Exploring the high dimensional geometry of HSI features

TL;DR

This paper investigates the geometric properties of hyperspectral image features generated by Fourier scattering transforms and deep neural networks, revealing differences and connections with neural collapse phenomena.

Contribution

It provides a comparative analysis of feature space geometries for different methods and explores their relation to neural collapse in hyperspectral imaging.

Findings

Fourier scattering features exhibit distinct geometric properties compared to deep neural network features.

Class mean distances and angles differ significantly between methods.

Insights into low-dimensional structures and class variability in hyperspectral features.

Abstract

We explore feature space geometries induced by the 3-D Fourier scattering transform and deep neural network with extended attribute profiles on four standard hyperspectral images. We examine the distances and angles of class means, the variability of classes, and their low-dimensional structures. These statistics are compared to that of raw features, and our results provide insight into the vastly different properties of these two methods. We also explore a connection with the newly observed deep learning phenomenon of neural collapse.