How to quantify fields or textures? A guide to the scattering transform
This addresses the need for interpretable and efficient data analysis in fields like physics and biology, offering an incremental improvement over existing methods like power spectrum analysis and CNNs.
The paper tackles the problem of quantifying stochastic fields or textures by advocating for the scattering transform as a powerful, interpretable statistic that does not require training, providing a compact set of summary statistics with visual interpretation for various scientific applications.
Extracting information from stochastic fields or textures is a ubiquitous task in science, from exploratory data analysis to classification and parameter estimation. From physics to biology, it tends to be done either through a power spectrum analysis, which is often too limited, or the use of convolutional neural networks (CNNs), which require large training sets and lack interpretability. In this paper, we advocate for the use of the scattering transform (Mallat 2012), a powerful statistic which borrows mathematical ideas from CNNs but does not require any training, and is interpretable. We show that it provides a relatively compact set of summary statistics with visual interpretation and which carries most of the relevant information in a wide range of scientific applications. We present a non-technical introduction to this estimator and we argue that it can benefit data analysis, comparison to models and parameter inference in many fields of science. Interestingly, understanding the core operations of the scattering transform allows one to decipher many key aspects of the inner workings of CNNs.