Transport Generative Models in Pattern Analysis and Recognition

There exists a growing need for computational models for pattern analysis and recognition in numerous scientific and technological fields, including computer vision, biology, and healthcare. Although generic feature approximation and deep learning approaches have been widely used in this aspect, they suffer from limitations in robustness, generalizability, and interpretability. Moreover, they are computationally expensive, require a vast amount of training data, and are vulnerable to out-of-distribution samples. In this study, we introduce a transport-based modeling approach for solving pattern analysis and recognition problems. Our approach focuses on modeling data obtained from processes involving some kind of transport of mass or intensity of pixels, tissue, or molecules, such as tissue growth, cell division, carcinogenesis, and gene expression. We postulate that data classes obtained from such processes can be represented as instances of an unknown template under the effect of unknown spatial deformations. Using this hypothesis, we aim to demonstrate that our classification and modeling approach can solve problems involving segmented data in closed-form. We show that our proposed method has the potential to achieve better accuracy, generalizability, interpretability, and data efficiency compared to existing approaches. Moreover, our method is designed to be simple and computationally efficient, potentially making it a more practical solution for real-world applications.

In order to accomplish our research objectives, we introduce a novel transport-based data generative model for image classification and develop a new supervised image classification method applicable to a broad class of image deformation models. We formulate and derive the mathematical properties of the data generative model and solve the classification problem in closed-form using transport-based embeddings. Additionally, we demonstrate how the method can learn data invariances without the need for data augmentation. Furthermore, we extend the aforementioned framework to formulate transport-based embeddings for the classification of high-dimensional distributions, which can be applied in a variety of applications. Our approach is not only simple to implement, but also non-iterative, computationally efficient, data-efficient, and possesses out-of-distribution generalization. Lastly, we introduce a transport-based morphometry framework for modeling nuclear structures of digital pathology images in cancer and use this framework to explore the existence of shared nuclear structure biomarkers across different cancer types. We show that our model can reveal meaningful information within and across various tissue types by identifying morphological differences among them. We show that our framework can provide quantitative measurements for comparisons across diverse datasets and cancer types that can potentially enable numerous cancer studies, technologies, and clinical applications and help elevate the role of nuclear morphometry into a more quantitative science.