Unimodal probability distributions for deep ordinal classification](https://mlsanity.com/paper/1705.05278/) (2017)
- [Label Distribution Learning Forests](https://mlsanity.com/paper/1702.06086/) (2017)
- [A Tutorial on Dual Decomposition and Lagrangian Relaxation for Inference in Natural Language Processing](https://mlsanity.com/paper/1405.5208/) (2014)
- [Meta Ordinal Regression Forest for Medical Image Classification with Ordinal Labels](https://mlsanity.com/paper/2203.07725/) (2022)
- [Deep Ordinal Hashing with Spatial Attention](https://mlsanity.com/paper/1805.02459/) (2018)
- [Ordinal-Content VAE: Isolating Ordinal-Valued Content Factors in Deep Latent Variable Models](https://mlsanity.com/paper/2009.03034/) (2020)
- [Dual Decomposition of Convex Optimization Layers for Consistent Attention in Medical Images](https://mlsanity.com/paper/2206.02761/) (2022)
- [Robust Hyperspectral Image Fusion with Simultaneous Guide Image Denoising via Constrained Convex Optimization](https://mlsanity.com/paper/2209.11979/) (2022)

## Abstract (arXiv)

The goal of image ordinal estimation is to estimate the ordinal label of a given image with a convolutional neural network. Existing methods are mainly based on ordinal regression and particularly focus on modeling the ordinal mapping from the feature representation of the input to the ordinal label space. However, the manifold of the resultant feature representations does not maintain the intrinsic ordinal relations of interest, which hinders the effectiveness of the image ordinal estimation. Therefore, this paper proposes learning intrinsic Consistent Ordinal REpresentations (CORE) from ordinal relations residing in groundtruth labels while encouraging the feature representations to embody the ordinal low-dimensional manifold. First, we develop an ordinal totally ordered set (toset) distribution (OTD), which can (i) model the label embeddings to inherit ordinal information and measure distances between ordered labels of samples in a neighborhood, and (ii) model the feature embeddings to infer numerical magnitude with unknown ordinal information among the features of different samples. Second, through OTD, we convert the feature representations and labels into the same embedding space for better alignment, and then compute the Kullback Leibler (KL) divergence between the ordinal labels and feature representations to endow the latent space with consistent ordinal relations. Third, we optimize the KL divergence through ordinal prototype-constrained convex programming with dual decomposition; our theoretical analysis shows that we can obtain the optimal solutions via gradient backpropagation. Extensive experimental results demonstrate that the proposed CORE can accurately construct an ordinal latent space and significantly enhance existing deep ordinal regression methods to achieve better results.