Transport-based analysis, modeling, and learning from signal and data distributions

TL;DR

This paper reviews transport-based methods for analyzing, modeling, and learning from data distributions, highlighting their mathematical foundations, numerical techniques, and diverse applications in fields like image processing and machine learning.

Contribution

It provides a comprehensive overview of the mathematical principles, computational methods, and practical applications of transport-based data analysis techniques.

Findings

Transport methods enable accurate generative modeling of data distributions.

They have achieved state-of-the-art results in various applications.

Transport metrics offer new insights into data interpretation.

Abstract

Transport-based techniques for signal and data analysis have received increased attention recently. Given their abilities to provide accurate generative models for signal intensities and other data distributions, they have been used in a variety of applications including content-based retrieval, cancer detection, image super-resolution, and statistical machine learning, to name a few, and shown to produce state of the art in several applications. Moreover, the geometric characteristics of transport-related metrics have inspired new kinds of algorithms for interpreting the meaning of data distributions. Here we provide an overview of the mathematical underpinnings of mass transport-related methods, including numerical implementation, as well as a review, with demonstrations, of several applications.