# Invariance encoding in sliced-Wasserstein space for image classification with limited training data Source: [Invariance encoding in sliced-Wasserstein space for image classification with limited training data]() Collection index: [llms.txt]() Data updated: 2025-10-28T13:56:54.500Z Authors: Mohammad Shifat E Rabbi, Yan Zhuang, Shiying Li, Abu Hasnat Mohammad Rubaiyat, Xuwang Yin, Gustavo K. Rohde Published: 2022-01-09T10:25:27.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()