There exist growing interests in intelligent systems for numerous medical imaging, image processing, and computer vision applications, such as face recognition, medical diagnosis, character recognition, and self-driving cars, among others. These applications usually require solving complex classification problems involving complex images with unknown data generative processes. In addition to recent successes of the current classification approaches relying on feature engineering and deep learning, several shortcomings of them, such as the lack of robustness, generalizability, and interpretability, have also been observed. These methods often require extensive training data, are computationally expensive, and are vulnerable to out-of-distribution samples, e.g., adversarial attacks. Recently, an accurate, data-efficient, computationally efficient, and robust transport-based classification approach has been proposed, which describes a generative model-based problem formulation and closed-form solution for a specific category of classification problems. However, all these approaches lack mechanisms to detect test samples outside the class distributions used during training. In real-world settings, where the collected training samples are unable to exhaust or cover all classes, the traditional classification schemes are unable to handle the unseen classes effectively, which is especially an important issue for safety-critical systems, such as self-driving and medical imaging diagnosis. In this work, we propose a method for detecting out-of-class distributions based on the distribution of sliced-Wasserstein distance from the Radon Cumulative Distribution Transform (R-CDT) subspace. We tested our method on the MNIST and two medical image datasets and reported better accuracy than the state-of-the-art methods without an out-of-class distribution detection procedure.

翻译：随着人工智能系统在人脸识别、医学诊断、字符识别、自动驾驶等医学影像、图像处理和计算机视觉领域的广泛应用，学术界对相关技术的研究兴趣日益增长。这些应用通常需要解决涉及具有未知数据生成过程的复杂图像的分类问题。尽管当前基于特征工程和深度学习的分类方法取得了成功，但也暴露出缺乏鲁棒性、泛化能力和可解释性等缺陷。这些方法通常需要大量训练数据、计算成本高昂，且容易受到对抗攻击等分布外样本的影响。近期，一种基于传输理论的分类方法被提出，该方法兼具准确性、数据高效性、计算高效性和鲁棒性，能够针对特定类别的分类问题建立生成模型并给出闭式解。然而，这些方法均缺乏检测训练类别分布之外的测试样本的机制。在实际应用中，采集的训练样本往往无法穷举所有类别，传统分类方案难以有效处理未见类别，这对自动驾驶和医学影像诊断等安全关键系统尤为重要。本文提出了一种基于Radon累积分布变换（R-CDT）子空间中切片Wasserstein距离分布特征的类外分布检测方法。我们在MNIST和两个医学影像数据集上进行了测试，结果表明，与未采用类外分布检测流程的最新方法相比，本方法具有更高的准确率。