2024/05/13 by Jingwei Zhang, Zhang, Jingwei, Farzan Farnia +1
Engineering · Medicine · #Computer Vision and Pattern Recognition (cs.CV) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Piezoelectric Actuators and Control #Sparse and Compressive Sensing Techniques #Ultrasound Imaging and Elastography
paper · pdf · doi:10.48550/arxiv.2405.07489
openalex publication_date 2024/05/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Transportation of samples across different domains is a central task in several machine learning problems. A sensible requirement for domain transfer tasks in computer vision and language domains is the sparsity of the transportation map, i.e., the transfer algorithm aims to modify the least number of input features while transporting samples across the source and target domains. In this work, we propose Elastic Net Optimal Transport (ENOT) to address the sparse distribution transfer problem. The ENOT framework utilizes the L1-norm and L2-norm regularization mechanisms to find a sparse and stable transportation map between the source and target domains. To compute the ENOT transport map, we consider the dual formulation of the ENOT optimization task and prove that the sparsified gradient of the optimal potential function in the ENOT's dual representation provides the ENOT transport map. Furthermore, we demonstrate the application of the ENOT framework to perform feature selection for sparse domain transfer. We present the numerical results of applying ENOT to several domain transfer problems for synthetic Gaussian mixtures and real image and text data. Our empirical results indicate the success of the ENOT framework in identifying a sparse domain transport map.