# Invariance encoding in sliced-Wasserstein space for image classification with limited training data

arXiv: https://arxiv.org/abs/2201.02980 · HTML: https://mlsanity.com/paper/2201.02980/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 79 references that are in the map.
- First posted on arXiv 9 Jan 2022.

## Builds on (most cited first, 25 of 25)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [A Simple Unified Framework for Detecting Out-of-Distribution Samples and Adversarial Attacks](https://mlsanity.com/paper/1807.03888/) (2018)
- [Deep Networks with Stochastic Depth](https://mlsanity.com/paper/1603.09382/) (2016)
- [Dynamic Routing Between Capsules](https://mlsanity.com/paper/1710.09829/) (2017)
- [Threat of Adversarial Attacks on Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/1801.00553/) (2018)
- [The Effectiveness of Data Augmentation in Image Classification using Deep Learning](https://mlsanity.com/paper/1712.04621/) (2017)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [3D Bounding Box Estimation Using Deep Learning and Geometry](https://mlsanity.com/paper/1612.00496/) (2016)
- [Why do deep convolutional networks generalize so poorly to small image transformations?](https://mlsanity.com/paper/1805.12177/) (2018)
- [Understanding data augmentation for classification: when to warp?](https://mlsanity.com/paper/1609.08764/) (2016)
- [Improving Deep Learning using Generic Data Augmentation](https://mlsanity.com/paper/1708.06020/) (2017)
- [The Radon cumulative distribution transform and its application to image classification](https://mlsanity.com/paper/1511.03206/) (2015)
- [The Cumulative Distribution Transform and Linear Pattern Classification](https://mlsanity.com/paper/1507.05936/) (2015)
- [Radon cumulative distribution transform subspace modeling for image classification](https://mlsanity.com/paper/2004.03669/) (2020)
- [Unsupervised Learning using Pretrained CNN and Associative Memory Bank](https://mlsanity.com/paper/1805.01033/) (2018)
- [Deep Neural Network Hyperparameter Optimization with Orthogonal Array Tuning](https://mlsanity.com/paper/1907.13359/) (2019)
- [Discovery and visualization of structural biomarkers from MRI using transport-based morphometry](https://mlsanity.com/paper/1705.04919/) (2017)
- [Nearest Subspace Search in The Signed Cumulative Distribution Transform Space for 1D Signal Classification](https://mlsanity.com/paper/2110.05606/) (2021)
- [Low-cost and high-performance data augmentation for deep-learning-based skin lesion classification](https://mlsanity.com/paper/2101.02353/) (2021)

## Built on by (most cited first, 7 of 7)

- [End-to-End Signal Classification in Signed Cumulative Distribution Transform Space](https://mlsanity.com/paper/2205.00348/) (2022)
- [Local Sliced-Wasserstein Feature Sets for Illumination-invariant Face Recognition](https://mlsanity.com/paper/2202.10642/) (2022)
- [Fast rigid alignment of heterogeneous images in sliced Wasserstein distance](https://mlsanity.com/paper/2503.13756/) (2025)
- [Normalized Radon Cumulative Distribution Transforms for Invariance and Robustness in Optimal Transport Based Image Classification](https://mlsanity.com/paper/2506.08761/) (2025)
- [The Radon Signed Cumulative Distribution Transform and its applications in classification of Signed Images](https://mlsanity.com/paper/2307.15339/) (2023)
- [Linear optimal transport subspaces for point set classification](https://mlsanity.com/paper/2403.10015/) (2024)
- [Generalizations of the Normalized Radon Cumulative Distribution Transform for Limited Data Recognition](https://mlsanity.com/paper/2512.08099/) (2025)

## Abstract (arXiv)

Deep convolutional neural networks (CNNs) are broadly considered to be state-of-the-art generic end-to-end image classification systems. However, they are known to underperform when training data are limited and thus require data augmentation strategies that render the method computationally expensive and not always effective. Rather than using a data augmentation strategy to encode invariances as typically done in machine learning, here we propose to mathematically augment a nearest subspace classification model in sliced-Wasserstein space by exploiting certain mathematical properties of the Radon Cumulative Distribution Transform (R-CDT), a recently introduced image transform. We demonstrate that for a particular type of learning problem, our mathematical solution has advantages over data augmentation with deep CNNs in terms of classification accuracy and computational complexity, and is particularly effective under a limited training data setting. The method is simple, effective, computationally efficient, non-iterative, and requires no parameters to be tuned. Python code implementing our method is available at https://github.com/rohdelab/mathematical_augmentation. Our method is integrated as a part of the software package PyTransKit, which is available at https://github.com/rohdelab/PyTransKit.