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.
Min Generalized Sliced Gromov Wasserstein: A Scalable Path to Gromov Wasserstein
Department of Computer Science, College of Connected Computing, Vanderbilt University（计算机科学系，连接计算学院，范德比尔特大学）；Department of Electrical and Computer Engineering, Vanderbilt University（电气与计算机工程系，范德比尔特大学）
Fast rigid alignment of heterogeneous images in sliced Wasserstein distance
Department of Mathematics, University of California at Davis（加州大学戴维斯分校数学系）；Princeton University（普林斯顿大学）；Program in Applied and Computational Mathematics, Princeton University（普林斯顿大学应用与计算数学项目）
Multiscale Sliced Wasserstein Distances as Perceptual Color Difference Measures
City University of Hong Kong（香港城市大学）；Shenzhen Research Institute, City University of Hong Kong（香港城市大学深圳研究院）；Shenzhen MSU-BIT University（深圳北理莫斯科大学）；Guangdong OPPO Mobile Telecommunications Corp., Ltd.（广东欧珀移动通信有限公司）；Jiangxi University of Finance and Economics（江西财经大学）；The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））
Encoded Prior Sliced Wasserstein AutoEncoder for learning latent manifold representations
Gatsby Computational Neuroscience Unit, University College London（伦敦大学学院盖茨比计算神经科学单元）；Department of Mathematics and Center for Scientific Computation and Mathematical Modeling, University of Maryland College Park（马里兰大学帕克分校数学系与科学计算与数学建模中心）
SGWIB:Sliced Gromov-Wasserstein Information Bottleneck for Video Highlight Detection
Key Laboratory of Agricultural Machinery Intelligent Control and Manufacturing of Fujian Province University, College of Mechanical and Electrical Engineering, Wuyi University（武夷大学机电工程学院福建省高校农业机械智能控制与制造重点实验室）；National Taiwan University of Science and Technology（国立台湾科技大学）
AdamFlow: Adam-based Wasserstein Gradient Flows for Surface Registration in Medical Imaging
Department of Brain Sciences, Imperial College London（帝国理工学院脑科学系）；Department of Computing, Imperial College London（帝国理工学院计算系）；School of Computer Science, University of Birmingham（伯明翰大学计算机科学学院）；Department of Computer Science, Columbia University（哥伦比亚大学计算机科学系）；Data Science Institute, Imperial College London（帝国理工学院数据科学研究所）
