Mohammad Shifat E Rabbi

Abu Hasnat Mohammad Rubaiyat, Shiying Li, Xuwang Yin et al.

This paper presents a new end-to-end signal classification method using the signed cumulative distribution transform (SCDT). We adopt a transport-based generative model to define the classification problem. We then make use of mathematical properties of the SCDT to render the problem easier in transform domain, and solve for the class of an unknown sample using a nearest local subspace (NLS) search algorithm in SCDT domain. Experiments show that the proposed method provides high accuracy classification results while being data efficient, robust to out-of-distribution samples, and competitive in terms of computational complexity with respect to the deep learning end-to-end classification methods. The implementation of the proposed method in Python language is integrated as a part of the software package PyTransKit (https://github.com/rohdelab/PyTransKit).

Mohammad Shifat E Rabbi, Abu Hasnat Mohammad Rubaiyat, Yan Zhuang et al.

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.

Mohammad Shifat E Rabbi, Yan Zhuang, Shiying Li et al.

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.

Mohammad Shifat E Rabbi, Naqib Sad Pathan, Shiying Li et al.

Learning from point sets is an essential component in many computer vision and machine learning applications. Native, unordered, and permutation invariant set structure space is challenging to model, particularly for point set classification under spatial deformations. Here we propose a framework for classifying point sets experiencing certain types of spatial deformations, with a particular emphasis on datasets featuring affine deformations. Our approach employs the Linear Optimal Transport (LOT) transform to obtain a linear embedding of set-structured data. Utilizing the mathematical properties of the LOT transform, we demonstrate its capacity to accommodate variations in point sets by constructing a convex data space, effectively simplifying point set classification problems. Our method, which employs a nearest-subspace algorithm in the LOT space, demonstrates label efficiency, non-iterative behavior, and requires no hyper-parameter tuning. It achieves competitive accuracies compared to state-of-the-art methods across various point set classification tasks. Furthermore, our approach exhibits robustness in out-of-distribution scenarios where training and test distributions vary in terms of deformation magnitudes.