  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.
