Jung Hun Oh

Jung Hun Oh, Rena Elkin, Anish Kumar Simhal et al.

The Wasserstein distance from optimal mass transport (OMT) is a powerful mathematical tool with numerous applications that provides a natural measure of the distance between two probability distributions. Several methods to incorporate OMT into widely used probabilistic models, such as Gaussian or Gaussian mixture, have been developed to enhance the capability of modeling complex multimodal densities of real datasets. However, very few studies have explored the OMT problems in a reproducing kernel Hilbert space (RKHS), wherein the kernel trick is utilized to avoid the need to explicitly map input data into a high-dimensional feature space. In the current study, we propose a Wasserstein-type metric to compute the distance between two Gaussian mixtures in a RKHS via the kernel trick, i.e., kernel Gaussian mixture models.

Chungpa Lee, Jeongheon Oh, Kibok Lee et al.

Supervised contrastive learning (SupCL) has emerged as a prominent approach in representation learning, leveraging both supervised and self-supervised losses. However, achieving an optimal balance between these losses is challenging; failing to do so can lead to class collapse, reducing discrimination among individual embeddings in the same class. In this paper, we present theoretically grounded guidelines for SupCL to prevent class collapse in learned representations. Specifically, we introduce the Simplex-to-Simplex Embedding Model (SSEM), a theoretical framework that models various embedding structures, including all embeddings that minimize the supervised contrastive loss. Through SSEM, we analyze how hyperparameters affect learned representations, offering practical guidelines for hyperparameter selection to mitigate the risk of class collapse. Our theoretical findings are supported by empirical results across synthetic and real-world datasets.

Siwon Kim, Wooyung Yun, Jeongbin Oh et al.

Deep learning has emerged as the predominant solution for classifying medical images. We intend to apply these developments to the ultra-widefield (UWF) retinal imaging dataset. Since UWF images can accurately diagnose various retina diseases, it is very important to clas sify them accurately and prevent them with early treatment. However, processing images manually is time-consuming and labor-intensive, and there are two challenges to automating this process. First, high perfor mance usually requires high computational resources. Artificial intelli gence medical technology is better suited for places with limited medical resources, but using high-performance processing units in such environ ments is challenging. Second, the problem of the accuracy of colour fun dus photography (CFP) methods. In general, the UWF method provides more information for retinal diagnosis than the CFP method, but most of the research has been conducted based on the CFP method. Thus, we demonstrate that these problems can be efficiently addressed in low performance units using methods such as strategic data augmentation and model ensembles, which balance performance and computational re sources while utilizing UWF images.

Jung Hun Oh, Maryam Pouryahya, Aditi Iyer et al.

The Wasserstein distance is a powerful metric based on the theory of optimal transport. It gives a natural measure of the distance between two distributions with a wide range of applications. In contrast to a number of the common divergences on distributions such as Kullback-Leibler or Jensen-Shannon, it is (weakly) continuous, and thus ideal for analyzing corrupted data. To date, however, no kernel methods for dealing with nonlinear data have been proposed via the Wasserstein distance. In this work, we develop a novel method to compute the L2-Wasserstein distance in a kernel space implemented using the kernel trick. The latter is a general method in machine learning employed to handle data in a nonlinear manner. We evaluate the proposed approach in identifying computerized tomography (CT) slices with dental artifacts in head and neck cancer, performing unsupervised hierarchical clustering on the resulting Wasserstein distance matrix that is computed on imaging texture features extracted from each CT slice. Our experiments show that the kernel approach outperforms classical non-kernel approaches in identifying CT slices with artifacts.