Shifat-E-Rabbi Mohammad, Zhuang Yan, Li Shiying, Rubaiyat Abu Hasnat Mohammad, Yin Xuwang, Rohde Gustavo K
Imaging and Data Science Laboratory, University of Virginia, Charlottesville, VA 22908, USA.
Department of Biomedical Engineering, University of Virginia, Charlottesville, VA 22908, USA.
Pattern Recognit. 2023 May;137. doi: 10.1016/j.patcog.2022.109268. Epub 2022 Dec 22.
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.
深度卷积神经网络（CNNs）被广泛认为是最先进的通用端到端图像分类系统。然而，众所周知，当训练数据有限时，它们的性能会下降，因此需要数据增强策略，这使得该方法在计算上成本高昂且并不总是有效。与通常在机器学习中使用数据增强策略来编码不变性不同，在这里，我们建议通过利用最近引入的图像变换——拉东累积分布变换（R-CDT）的某些数学特性，在切片瓦瑟斯坦空间中对最近子空间分类模型进行数学增强。我们证明，对于特定类型的学习问题，我们的数学解决方案在分类准确性和计算复杂度方面优于使用深度CNN进行数据增强，并且在训练数据有限的情况下特别有效。该方法简单、有效、计算效率高、非迭代，且无需调整参数。实现我们方法的Python代码可在https://github.com/rohdelab/mathematical augmentation获取。我们的方法作为软件包PyTransKit的一部分进行了集成，该软件包可在https://github.com/rohdelab/PyTransKit获取。
